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@article{peltola_mechanical_2000,  title = {Mechanical stability of Scots pine, Norway spruce and birch: an analysis of tree-pulling experiments in {F}inland},  volume = {135},  issn = {0378-1127},  url = {http://www.sciencedirect.com/science/article/pii/S0378112700003066},  doi = {http://dx.doi.org/10.1016/S0378-1127(00)00306-6},  number = {1--3},  journal = {Forest Ecology and Management},  author = {Peltola, Heli and Kellomäki, Seppo and Hassinen, Alpo and Granander, Markku},  year = {2000},  keywords = {damage, Wind},  pages = {143--153}  }  @article{yoshihara_prediction_2009,  title = {Prediction of the off-axis stress-strain relation of wood under compression loading},  volume = {67},  url = {http://dx.doi.org/10.1007/s00107-009-0320-6},  doi = {10.1007/s00107-009-0320-6},  number = {2},  journal = {European Journal of Wood and Wood Products},  author = {Yoshihara, Hiroshi},  month = may,  year = {2009},  pages = {183--188}  }  @book{kollmann_f._cote_principles_1968,  title = {Principles of Wood Science and Technology. {P}art I Solid Wood},  publisher = {Springer-Verlag Berlin Heidelberg New York},  author = {Kollmann, F. and Cote, W.},  year = {1968}  }  @book{Hibbeler_mechanics_2000,  title = {Mechanics of materials},  publisher = {New Jersey: Prentice Hall},  author = {Hibbeler, R.C.},  Edition = {{F}ourth},  year = {2000}  }  @article{Chauhan_methods_2013,  year={2013},  issn={1286-4560} ,  journal={Annals of Forest Science},  volume={70},  number={4},  doi={10.1007/s13595-013-0270-3},  title={Methods for the very early selection of \textit{{P}inus radiata} {D.} {D}on. for solid wood products},  url={http://dx.doi.org/10.1007/s13595-013-0270-3},  publisher={Springer-Verlag},  keywords={Early selection; Leaning; Radiata pine; Tree clones; Wood properties},  author={Chauhan, Shakti S. and Sharma, Monika and Thomas, Jimmy and Apiolaza, Luis A. and Collings, David A. and Walker, John C.F.},  pages={439-449},  language={English}  }  @article{lindstrom_methods_2002,  title = {Methods for measuring stiffness of young trees},  volume = {60},  issn = {0018-3768},  url = {http://dx.doi.org/10.1007/s00107-002-0292-2},  doi = {10.1007/s00107-002-0292-2},  language = {English},  number = {3},  journal = {Holz als Roh- und Werkstoff},  author = {Lindström, H. and Harris, P. and Nakada, R.},  year = {2002},  pages = {165--174}  }  @article{burdon_juvenile_2004,  title = {Juvenile Versus Mature Wood: A New Concept, Orthogonal to Corewood Versus Outerwood, with Special Reference to \textit{Pinus radiata} and \textit{P. taeda}},  volume = {50},  number = {4},  journal = {Forest Science},  author = {Burdon, Rowland D. and Kibblewhite, R. Paul and Walker, John C. F. and Megraw, Robert A. and Evans, Robert and Cown, David J.},  year = {2004},  pages = {399--415}  }  @article{blomberg_plastic_2004,  title = {Plastic deformation in small clear pieces of Scots pine (Pinus sylvestris) during densification with the {CaLignum} process},  volume = {50},  issn = {1435-0211, 1611-4663},  url = {http://link.springer.com.ezproxy.canterbury.ac.nz/article/10.1007/s10086-003-0566-2},  doi = {10.1007/s10086-003-0566-2},  abstract = {Specimens made of clear wood from Scots pine (Pinus sylvestris L.) were compressed semi-isostatically at {25°C} in a Quintus press. Pressure ranged from 0 to 140 {MPa} and the maximum decrease in the crosscut area was about 60\%. Quarter-sawn and plain-sawn specimens were densified with the inside face (pith side) up or down. A laser-made dot grid on the crosscut area of the uncompressed specimen was used to calculate plastic strains by image analysis of the displacement of dots after compression. Multivariate models were developed to determine the causes of deformation. The lower face was restrained by the press table and remained flat whereas sides attached to the rubber diaphragm became more irregularly shaped when compressed. Most of the total compression occurred below 50 {MPa} and was determined exclusively by pressure. Above 50 {MPa}, wood density was more important and compression was lower in the interior of specimens and in heartwood. Plastic compressive strain occurred predominately in the radial direction and toward the rigid press table. Strains were dependent on the sawing pattern and orientation. The growth rings of quarter-sawn specimens oriented with the outer face (bark side) down tended to buckle.},  language = {en},  number = {4},  urldate = {2013-11-13},  journal = {Journal of Wood Science},  author = {Blomberg, Jonas and Persson, Bengt},  month = aug,  year = {2004},  keywords = {Compressed wood, Multivariate models, Plastic strain, Quintus press},  pages = {307--314}  }  @article{schopfer_biomechanics_2006,  title = {Biomechanics of plant growth},  volume = {93},  issn = {0002-9122},  shorttitle = {Biomechanics of plant growth},  url = {://000241601800005},  abstract = {Growth of turgid cells, defined as an irreversible increase in cell volume and surface area, can be regarded as a physical process governed by the mechanical properties of the cell wall and the osmotic properties of the protoplast. Irreversible cell expansion is produced by creating a driving force for water uptake by decreasing the turgor through stress relaxation in the cell wall. This mechano-hydraulic process thus depends on and can be controlled by the mechanical properties of the wall, which in turn are subject to modification by wall loosening and wall stiffening reactions. The biochemical mechanisms of these changes in mechanical wall properties and their regulation by internal signals (e.g., hormones) or external signals (e.g., light, drought stress) are at present incompletely understood and subject to intensive research. These signals act on walls that have the properties of composite materials in which the molecular structure and spatial organization of polymers rather than the distribution of mechanical stresses dictate the allometry of cell and organ growth and thus cell and organ shape. The significance of cell wall architecture for allometric growth can be demonstrated by disturbing the oriented deposition of wall polymers with microtubuleinterfering drugs such as colchicine. Elongating organs (e.g., cylindrical stems or coleoptiles) composed of different tissues with different mechanical properties exhibit longitudinal tissue tensions resulting in the transfer of wall stress from inner to peripheral cell layers that adopt control over organ growth. For physically analyzing the growth process leading to seed germination, the same mechanical and hydraulic parameters as in normal growth are principally appropriate. However, for covering the influences of the tissues that restrain embryo expansion (seed coat, endosperm), an additional force and a water permeability term must be considered.},  language = {English},  journal = {American Journal of Botany},  author = {Schopfer, P.},  month = oct,  year = {2006},  keywords = {{ABSCISIC-ACID}, {AUXIN-MEDIATED} {GROWTH}, Cellulose, cell wall extensibility, {CELL-WALL} {EXTENSIBILITY}, cell wall stress relaxation, {COLEOPTILES}, {ELONGATION} {GROWTH}, growth allometry, {HELIANTHUS-ANNUUS} L, {HYDROXYL-RADICAL} {PRODUCTION}, {INDUCED} {WATER}, maize, microfibril orientation, {POTENTIALS}, seed germination, {SEED-GERMINATION}, {STRESS-RELAXATION}, {TENSION}, tissue, wall loosening, wall stiffening},  pages = {1415--1425}  }  @article{sonderegger_investigation_2008,  title = {An investigation of the influence of selected factors on the properties of spruce wood},  volume = {42},  issn = {0043-7719, 1432-5225},  url = {http://link.springer.com.ezproxy.canterbury.ac.nz/article/10.1007/s00226-007-0173-2},  doi = {10.1007/s00226-007-0173-2},  abstract = {Thirty Norway spruce trees (Picea abies (L.) Karst.) from the forest district of the {ETH} Zurich were tested for bending {MOR}, static {MOE} of bending and dynamic {MOE} (calculated from eigenfrequency and sound velocity). The specimens were clear and were sampled from the whole of the stem. Their correlations to density, annual ring width, height in the tree, distribution over the stem diameter and the percentage of compression wood were statistically analysed. All three elasticity modules and the maximal stress can be very well predicted from a linear function of the sample density with a common gradient across the compression wood values but with different intercepts that decrease with increasing compression wood content. The other variables have highly significant impacts on the response variables too, however, this is largely irrelevant for the goodness of fit. Further, a clear increase of density, of {MOE} and of bending {MOR} was measured from pith to bark and similarly with decreasing annual ring width. Concerning the height of the stem, no distinct trend for the mechanical properties could be found.},  language = {en},  number = {4},  urldate = {2013-11-13},  journal = {Wood Science and Technology},  author = {Sonderegger, Walter and Mandallaz, Daniel and Niemz, Peter},  month = apr,  year = {2008},  keywords = {Ceramics, Composites, Glass, Materials Treatment, Natural Methods, Operating Procedures, Wood Science \& Technology},  pages = {281--298}  }  @article{p_theory_1973,  title = {Theory of Growth Stresses},  volume = {27},  url = {http://dx.doi.org/10.1515/hfsg.1973.27.6.197},  doi = {10.1515/hfsg.1973.27.6.197},  number = {6},  journal = {Holzforschung},  author = {Gillis, Peter},  month = jan,  year = {1973},  pages = {197--207}  }  @article{lachenbruch_relationships_2010,  title = {Relationships of density, microfibril angle, and sound velocity with stiffness and strength in mature wood of Douglas-fir},  volume = {40},  issn = {0045-5067},  url = {http://www.nrcresearchpress.com.ezproxy.canterbury.ac.nz/doi/abs/10.1139/X09-174},  doi = {10.1139/X09-174},  abstract = {The relative importance of density, acoustic velocity, and microfibril angle ({MFA)} for the prediction of stiffness ({MOE)} and strength ({MOR)} has not been well established for Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco). {MOE} and {MOR} of small clear specimens of mature wood were better predicted by density and velocity than by either variable alone (183 trees {\textbackslash}textgreater20 years old, six specimens per tree, 1087 specimens total). Specimens sampled around the stem circumference had similar density (intraclass correlation coefficient t = 0.74) but not {MOE} (t = 0.40) or acoustic velocity (t = 0.32), indicating benefits from sampling several circumferential positions. For {MOE}, the path coefficients (β) were moderate for density and velocity. For {MOR}, β was only high for density. End-matched samples of one specimen per tree were analyzed with {SilviScan.} Simple correlations with {MOE} were highest for density (r = 0.67) and then acoustic velocity2 (0.53), {MFA} (–0.50), earlywood {MFA} (–0.45), and latewood proportion (0.40..., L’importance relative de la densité, de la vitesse sonique et de l’angle des microfibrilles ({AMF)} pour prédire la rigidité ({MOE)} et la résistance mécanique ({MOR)} n’a pas été clairement établie pour le Douglas vert (Pseudotsuga menziesii (Mirb.) Franco). Le {MOE} et le {MOR} de petites éprouvettes de bois mature sans défauts ont été mieux prédits par une combinaison de la densité et de la vitesse sonique que par seulement l’une ou l’autre de ces variables (183 arbres {\textbackslash}textgreater20 ans, six éprouvettes par arbre, 1 087 éprouvettes au total). Les éprouvettes prélevées autour de la circonférence de la tige avaient une densité similaire (coefficient de corrélation intra-catégorie t = 0,74), mais ce n’était pas le cas pour le {MOE} (t = 0,40) ou la vitesse sonique (t = 0,32). Ce résultat indique qu’il serait bénéfique d’échantillonner plusieurs positions circonférentielles. Dans le cas du {MOE}, les coefficients de pistes (β) étaient modérés avec la densité et la vitesse sonique. Dans le cas du {MOR}, β était élevé seulement avec ...},  number = {1},  urldate = {2013-11-12},  journal = {Canadian Journal of Forest Research},  author = {Lachenbruch, B. and Johnson, G. R. and Downes, G. M. and Evans, R.},  month = jan,  year = {2010},  pages = {55--64}  }  @book{hill_mathematical_1950,  title = {The mathematical theory of plasticity},  publisher = {Oxford: Clarendon Press},  author = {Hill, Rodney},  year = {1950},  keywords = {1921, origonal}  }  @book{anders_logg_automated_2011,  title = {Automated Solution of Differential Equations by the Finite Element Method - The {FEniCS} Book},  url = {http://www.springer.com/mathematics/computational+science+%26+engineering/book/978-3-642-23098-1},  urldate = {2013-04-14},  publisher = {{GNU} Free Documentation License Version 1.3},  author = {Logg, Anders and Mardal, Kent-Andre and Wells, Garth N.},  year = {2011},  }  @MANUAL{1999_np,  author = {Ascher, David and Dubois, Paul F. and Hinsen, Konrad and Hugunin, James and Oliphant, Travis},  year = {1999},  title = {Numerical Python},  edition = {UCRL-MA-128569},  address = {Livermore, CA},  organization = {Lawrence Livermore National Laboratory},  keywords = {numpy}  }  @Misc{jones_scipy:_2001,  author = {Eric Jones and Travis Oliphant and Pearu Peterson and others},  title = {{SciPy}: Open source scientific tools for {Python}},  year = {2001--},  url = "http://www.scipy.org/"  }  @article{chauhan_variations_2006,  title = {Variations in acoustic velocity and density with age, and their interrelationships in radiata pine},  volume = {229},  issn = {0378-1127},  url = {http://www.sciencedirect.com/science/article/pii/S0378112706002684},  doi = {10.1016/j.foreco.2006.04.019},  abstract = {Acoustic velocity by the Fakopp time of flight ({ToF)} tool was used to estimate outerwood stiffness of trees within stands and between stands of different age classes (ages 8, 16 and 25). The {TOF} acoustic velocity measured in the standing trees was generally higher than the acoustic velocity measured by the Hitman (resonance) tool on the associated logs. The difference between the two velocities tended to be greater in the older and large diameter trees. The large variability in acoustic velocity, or preferably V2, makes it an efficient wood quality variable for screening trees. Wood density variables did not exhibit any relationship with acoustic velocity or modulus of elasticity ({MoE)} within each age-class. The classic pseudo-relationship observed with pooled data from all stand ages is mainly due to a stand age-effect and so one should be cautious in relying on any significant association between density and {MoE.}},  number = {1--3},  urldate = {2013-11-12},  journal = {Forest Ecology and Management},  author = {Chauhan, {S.S.} and Walker, {J.C.F.}},  month = jul,  year = {2006},  keywords = {Acoustic, Density, Modulus of elasticity, Outerwood, Radiata pine},  pages = {388--394}  }  @article{watanabe_cell_2000,  title = {Cell wall thickness and tangential Youngs modulus in coniferous early wood},  volume = {46},  issn = {1435-0211, 1611-4663},  url = {http://link.springer.com.ezproxy.canterbury.ac.nz/article/10.1007/BF00777356},  doi = {10.1007/BF00777356},  abstract = {To investigate the effect of wall thickening around cell corners on the tangential Young's modulus of coniferous early wood, tapered beam cell models in which the variation of the cell wall thickness in the axial direction was taken into account were constructed for seven species. Their tangential Young's moduli were compared with the experimental results. The calculated Young's moduli of tapered beam cell models were larger than those of the models composed of the cell walls with uniform thickness, although both models showed almost the same density. For some species the calculated Young's moduli of the models in which the cell wall thickness increased curvilinearly in the axial direction were much closer to the experimental values. The reduction of the radial cell wall deflection due to the increase of the stiffness around cell corners was considered to increase the tangential Young's modulus of a wood cell.},  language = {en},  number = {2},  urldate = {2013-04-14},  journal = {Journal of Wood Science},  author = {Watanabe, Ugai and Norimoto, Misato and Morooka, Toshiro},  month = apr,  year = {2000},  keywords = {Cell corner, Cell wall thickness, Characterization and Evaluation of Materials, Materials Science, Tangential Young's modulus, Wood cell model, Wood Science and Technology},  pages = {109--114}  }  @article{p_multi-surface_2003,  title = {A multi-surface plasticity model for clear wood and its application to the finite element analysis of structural details},  volume = {31},  url = {http://dx.doi.org/10.1007/s00466-003-0423-6},  doi = {10.1007/s00466-003-0423-6},  number = {1-2},  journal = {Computational Mechanics},  author = {Mackenzie-Helnwein, P. and Eberhardsteiner, J. and Mang, H. A.},  month = may,  year = {2003},  pages = {204--218}  }  @article{salmen_model_1985,  title = {A Model for the Prediction of Fiber Elasticity},  volume = {17},  url = {http://swst.metapress.com/content/T02433757724L815},  abstract = {A model is presented that enables the elastic properties of wood fibers to be estimated from the properties of its polymeric constituents, cellulose, hemicellulose, and lignin. The influence of the value of the axial stiffness of the cellulose crystal is demonstrated, its proper value being discussed in comparison with experimental data on fibers. The effects on fiber stiffness of the S2 fibril angle, the fibril angles of other layers, the crystallinity, and layer thicknesses are analyzed. The manner in which the effect of a variation in yield can be simulated by a change in shape factor of the reinforcing cellulose crystals is demonstrated, the cell wall thus being considered to be a discontinuous reinforced composite.},  number = {3},  urldate = {2013-04-15},  journal = {Wood and Fiber Science},  author = {Salmen, Lennart and de Ruvo, Alf},  month = jul,  year = {1985},  pages = {336--350}  }  @book{barbero_finite_2008,  title = {Finite Element Analysis of Composite Materials},  isbn = {9781420054330},  abstract = {Designing structures using composite materials poses unique challenges due especially to the need for concurrent design of both material and structure. Students are faced with two options: textbooks that teach the theory of advanced mechanics of composites, but lack computational examples of advanced analysis; and books on finite element analysis that may or may not demonstrate very limited applications to composites. But now there is third option that makes the other two obsolete: Ever J. Barbero's Finite Element Analysis of Composite {Materials.By} layering detailed theoretical and conceptual discussions with fully developed examples, this text supplies the missing link between theory and implementation. In-depth discussions cover all of the major aspects of advanced analysis, including three-dimensional effects, viscoelasticity, edge effects, elastic instability, damage, and delamination. More than 50 complete examples using mainly {ANSYS™}, but also including some use of {MATLAB®}, demonstrate how to use the concepts to formulate and execute finite element analyses and how to interpret the results in engineering terms. Additionally, the source code for each example is available for download {online.Cementing} applied computational and analytical experience to a firm foundation of basic concepts and theory, Finite Element Analysis of Composite Materials offers a modern, practical, and versatile classroom tool for today's engineering classroom.},  language = {en},  publisher = {{CRC} Press},  author = {Barbero, Ever J.},  year = {2008},  keywords = {Mathematics / Applied, Mathematics / Numerical Analysis, Science / Mechanics / General, Technology \& Engineering / Engineering (General), Technology \& Engineering / Materials Science, Technology \& Engineering / Mechanical}  }  @book{gibson_l._ashby_cellular_1997,  title = {Cellular solids: structure and properties},  isbn = {0521495601},  publisher = {Cambridge; New York: Cambridge University Press},  author = {Gibson, L.and Ashby, M.},  year = {1997},  Edition = {2nd},  keywords = {edition, second}  }  @article{raffaele_morphology_2011,  title = {Morphology-based macro-scale finite-element timber models},  volume = {43},  issn = {0010-4485},  url = {http://dx.doi.org/10.1016/j.cad.2010.09.003},  doi = {10.1016/j.cad.2010.09.003},  number = {1},  journal = {Computer-Aided Design},  author = {Raffaele, De Amicis and Riggio, Mariapaola and Girardi, Gabrio and Piazza, Maurizio},  month = jan,  year = {2011},  keywords = {Geometrical modeling, image analysis, Wood growth layer},  pages = {72--87}  }  @book{niklas_plant_1992,  title = {Plant Biomechanics: An Engineering Approach to Plant Form and Function},  isbn = {9780226586311},  shorttitle = {Plant Biomechanics},  abstract = {In this first comprehensive treatment of plant biomechanics, Karl J. Niklas analyzes plant form and provides a far deeper understanding of how form is a response to basic physical laws. He examines the ways in which these laws constrain the organic expression of form, size, and growth in a variety of plant structures, and in plants as whole organisms, and he draws on the fossil record as well as on studies of extant species to present a genuinely evolutionary view of the response of plants to abiotic as well as biotic constraints. Well aware that some readers will need an introduction to basic biomechanics or to basic botany, Niklas provides both, as well as an extensive glossary, and he has included a number of original drawings and photographs to illustrate major structures and {concepts.This} volume emphasizes not only methods of biomechanical analysis but also the ways in which it allows one to ask, and answer, a host of interesting questions. As Niklas points out in the first chapter, From the archaic algae to the most derived multicellular terrestrial plants, from the spectral properties of light-harvesting pigments in chloroplasts to the stacking of leaves in the canopies of trees, the behavior of plants is in large part responsive to and intimately connected with the physical environment. In addition, plants tend to be exquisitely preserved in the fossil record, thereby giving us access to the past. Its biomechanical analyses of various types of plant cells, organs, and whole organisms, and its use of the earliest fossil records of plant life as well as sophisticated current studies of extant species, make this volume a unique and highly integrative contribution to studies of plant form, evolution, ecology, and systematics.},  language = {en},  publisher = {University of Chicago Press},  author = {Niklas, Karl J.},  month = aug,  year = {1992}  }  @article{carrington_cv._1923,  title = {{CV.} The elastic constants of spruce},  volume = {45},  issn = {1941-5982},  url = {http://www.tandfonline.com/doi/abs/10.1080/14786442308636317},  doi = {10.1080/14786442308636317},  number = {269},  urldate = {2013-04-15},  journal = {Philosophical Magazine Series 6},  author = {Carrington, H.},  year = {1923},  pages = {1055--1057}  }  @book{anders_logg_automated_2011,  title = {Automated Solution of Differential Equations by the Finite Element Method - The {FEniCS} Book},  url = {http://www.springer.com/mathematics/computational+science+%26+engineering/book/978-3-642-23098-1},  abstract = {This book is written by researchers and developers behind the {FEniCS} Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design ...},  urldate = {2013-04-14},  publisher = {{GNU} Free Documentation License Version 1.3},  author = {Anders Logg, Kent-Andre Mardal and Wells, Garth N.},  year = {2011},  keywords = {Automated Solution of Differential Equations by the Finite Element Method - The {FEniCS} Book, Mathematical and Computational Physics, Mathematical Software, Theoretical}  }  @article{gardiner_comparison_2000,  title = {Comparison of two models for predicting the critical wind speeds required to damage coniferous trees},  volume = {129},  issn = {0304-3800},  url = {http://www.sciencedirect.com/science/article/pii/S0304380000002209},  doi = {10.1016/S0304-3800(00)00220-9},  abstract = {Two independently developed mathematical models ({GALES} and {HWIND)} for predicting the critical wind speed and turning moment needed to uproot and break the stems of coniferous trees were compared and the results tested against field data on the forces experienced by forest trees and the wind speeds required to damage them. The {GALES} model calculates the aerodynamic roughness and zero-plane displacement of a forest stand. The aerodynamic roughness provides a measure of the stress (force/unit area) imposed on the canopy as a function of wind speed and the zero-plane displacement provides a measure of the average height on the tree at which the wind acts. Together they allow a calculation of the bending moment imposed on the tree for any wind speed. Data from almost 2000 trees uprooted during pulling experiments and destructive sampling of green wood then allow the model to make predictions of the wind speed at which the tree will be overturned and at which the tree will break for a number of coniferous species. The model assumes a linear relationship between tree stem weight and the maximum resistive moment that can be provided by the root system and it assumes that the stress in the outer fibres of the stem induced by the wind is constant with height. In the {HWIND} model the turning moment arising from the wind drag on the crown is calculated assuming a logarithmic upwind profile. Together with the contribution from the overhanging weight of the stem and branches caused by bending of the stem this provides the total bending moment. The angle of stem bend is explicitly calculated from the stiffness of the stem. The breaking strength of the stem and the support given by the root-soil plate are calculated from previous experiments on timber strength, and tree resistance to overturning by using root-soil plate mass to derive the resistive moment. This allows calculation of the wind speed required to break and overturn the tree. Model comparisons were performed for individual Scots pine (Pinus sylvestris L.) and Norway spruce (Picea abies L.) with varying tree height and stem taper (dbh/height). Tree location was at the forest stand edge on a podzolic soil. Model comparisons gave good agreement for the critical wind speeds at the forest edge required to break and overturn trees with a maximum difference in prediction of 26\%. Slightly better agreement was obtained for Norway spruce (mean difference of 10.8\%) than Scots pine (mean difference of 12.3\%) and the best agreement was for trees with a taper of 100. At higher taper the {GALES} model generally predicted higher critical wind speeds than the {HWIND} model whereas at lower taper the reverse applied.},  number = {1},  urldate = {2013-11-20},  journal = {Ecological Modelling},  author = {Gardiner, Barry and Peltola, Heli and Kellomäki, Seppo},  month = may,  year = {2000},  keywords = {Breaking stress, Critical wind speed, Model calculation, Model comparisons, Stem breakage, Turning moment, Uprooting, Wind load},  pages = {1--23}  }  @phdthesis{aikin_testing_2013,  address = {United States -- California},  type = {{Ph.D.}},  title = {Testing Inflationary Cosmology with the Bicep1 and Bicep2 Experiments},  copyright = {Copyright {ProQuest}, {UMI} Dissertations Publishing 2013},  url = {http://search.proquest.com.ezproxy.canterbury.ac.nz/docview/1468453237/abstract?accountid=14499},  abstract = {Recent observations of the temperature anisotropies of the cosmic microwave background ({CMB)} favor an inflationary paradigm in which the scale factor of the universe inflated by many orders of magnitude at some very early time. Such a scenario would produce the observed large-scale isotropy and homogeneity of the universe, as well as the scale-invariant perturbations responsible for the observed (10 parts per million) anisotropies in the {CMB.} An inflationary epoch is also theorized to produce a background of gravitational waves (or tensor perturbations), the effects of which can be observed in the polarization of the {CMB.} The E-mode (or parity even) polarization of the {CMB}, which is produced by scalar perturbations, has now been measured with high significance. Con- trastingly, today the B-mode (or parity odd) polarization, which is sourced by tensor perturbations, has yet to be observed. A detection of the B-mode polarization of the {CMB} would provide strong evidence for an inflationary epoch early in the universe's history. In this work, we explore experimental techniques and analysis methods used to probe the B- mode polarization of the {CMB.} These experimental techniques have been used to build the Bicep2 telescope, which was deployed to the South Pole in 2009. After three years of observations, Bicep2 has acquired one of the deepest observations of the degree-scale polarization of the {CMB} to date. Similarly, this work describes analysis methods developed for the Bicep1 three-year data analysis, which includes the full data set acquired by Bicep1. This analysis has produced the tightest constraint on the B-mode polarization of the {CMB} to date, corresponding to a tensor-to-scalar ratio estimate of r = 0.04±0.32, or a Bayesian 95\% credible interval of r {\textless} 0.70. These analysis methods, in addition to producing this new constraint, are directly applicable to future analyses of Bicep2 data. Taken together, the experimental techniques and analysis methods described herein promise to open a new observational window into the inflationary epoch and the initial conditions of our universe.},  language = {English},  urldate = {2014-03-25},  school = {California Institute of Technology},  author = {Aikin, Randol Wallace},  year = {2013},  keywords = {Bicep experiments, Cosmic microwave background, Cosmology, Physics, Polarization, Pure sciences},  file = {Full Text PDF:/home/nick/.zotero/zotero/z4b3je6k.default/zotero/storage/S5ZZRFHF/Aikin - 2013 - Testing Inflationary Cosmology with the Bicep1 and.pdf:application/pdf;Snapshot:/home/nick/.zotero/zotero/z4b3je6k.default/zotero/storage/JEWSTGZ4/abstract.html:text/html}  }  @article{qing_3d_2009,  title = {{3D} hierarchical computational model of wood as a cellular material with fibril reinforced heterogeneous multiple layers},  volume = {41},  issn = {0167-6636},  url = {http://dx.doi.org/10.1016/j.mechmat.2009.04.011},  doi = {10.1016/j.mechmat.2009.04.011},  number = {9},  journal = {Mechanics of Materials},  author = {Qing, Hai and Mishnaevsky, Leon},  month = sep,  year = {2009},  pages = {1034--1049}  }  @article{harrington_modelling_1998,  title = {Modelling the elastic properties of softwood},  volume = {56},  issn = {0018-3768, 1436-{736X}},  url = {http://link.springer.com.ezproxy.canterbury.ac.nz/article/10.1007/PL00002608},  doi = {10.1007/PL00002608},  abstract = {A procedure for determining the nine equivalent orthotropic elastic constants for a cell-wall lamella is presented. A two-stage analytic homogenization method is proposed. It is shown to give results which are similar to those obtained from a full numerical finite element solution for an idealised representative volume element. The method, which can accommodate arbitrary proportions of cell wall constituents, is used to determine the equivalent elastic constants for lamellae in the secondary cell wall layers and the compound middle lamella of a typical softwood tracheid at a nominal 12\% moisture Content.},  language = {en},  number = {1},  urldate = {2013-04-15},  journal = {Holz als Roh- und Werkstoff},  author = {Harrington, J. J. and Astley, R. J. and Booker, R.},  month = jan,  year = {1998},  keywords = {Ceramics, Composites, Glass, Materials Treatment, Natural Methods, Operating Procedures, Wood Science \& Technology},  pages = {37--41}  }  @article{cave_modelling_1978,  title = {Modelling moisture-related mechanical properties of wood Part {II:} Computation of Properties of a Model of wood and Comparison with Exprimental Data},  volume = {12},  number = {1},  journal = {Wood Science and Technology},  author = {Cave, I. D.},  year = {1978},  pages = {127--139}  }  @article{archer_origin_1989,  title = {On the origin of growth stresses in trees. {P}art {II:} {S}tresses generated in a tissue of developing cells},  volume = {23},  url = {http://dx.doi.org/10.1007/BF00353247},  doi = {10.1007/BF00353247},  number = {4},  journal = {Wood Science and Technology},  author = {Archer, R.},  year = {1989},  pages = {311--322}  }  @article{cave_interpretation_1998,  title = {Interpretation of (002) diffraction arcs by means of a minimalist model},  journal = {Mircofibril Angle in Wood, International Association of Wood Anatomists},  author = {Cave, I. and Robinson, {W.T.}},  year = {1998},  pages = {108--115}  }  @book{salencon_handbook_2001,  title = {Handbook of continuum mechanics: general concepts, thermoelasticity},  isbn = {3540414436},  shorttitle = {Handbook of continuum mechanics},  publisher = {Berlin; New York: Springer},  author = {Salençon, Jean.},  year = {2001}  }  @article{archer_distribution_1981,  title = {On the distribution of tree growth stresses. {P}art {IV}: The general case allowign longitudinal and circumferential variation of growth stresses},  volume = {15},  url = {http://dx.doi.org/10.1007/BF00353472},  doi = {10.1007/BF00353472},  number = {3},  journal = {Wood Science and Technology},  author = {Archer, R.},  month = sep,  year = {1981},  pages = {201--209}  }  @article{cave_measuring_1998,  title = {Measuring microfibril angle distribution in the cell wall by means of x-ray diffraction},  journal = {Mircofibril Angle in Wood, International Association of Wood Anatomists},  author = {Cave, I. and Robinson, {W.T.}},  year = {1998},  pages = {94--107}  }  @book{lundh_python_1995,  title = {Python Imaging Library},  Notes = {http://www.pythonware.com/products/pil/},  author = {Lundh, Fredrik and others},  year = {1995--}  }  @phdthesis{harrington_hierarchical_2002,  address = {Christchurch, New Zealand},  type = {Mechanical Engineering},  title = {Hierarchical modelling of softwood hygro-elastic properties},  abstract = {The hygro-elastic behaviour of wood under load or when subjected to environmental changes is of considerable practical interest. This behaviour can be determined by exhaustive experimentation, but such an approach makes explaining its origin, which from some perspectives can be more important than its prediction, problematic. This thesis attempts to establish a model (actually a hierarchical set of models) that goes some way toward both predicting and explaining the mechanics of wood. Attention is focused on radiata pine because of the commercial importance of this species in New Zealand, but much of the modelling is applicable to other softwoods and, to a lesser extent, hardwoods. Wood can be looked on as a hierarchical material, that is as a material possessing structure at multiple scales. For many problems involving such materials the heteroge- neous structure at a particular scale can be replaced by a homogeneous one possessing similar properties. Homogenization theory defines what is meant by similar and also provides the means for determining these effective properties. In this thesis wood structure is treated at three different scales: namely the supramolecular or nanostructural, the cell-wall or ultrastructural and the cellular or microstructural scales. Homogenization across these levels is performed either analyt- ically or numerically, using the finite element method. At the smallest scale, the constituent phases are treated as homogeneous continua. Models for the hygro-elastic phase properties, as functions of temperature and moisture content are developed based on available experimental data. The models devised to describe wood at each of the above mentioned scales in- troduce a large number of structural parameters, such as constituent mass fractions and cell-wall layer volume fractions. In the abscence of specific data, estimates for these parameters are developed based on data from the literature. Together with these auxiliary models, the main sequence of structural models can then be used to obtain estimates for the material properties of small domains within macrostuctural models.},  school = {University of Canterbury},  author = {Harrington, Jonathan J.},  month = sep,  year = {2002},  pages = {296}  }  @article{ormarsson_finite_2009,  title = {Finite element study of growth stress formation in wood and related distortion of sawn timber},  volume = {43},  url = {http://dx.doi.org/10.1007/s00226-008-0209-2},  doi = {10.1007/s00226-008-0209-2},  number = {5-6},  journal = {Wood Science and Technology},  author = {Ormarsson, Sigurdur and Dahlblom, Ola and Johansson, Marie},  month = aug,  year = {2009},  pages = {387--403}  }  @article{niklas_mechanical_1997,  title = {Mechanical Properties of Black Locust (\textit{Robinia pseudoacacia}) Wood: Correlations among Elastic and Rupture Moduli, Proportional Limit,and Tissue Density and Specific Gravity},  volume = {79},  url = {http://dx.doi.org/10.1006/anbo/79.5.479},  doi = {10.1006/anbo/79.5.479},  number = {5},  journal = {Annals of Botany},  author = {Niklas, K. J.},  month = may,  year = {1997},  pages = {479--485}  }  @book{timell_compression_1986-1,  address = {Berlin; New York},  title = {Compression wood in gymnosperms},  Volume = {1},  lccn = {Forestry QK 647 .T583},  publisher = {Springer-Verlag},  author = {Timell, T. E.},  year = {1986},  keywords = {Compression wood, Gymnosperms}  }  @book{timell_compression_1986-2,  address = {Berlin; New York},  title = {Compression wood in gymnosperms},  Volume = {2},  lccn = {Forestry QK 647 .T583},  publisher = {Springer-Verlag},  author = {Timell, T. E.},  year = {1986},  keywords = {Compression wood, Gymnosperms}  }  @book{timell_compression_1986-3,  address = {Berlin; New York},  title = {Compression wood in gymnosperms},  Volume = {3},  lccn = {Forestry QK 647 .T583},  publisher = {Springer-Verlag},  author = {Timell, T. E.},  year = {1986},  keywords = {Compression wood, Gymnosperms}  }  @book{hearmon_elasticity_1948,  title = {Elasticity of Wood and Plywood},  shorttitle = {Elasticity of Wood and Plywood},  url = {http://www.nature.com/nature/journal/v162/n4125/abs/162826a0.html},  abstract = {Nature is the international weekly journal of science: a magazine style journal that publishes full-length research papers in all disciplines of science, as well as News and Views, reviews, news, features, commentaries, web focuses and more, covering all branches of science and how science impacts upon all aspects of society and life.},  urldate = {2013-04-15},  publisher = {Nature Publishing Group},  author = {Hearmon, R. F. S.},  year = {1948},  keywords = {astronomy, astrophysics, biochemistry, bioinformatics, {BIOLOGY}, biotechnology, cancer, cell cycle, cell signalling, climate change, computational biology, development, developmental biology, {DNA}, drug discovery, earth science, ecology, environmental science, evolution, evolutionary biology, functional genomics, genetics, genomics, geophysics, immunology, interdisciplinary science, life, marine biology, Materials Science, medical research, medicine, metabolomics, molecular biology, molecular interactions, nanotechnology, Nature, neurobiology, neuroscience, palaeobiology, pharmacology, physics, proteomics, quantum physics, {RNA}, science, science news, science policy, signal transduction, structural biology, systems biology, transcriptomics}  }  @article{vidal_mechanical_2003,  title = {Mechanical parameters during static bending of \textit{Pinus radiata} growing in a silvopastoral system I: elasticity and strength},  volume = {49},  issn = {1435-0211, 1611-4663},  shorttitle = {Mechanical parameters during static bending of \textit{Pinus radiata} growing in a silvopastoral system I},  url = {http://link.springer.com.ezproxy.canterbury.ac.nz/article/10.1007/s100860300019},  doi = {10.1007/s100860300019},  abstract = {The effects of pasture fertilization frequency and two vertical positions in the stem on elasticity and strength parameters during static bending (modulus of elasticity, stress at proportional limit, modulus of rupture) of \textit{Pinus radiata} wood growing in a silvopastoral system were evaluated. Twenty-seven trees were selected randomly from three silvopastoral trials established at Tanumé Experimental Center (34°9′–34°15′ S; 72°53′–72°59′ W). The results indicated that pasture fertilization frequency had no significant effect on the physical and mechanical parameters evaluated. However, the vertical position in the stem did have a significant effect on stress at the proportional limit and on the modulus of rupture due to different average values for the annual ring width and nominal density found in the specimens obtained from logs at two different heights of the stem.},  language = {en},  number = {2},  urldate = {2013-11-13},  journal = {Journal of Wood Science},  author = {Vidal, M. H. R. and Sánchez, C. I. D. and Hurtado, L. a. V.},  month = apr,  year = {2003},  keywords = {Characterization and Evaluation of Materials, Fertilization, general, Key words Modulus of elasticity, Materials Science, Modulus of rupture, \textit{Pinus radiata}, Silvopastoral system, Wood Science \& Technology},  pages = {125--130}  }  @article{mayer_windthrow_1989,  title = {Windthrow [and Discussion]},  volume = {324},  issn = {0962-8436, 1471-2970},  url = {http://rstb.royalsocietypublishing.org/content/324/1223/267},  doi = {10.1098/rstb.1989.0048},  abstract = {The factors that influence storm damage in forests are summarized and the four kinds of storm damage in forests are presented. Two equations for the estimation of windloads are explained including the problems that their use involves. By use of wind-induced bending moments of trees the occurrence of windbreakage or windthrow is discussed. The response of trees to windloads is mostly in form of damped bending sways. Based on artificial force effects, their shapes are shown to be dependent on soil conditions. If trees are continually exposed to dynamic windloads the shape of their sways is irregular at first sight. During strong winds and storms, the most important load on trees is generally stochastic and can be analysed by the spectral method. Based on this method, results from experimental investigations on wind-induced sways of tall spruce trees within a stand are shown, including power spectra of Reynold's stress as measure of windload, stem accelerations as measures of tree response, and magnitudes of mechanical transfer functions. The main result is that conifers such as spruce trees can be compared to a narrow bandpass filter, i.e. they can take in energy from the turbulent wind field only at a certain frequency range.},  language = {en},  number = {1223},  urldate = {2013-11-20},  journal = {Philosophical Transactions of the Royal Society of London. B, Biological Sciences},  author = {Mayer, H. and Raupach, M. R. and Kohsiek, W. and Gardiner, B. and Clarke, J. A. and Amtmann, R. and Crowther, J. M. and Jarvis, P. G. and Milne, R.},  month = aug,  year = {1989},  pages = {267--281}  }  @article{xinguo_transcriptome_2011,  title = {Transcriptome profiling of \textit{Pinus radiata} juvenile wood with contrasting stiffness identifies putative candidate genes involved in microfibril orientation and cell wall mechanics},  volume = {12},  issn = {1471-2164},  url = {http://dx.doi.org/10.1186/1471-2164-12-480},  doi = {10.1186/1471-2164-12-480},  number = {1},  journal = {{BMC} Genomics},  author = {Xinguo, Li and Wu, Harry X and Southerton, Simon G},  year = {2011},  pages = {480}  }  @article{s_modelling_2008,  title = {Modelling the influence of environment and stand characteristics on basic density and modulus of elasticity for young \textit{Pinus radiata} and \textit{Cupressus lusitanica}},  volume = {255},  issn = {0378-1127},  url = {http://dx.doi.org/10.1016/j.foreco.2007.09.086},  doi = {10.1016/j.foreco.2007.09.086},  number = {3-4},  journal = {Forest Ecology and Management},  author = {Watt, Michael S. and Clinton, Peter W. and Coker, Graham and Davis, Murray R. and Simcock, Robyn and Parfitt, Roger L. and Dando, John},  month = mar,  year = {2008},  pages = {1023--1033}  }  @article{yamashita_longitudinal_2009,  title = {Longitudinal shrinkage variations within trees of sugi (\textit{Cryptomeria japonica}) cultivars},  volume = {55},  issn = {1435-0211},  url = {http://dx.doi.org/10.1007/s10086-008-0987-z},  doi = {10.1007/s10086-008-0987-z},  language = {English},  number = {1},  journal = {Journal of Wood Science},  author = {Yamashita, Kana and Hirakawa, Yasuhiko and Nakatani, Hiroshi and Ikeda, Motoyoshi},  year = {2009},  keywords = {Cryptomeria japonica, Longitudinal shrinkage, microfibril angle, Modulus of elasticity},  pages = {1--7}  }  @article{guillon_numerical_2012,  title = {Numerical methods for the biomechanics of growing trees},  volume = {64},  issn = {0898-1221},  shorttitle = {Mathematical Methods and Models in Biosciences},  url = {http://www.sciencedirect.com/science/article/pii/S0898122112001654},  doi = {10.1016/j.camwa.2012.02.040},  abstract = {Modelling the biomechanics of growing trees is a non-classical problem, as the usual framework of structural mechanics does not take into account the evolution of the domain geometry due to growth processes. Incremental approaches have been used in rod theory to bypass this problem and to model the addition of new material points on an existing deformed structure. However, these approaches are based on the explicit time numerical algorithm of an unknown continuous model, and thus, the accuracy of the numerical results obtained cannot be analysed. A new continuous space-time formulation has been recently proposed to model the biomechanical response of growing rods. The aim of this paper is to discretise the corresponding non-linear system of partial differential equations and the linearised system in order to compare the numerical results with analytical solutions of the linearised problem. The finite element method is implemented to compute the space boundary problem and different time integration schemes are considered to solve the associated initial value problem with a special attention to the forward Euler method which is the analogue of the previously used incremental approach. The numerical results point out that the accuracy of the time integration schemes strongly depends on the value of the parameters. The forward Euler method may present slow convergence property and errors with significant orders of magnitude. Nevertheless, attention must be paid to implicit methods since, for specific values of the parameters and large time steps, they may lead to spurious solutions that may come from numerical instabilities. Hence, the second order Heun’s method is an interesting alternative even if it is more time consuming.},  number = {3},  urldate = {2013-04-14},  journal = {Computers \& Mathematics with Applications},  author = {Guillon, Thomas and Dumont, Yves and Fourcaud, Thierry},  month = aug,  year = {2012},  keywords = {Hermite finite element, Partial differential equation, Plant growth model, Rod theory, Surface growth problem, Time integration scheme},  pages = {289--309}  }  @phdthesis{moden_micromechanics_2008,  address = {Stockholm, Sweden},  title = {Micromechanics of softwoods in the transverse plane: effects on cell and annual ring scales},  shorttitle = {Micromechanics of softwoods in the transverse plane},  url = {http://kth.diva-portal.org/smash/record.jsf?pid=diva2:126704},  abstract = {Transverse mechanical properties of wood are important in many practial applications and an interesting scientific subject. A very low transverse shear modulus has been identified in spruce, which ...},  language = {eng},  urldate = {2013-04-15},  school = {{KTH} Royal Institute of Technology},  author = {Moden, Carl S.},  year = {2008},  keywords = {Dentistry, Maskinteknik, Mechanical Engineering, Odontologi, Trävetenskap, Wood Science}  }  @article{archer_distribution_1985,  title = {On the distribution of tree growth stresses. {P}art {V}: Asymmetric peripheral growth strains with orthotropic material behavior},  volume = {19},  url = {http://dx.doi.org/10.1007/BF00392055},  doi = {10.1007/BF00392055},  number = {3},  journal = {Wood Science and Technology},  author = {Archer, R.},  year = {1985},  pages = {259--276}  }  @article{apiolaza_characterization_2011,  title = {Characterization of mechanically perturbed young stems: Can it be used for wood quality screening?},  volume = {68},  url = {http://dx.doi.org/10.1007/s13595-011-0028-8},  doi = {10.1007/s13595-011-0028-8},  number = {2},  journal = {Annals of Forest Science},  author = {Apiolaza, Luis A. and Butterfield, Brian and Chauhan, Shakti S. and Walker, John C. F.},  month = mar,  year = {2011},  pages = {407--414}  }  @article{wimmer_intra-annular_1994,  title = {Intra-annular cellular characteristics and theiry implications for modeling softwood density},  volume = {27},  number = {4},  journal = {Wood and Fibre Science},  author = {Wimmer, R},  year = {1994},  pages = {413--420}  }  @book{niklas_plant_2012,  title = {Plant Physics},  isbn = {9780226150819},  url = {http://dx.doi.org/10.7208/chicago/9780226586342.001.0001},  publisher = {University of Chicago Press},  author = {Niklas, Karl J. and Spatz, Hanns-Christof},  year = {2012}  }  @book{bs_methods_1957,  title = {Methods of testing small clear specimens of timber, {BS} 373:1957},  url = {http://dx.doi.org/10.3403/00041660},  publisher = {{BSI} British Standards},  author = {{BS}},  month = feb,  year = {1957}  }  @article{auty_models_2013,  title = {Models for predicting microfibril angle variation in Scots pine},  volume = {70},  issn = {1286-4560, 1297-{966X}},  url = {http://link.springer.com.ezproxy.canterbury.ac.nz/article/10.1007/s13595-012-0248-6},  doi = {10.1007/s13595-012-0248-6},  abstract = {Context Microfibril angle ({MFA)} is one of the key determinants of solid timber performance due to its strong influence on the stiffness, strength, shrinkage properties and dimensional stability of wood. Aims The aim of this study was to develop a model for predicting {MFA} variation in plantation-grown Scots pine (Pinus sylvestris L). A specific objective was to quantify the additional influence of growth rate on the radial variation in {MFA.} Methods Twenty-three trees were sampled from four mature Scots pine stands in Scotland, {UK.} Pith-to-bark {MFA} profiles were obtained on 69 radial samples using scanning X-ray diffractometry. A nonlinear mixed-effects model based on a modified {Michaelis–Menten} equation was developed using cambial age and annual ring width as explanatory variables. Results The largest source of variation in {MFA} ({\textbackslash}textgreater90 \%) was within trees, while between-tree variation represented just 7 \% of the total. Microfibril angle decreased rapidly near the pith before reaching stable values in later annual rings. The effect of ring width on {MFA} was greater at higher cambial ages. Conclusion A large proportion of the variation in {MFA} was explained by the fixed effects of cambial age and annual ring width. The final model is intended for integration into growth, yield and wood quality simulation systems.},  language = {en},  number = {2},  urldate = {2013-11-12},  journal = {Annals of Forest Science},  author = {Auty, David and Gardiner, Barry A. and Achim, Alexis and Moore, John R. and Cameron, Andrew D.},  month = mar,  year = {2013},  keywords = {Environment, Forestry, Forestry Management, general, Growth rate, microfibril angle, Nonlinear mixed-effects models, Pinus sylvestris, Radial variation, Ring width, Tree Biology, Wood Science \& Technology},  pages = {209--218}  }  @article{barrett_three-dimensional_1973,  title = {Three-Dimensional Finite-Element Models of Cylindrical Wood Fibers},  volume = {5},  url = {http://swst.metapress.com/content/DM7130620LJ51256},  abstract = {A finite-element solution is presented for analysis of concentric, multilayered, orthotropic cylinders subjected to loadings that do not vary around the circumference. Model fibers are analyzed, and stress distributions are compared to those obtained, using a closed form solution technique. The influence of boundary-shear restraint on internal stress distribution is studied. Comparing results of the three-dimensional finite-element model to values of axial stiffness and relative twisting angles predicted using simpler, two-dimensional methods indicated that the two-dimensional models can give good estimates of these parameters, at least for the thin-walled models.},  number = {3},  urldate = {2013-04-15},  journal = {Wood and Fiber Science},  author = {Barrett, J. and Schniewind, A.},  month = oct,  year = {1973},  pages = {215--225}  }  @misc{center_for_history_and_new_media_zotero_????,  title = {Zotero Quick Start Guide},  url = {http://zotero.org/support/quick_start_guide},  author = {{Center for History and New Media}},  annote = {Welcome to {Zotero!View} the Quick Start Guide to learn how to begin collecting, managing, citing, and sharing your research {sources.Thanks} for installing Zotero.}  }  @article{gustafsson_modelling_2003,  title = {Modelling of mechanical properties of wood and wood-based materials},  volume = {154},  url = {http://dx.doi.org/10.3188/szf.2003.0504},  doi = {10.3188/szf.2003.0504},  number = {12},  journal = {Schweizerische Zeitschrift fur Forstwesen},  author = {Gustafsson, Per Johan},  month = dec,  year = {2003},  pages = {504--509}  }  @article{lindstrom_stiffness_2004,  title = {Stiffness and wood variation of 3-year old \textit{Pinus radiata} clones},  volume = {38},  issn = {0043-7719, 1432-5225},  url = {http://link.springer.com.ezproxy.canterbury.ac.nz/article/10.1007/s00226-004-0249-1},  doi = {10.1007/s00226-004-0249-1},  abstract = {The objective of this study was to explore wood variation, especially modulus of elasticity ( moe), density, and microfibril angle ( mfa), in a three-year old Pinus radiata tree clone trial. Moreover, the study examined the potential for genetic selection of radiata pine clones with high moe using current acoustic technology. The clone selection criteria were based on growth traits, basic density, and sound velocity indices to mirror the range in wood density and moe amongst c. 1000 clones. The selected 22 clones, represented by two trees each, were measured for moe, spiral grain, wood density, compression wood percentage, and mfa. Good agreement was found between static moe and dynamic moe. Both static and dynamic moe measurements were found to be primarily dependent on mfa (clonal range 28–39 degrees). Although wood density (clonal range 300–400 kg/m3) did not have a significant influence on moe alone, it was significant in combination with mfa. Compression wood tended to reduce moe and inflate wood density. The opportunities for genetic selection of radiata clones with high stiffness seem promising as the 22 selected clones exhibited a two-fold range of static moe (2.2–4.7 {GPa)} and the clonal heritabilities ( {TeXHˆ\{2\}\_\{i\}} ) for moe, density and mfa were high.},  language = {en},  number = {8},  urldate = {2013-11-12},  journal = {Wood Science and Technology},  author = {Lindström, H. and Harris, P. and Sorensson, C. T. and Evans, R.},  month = dec,  year = {2004},  pages = {579--597}  }  @article{moden_elastic_2008,  title = {Elastic deformation mechanisms of softwoods in radial tension: Cell wall bending or stretching?},  volume = {62},  number = {5},  journal = {Holzforschung},  author = {Moden, Carl S. and Berglund, Lars},  year = {2008},  pages = {562--568}  }  @article{geitmann_mechanical_2010,  title = {Mechanical modeling and structural analysis of the primary plant cell wall},  volume = {13},  issn = {1369-5266},  url = {http://www.sciencedirect.com/science/article/pii/S1369526610001366},  doi = {10.1016/j.pbi.2010.09.017},  abstract = {Plant cell growth is a fundamental process during plant development whose spatial and temporal dynamics are controlled by the cell wall. Modeling mechanical aspects of cell growth therefore requires the integration of structural cell wall details with quantitative biophysical parameters. Recent advances in microscopic techniques and mechanical modeling have made significant contributions to the field of cell wall biomechanics. Live observation of cellulose microfibrils at high z-resolution now enables determining the dynamic orientation of these polymers in the different wall layers of growing cells. Mechanical modeling approaches have been developed to operate at the scale of individual molecules and will thus be able to exploit the availability of the high-resolution structural data. The combination of these techniques has the potential to make a significant and quantitative contribution to our understanding of plant growth and development.},  number = {6},  urldate = {2013-04-15},  journal = {Current Opinion in Plant Biology},  author = {Geitmann, Anja},  month = dec,  year = {2010},  pages = {693--699}  }  @article{guillon_new_2012,  title = {A new mathematical framework for modelling the biomechanics of growing trees with rod theory},  volume = {55},  issn = {0895-7177},  url = {http://www.sciencedirect.com/science/article/pii/S0895717711007874},  doi = {10.1016/j.mcm.2011.12.024},  abstract = {The analysis of the shape evolution of growing trees requires an accurate modelling of the interaction between growth and biomechanics, including both static and adaptive responses. However, this coupling is a problematic issue since the progressive addition of a new material on an existing deformed body makes the definition of a reference configuration unclear. This article presents a new mathematical framework for rod theory that allows overcoming this difficulty in the case of slender structures that grow both in length and diameter like tree branches. A key point in surface growth problems is the strong dependency between space and time. On this basis, the virtual reference configuration was defined as the set of initial geometric properties of the cross-sections at their date of appearance. The classical balance equations of the rod theory were then reformulated with respect to this evolving reference configuration. This new continuous formulation leads to an evolution equation of the relaxed configuration that takes into account changes in material and geometrical properties of the growing rod. Primary (linked to growth in length) and secondary (linked to growth in diameter) tropisms, i.e. the adaptive biomechanical response of growing trees to the local environment, were also considered as a component of remodelling in tree growth, which modifies the relaxed configuration. Analytical solutions of our growth model was found in simple cases, i.e. assuming planar and small deflections and considering a linear elastic constitutive law. Corresponding motion results were compared with results provided by the classical rod theory and analysed with regards to growth strategies involved in gravitropic responses. These first qualitative results show that the proposed mathematical model was able to simulate the main processes involved in tree growth. This mathematical formalism is particularly suited to study the biomechanical response of trees subjected to quasi-static loads. This contribution also provides new insight into a more general three-dimensional theory of surface growth and raises new mathematical challenges about the analysis of this original system of partial differential equations.},  number = {9--10},  urldate = {2013-04-14},  journal = {Mathematical and Computer Modelling},  author = {Guillon, Thomas and Dumont, Yves and Fourcaud, Thierry},  month = may,  year = {2012},  keywords = {cambial growth, Cell maturation strain, Continuous modelling, gravitropism, Nonlinear partial differential equations, Surface growth},  pages = {2061--2077}  }  @article{england_dynamic_2000,  title = {A dynamic analysis of windthrow of trees},  volume = {73},  url = {http://dx.doi.org/10.1093/forestry/73.3.225},  doi = {10.1093/forestry/73.3.225},  number = {3},  journal = {Forestry},  author = {England, {A.H.}},  month = mar,  year = {2000},  pages = {225--238}  }  @article{ormarsson_moisture-related_2005,  title = {Moisture-Related Distortion of Timber Boards of Radiata Pine: Comparison With Norway Spruce},  volume = {37},  shorttitle = {Moisture-Related Distortion of Timber Boards of Radiata Pine},  url = {http://swst.metapress.com/content/W05V2L0754J66088},  abstract = {Based on material data obtained by several researchers at Forest Research in New Zealand, with respect to variations in the main material properties from pith to bark, the distortion model developed earlier for Norway spruce has been further modified for radiata pine. Numerical simulations were performed for both pine and spruce to investigate how different sawn pattern options affect the shape stability of individual boards. Results for spruce presented earlier have shown clearly that warping of the timber products is strongly influenced by the annual ring patterns within the individual boards. Comparisons between the two species were performed to study how the radial variations in the basic properties such as shrinkage parameters, stiffness parameters, and spiral grain have influence on the warping. Generally, the intrinsic patterns of variation in wood properties within stems were similar, and both species show a tendency to distort with changing moisture environment. There are strong indications that intelligent re-combination of material in glued products may overcome many of the inherent problems in using biological material with predictable variation in material properties.},  number = {3},  urldate = {2013-11-13},  journal = {Wood and Fiber Science},  author = {Ormarsson, Sigurdur and Cown, Dave},  month = jul,  year = {2005},  pages = {424--436}  }  @article{asnacios_mechanics_2012,  title = {The mechanics behind cell polarity},  volume = {22},  issn = {0962-8924},  url = {http://www.sciencedirect.com/science/article/pii/S0962892412001444},  doi = {10.1016/j.tcb.2012.08.005},  abstract = {The generation of cell polarity is one of the most intriguing symmetry-breaking events in biology. It is involved in almost all physiological and developmental processes and, despite the differences between plant and animal cell structures, cell polarity is generated by a similar core mechanism that comprises the extracellular matrix ({ECM)}, Rho {GTPase}, the cytoskeleton, and the membranes. Several recent articles show that mechanical factors also contribute to the establishment and robustness of cell polarity, and the different molecular actors of cell polarity are now viewed as integrators of both biochemical and mechanical signals. Although cell polarity remains a complex process, some level of functional convergence between plants and animals is revealed. Following comparative presentation of cell polarity in plants and animals, we will discuss the theoretical background behind the role of mechanics in polarity and the relevant experimental tests, focusing on {ECM} anchorage, cytoskeleton behavior, and membrane tension.},  number = {11},  urldate = {2013-04-14},  journal = {Trends in Cell Biology},  author = {Asnacios, Atef and Hamant, Olivier},  month = nov,  year = {2012},  keywords = {cytoskeleton, endocytosis, extracellular matrix, membrane tension, osmotic pressure, Stiffness},  pages = {584--591}  }  @book{mattheck_wood_1995,  address = {Berlin},  series = {Springer series in wood science},  title = {Wood - The internal optimization of trees},  isbn = {3540593187},  shorttitle = {Wood - The internal optimization of trees},  publisher = {Springer},  author = {Mattheck, C. and Kubler, H.},  year = {1995}  }  @article{archer_distribution_1979,  title = {On the distribution of tree growth stresses. {P}art {III}: The case of inclined grain},  volume = {13},  issn = {0043-7719, 1432-5225},  url = {http://link.springer.com.ezproxy.canterbury.ac.nz/content/pdf/10.1007%2FBF00350177},  doi = {10.1007/BF00350177},  number = {1},  urldate = {2013-04-15},  journal = {Wood Science and Technology},  author = {Archer, R.},  year = {1979},  pages = {67--78}  }  @article{green_general_1966,  title = {A General Theory of Rods},  volume = {293},  copyright = {Copyright © 1966 The Royal Society},  issn = {0080-4630},  url = {http://www.jstor.org/stable/2415647},  doi = {10.2307/2415647},  abstract = {A general thermodynamical theory is developed for rods. An elastic rod, and special cases of the general theory which are closely related to the classical theories of rods and strings, are also discussed.},  number = {1433},  urldate = {2013-03-19},  journal = {Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences},  author = {Green, A. E. and Laws, N.},  month = jul,  year = {1966},  pages = {145--155}  }  @article{moore_comparison_2000,  title = {A comparison of the relative risk of wind damage to planted forests in Border Forest Park, Great Britain, and the Central {N}orth {I}sland, {N}ew {Z}ealand},  volume = {135},  issn = {0378-1127},  url = {http://www.sciencedirect.com/science/article/pii/S0378112700002929},  doi = {10.1016/S0378-1127(00)00292-9},  abstract = {The risk of wind damage was assessed for Sitka spruce growing in the Border Forest Park, Great Britain and radiata pine growing in the Central North Island, New Zealand using a quantitative wind risk model ({FORESTGALES).} The model has been adapted for the two species using estimates of maximum resistive bending moment from historical tree winching studies performed in the two regions, drag coefficients obtained from wind tunnel tests, and wind data from representative meteorological stations. The risk is calculated as the probability that the threshold wind speed for damage will be exceeded at a particular site. This approach enables the effect of different growth rates, soil types, management regimes and wind climates to be investigated. The threshold wind speed for tree failure was calculated for stands of both species grown under standard regimes on typical soils and characteristic topography. The probability that the threshold wind speed is exceeded was determined using a recurrence function fitted to time-series of annual maximum hourly wind speeds from a representative long-term meteorological station for each region. The two species are grown over substantially different rotation lengths, so comparisons were made between the profile of risk over a single rotation, and also as cumulative risk over a time-span sufficient to contain multiple rotations. The results demonstrate substantial differences in the probability of wind damage between forests in the two regions as they are currently managed. Contrary to expectation, the risk is lowest for forests in the region of the most severe wind climate, because of the selection of a risk-minimising strategy. This finding emphasises the degree to which management of forests can affect the frequency and amount of damage that they experience. The model was portable and provided objective estimates of risk for two very different locations and silvicultural regimes. Further development should provide a tool of practical importance for those seeking to make comparisons between very different situations, such as multi-national companies and re-insurers.},  number = {1-3},  urldate = {2013-04-15},  journal = {Forest Ecology and Management},  author = {Moore, John and Quine, Christopher P},  month = sep,  year = {2000},  keywords = {Abiotic risk, Risk assessment, Wind damage},  pages = {345--353}  }  @article{morgan_shape_1994,  title = {Shape of tree stems—a re-examination of the uniform stress hypothesis},  volume = {14},  issn = {0829-{318X}, 1758-4469},  url = {http://treephys.oxfordjournals.org.ezproxy.canterbury.ac.nz/content/14/1/49},  doi = {10.1093/treephys/14.1.49},  abstract = {The transfer matrix method of structural analysis was used to examine the hypothesis that tree stems grow to a shape that tends to equalize the average bending plus axial stresses to which they are subjected along their length. The method and computational procedures were checked by comparing computed height–diameter profiles with those calculated using elementary stress theory for trees with simple force distributions in the crown. Measured height–diameter profiles for trees were then taken from the literature and shown to be well-fitted by profiles calculated to give uniform stress along the stems, using the most realistic average forces and force distributions within the crowns. At high wind speeds, the height–diameter profile giving uniform stress was more tapered than the profile giving uniform stress at low wind speeds. The profile giving uniform stress was similar over the normal range of average wind speeds of 2.5 to 10.0 m s−1 (at the top of the canopy). But a tree that had grown to give uniform stress along its stem in an average wind of 5 m s−1 showed markedly decreased stress with height at wind speeds of about 15 m s−1 or more, and increased stress with height (to the crown base) at wind speeds of about 1.25 m s−1 or less. The fact that tree stems develop shapes in response to average conditions, but show varying stress distribution in extreme conditions, may help to explain some of the apparent evidence for non-uniform stress distribution in the literature. In general, our analysis supports the above hypothesis for the stem region above the butt swell.},  language = {en},  number = {1},  urldate = {2013-11-12},  journal = {Tree Physiology},  author = {Morgan, John and Cannell, Melvin G. R.},  month = jan,  year = {1994},  keywords = {axial stress, bending stress, force, structural analysis, transfer matrix method, wind speed},  pages = {49--62}  }  @article{mackenzie-helnwein_rate-independent_2005,  title = {Rate-independent mechanical behavior of biaxially stressed wood: Experimental observations and constitutive modeling as an orthotropic two-surface elasto-plastic material},  volume = {59},  shorttitle = {Rate-independent mechanical behavior of biaxially stressed wood},  url = {http://www.degruyter.com.ezproxy.canterbury.ac.nz/view/j/hfsg.2005.59.issue-3/hf.2005.052/hf.2005.052.xml},  abstract = {{AbstractRecent} biaxial experiments on spruce wood show that consideration of an elliptic failure surface according to Tsai and Wu and an elastic model for stress states within this envelope lead to an insufficient description of the mechanical behavior. As compression perpendicular to the grain occurs, a non-linear stress path results from a proportional biaxial strain path. Investigation of characteristic samples with respect to loading-unloading-reloading cycles for states of stress below failure reveals behavior similar to what is known as hardening type {plasticity.The} experimentally observed mechanical behavior is described by means of a two-surface plasticity model addressing both failure and non-linear stress response below failure as separate mechanisms. Prediction of failure is achieved by means of a second-order failure envelope according to Tsai and Wu. The non-linear stress response has to be covered by a novel orthotropic hardening type plasticity model. Since available experimental data covers only plane stress in the {LR-plane}, both orthotropic failure and yield surfaces, respectively, are restricted to this case.},  number = {3},  urldate = {2013-11-13},  journal = {Holzforschung},  author = {Mackenzie-Helnwein, Peter and Eberhardsteiner, Josef and Mang, Herbert A.},  month = may,  year = {2005},  pages = {311--321}  }  @article{mackenzie-helnwein_computational_2003,  title = {Computational Analysis of Quality Reduction during Drying of Lumber due to Irrecoverable Deformation. {II:} Algorithmic Aspects and Practical Application},  volume = {129},  url = {http://ascelibrary.org/doi/abs/10.1061/%28ASCE%290733-9399%282003%29129%3A9%281006%29},  doi = {10.1061/(ASCE)0733-9399(2003)129:9(1006)},  number = {9},  journal = {Journal of Engineering Mechanics},  author = {Mackenzie-Helnwein, P. and Hanhijärvi, A.},  year = {2003},  pages = {1006--1016}  }  @article{cave_stiffness_1994,  title = {Stiffness of Wood in Fast-Grown Plantation Softwoods - the Influence of Microfibril Angle},  volume = {44},  shorttitle = {Stiffness of Wood in Fast-Grown Plantation Softwoods - the Influence of Microfibril Angle},  url = {://A1994NL71000007},  abstract = {in fast-grown softwoods, there are very large changes in the longitudinal Young's modulus of wood going outward from the pith. Typically, stiffness increases by a factor of 3 to 5 during the first 30 years of growth. A change in the microfibril angle of the S2 layer of the tracheid wall is the only mechanism that has been proposed that can account for this. There appear to be sufficient variations in microfibril angle between trees to justify selection of clones to yield stiffer timber.},  journal = {Forest Products Journal},  author = {Cave, I. D. and Walker, J. C. F.},  year = {1994},  pages = {43--48}  }  @book{bodig_jozsef_jayne_mechanics_1982,  title = {Mechanics of wood and wood composites},  isbn = {0442008228},  publisher = {New York: Van Nostrand Reinhold},  author = {Bodig, Jozsef and Jayne, Benjamin A.},  year = {1982},  keywords = {Composite materials., Wood}  }  @article{archer_distribution_1976,  title = {On the distribution of tree growth stresses. {P}art {II}: Stresses due to asymmetric growth strains},  volume = {10},  issn = {0043-7719},  url = {http://dx.doi.org/10.1007/BF00350833},  doi = {10.1007/BF00350833},  language = {English},  number = {4},  journal = {Wood Science and Technology},  author = {Archer, R.},  year = {1976},  pages = {293--309}  }  @book{pavliotis_multiscale_2008,  address = {New York},  series = {Texts in applied mathematics},  title = {Multiscale methods: averaging and homogenization},  isbn = {9780387738284},  lccn = {QA371 .P385 2008},  shorttitle = {Multiscale methods},  number = {53},  publisher = {Springer},  author = {Pavliotis, Grigorios A. and Stuart, A. M.},  year = {2008},  keywords = {Differential equations, Partial},  annote = {This introduction to multiscale methods gives readers a broad overview of their many uses and applications. The book begins by setting the theoretical foundations of the subject area and moves on to develop a unified approach to the simplification of a wide range of problems which possess multiple scales via perturbation expansions; differential equations and stochastic processes are studied in one unified framework. The book concludes with an overview of a range of theoretical tools used to justify the simplified models derived via the perturbation expansions. The presentation of the material is particularly suited to the range of mathematicians, scientists, and engineers who want to exploit multiscale methods in applications. Extensive use of examples shows how to apply multiscale methods to solve a variety of problems. Exercises then enable readers to build their own skills and put them into practice. Extensions and generalizations of the results presented in the book, as well as references to the literature, are provided in the Discussion and Bibliography section at the end of each chapter. With the exception of Chapter One, all of the 21 chapters are supplemented with {exercises.–BOOK} {JACKET}}  }  @article{s_development_2010,  title = {Development of a model describing modulus of elasticity across environmental and stand density gradients in plantation-grown \textit{Pinus radiata} within {N}ew {Z}ealand},  volume = {40},  issn = {1208-6037},  url = {http://dx.doi.org/10.1139/x10-103},  doi = {10.1139/x10-103},  number = {8},  journal = {Canadian Journal of Forest Research},  author = {Watt, Michael S. and Zoric, Branislav},  month = aug,  year = {2010},  pages = {1558--1566}  }  @article{ozyhar_moisture-dependent_2013,  title = {Moisture-dependent orthotropic tension-compression asymmetry of wood},  volume = {67},  url = {http://www.degruyter.com.ezproxy.canterbury.ac.nz/view/j/hfsg.2013.67.issue-4/hf-2012-0089/hf-2012-0089.xml;jsessionid=31F22A83593A712A6B45D86B802DA7AE},  abstract = {{AbstractThe} influence of moisture content ({MC)} on the tension-compression (Te-Co) asymmetry of beech wood has been examined. The elastic and strength parameters, including Te and Co Young’s moduli, Poisson’s ratios, and ultimate and yield stress values, were determined and compared in terms of different {MCs} for all orthotropic directions. The results reveal a distinctive Te-Co strength asymmetry with a moisture dependency that is visualized clearly by the Te to Co yield stress ratio. The Te-Co asymmetry is further shown by the inequality of the elastic properties, known as the “bimodular behavior”. The latter is proven for the Young’s moduli values in the radial and tangential directions and for individual Poisson’s ratios. Although the bimodularity of the Young’s moduli is significant at low {MC} levels, there is no evidence of moisture dependency on the Te-Co asymmetry of the Poisson’s ratios.},  number = {4},  urldate = {2013-11-19},  journal = {Holzforschung},  author = {Ozyhar, Tomasz and Hering, Stefan and Niemz, Peter},  month = may,  year = {2013},  pages = {395--404}  }  @article{downes_relationship_2002,  title = {Relationship between wood density, microfibril angle and stiffness in thinned and fertilized \textit{Pinus radiata}},  volume = {23},  issn = {0928-1541},  abstract = {The relationships between wood anatomy in standing trees and the strength of boards were examined in \textit{Pinus radiata} D. Don (thinned vs thinned and fertilized) at 2 contrasting sites. Fertilizer treatments were applied after mid-rotation thinning. Logs were taper sawn and boards, near the pre-treatment/post-treatment boundary, subjected to acoustic and strength assessment. Average wood property data from a 12-mm increment core obtained prior to harvest, was extracted from the relevant portion of the radius. In general, fertilizer resulted in lower density, higher microfibril angle ({MFA)} and slightly lower stiffness. However, stiffness was still relatively high as the affected wood was from the more mature portion of the radius. {SilviScan} density and {MFA} data were good predictors of stiffness. Acoustic measurements on boards were strongly correlated with board stiffness. Path analyses explained up to 45\% of the variance in stiffness, as a function of estimated {MOE} and log sweep.},  language = {English},  number = {3},  journal = {Iawa Journal},  author = {Downes, G. M. and Nyakuengama, J. G. and Evans, R. and Northway, R. and Blakemore, P. and Dickson, R. L. and Lausberg, M.},  year = {2002},  keywords = {Density, fertilizer, microfibril angle, \textit{Pinus radiata}, {SilviScan}, Stiffness},  pages = {253--265}  }  @article{peltola_mechanistic_1999,  title = {A mechanistic model for assessing the risk of wind and snow damage to single trees and stands of Scots pine, Norway spruce, and birch},  volume = {29},  issn = {0045-5067},  url = {http://www.nrcresearchpress.com/doi/abs/10.1139/x99-029},  doi = {10.1139/x99-029},  abstract = {A mechanistic model for assessing the risk of wind and snow damage to single trees and stands of Scots pine (Pinus sylvestris L.), Norway spruce (Picea abies (L.) Karst.), and birch (Betula spp.) is presented. The model predicts the critical turning moment and wind speed at which the trees will be uprooted or break at forest margins. The resistance to uprooting is predicted using the estimate of the root-soil plate weight to derive a resistive moment, while the resistance to stem breakage relies on values for the modulus of rupture determined for different species of timber. A tree is assumed to be uprooted if the total turning moment exceeds the support provided by the root-soil plate anchorage. Similarly, a tree is assumed to break if the breaking stress acting on the stem exceeds a critical value of the modulus of rupture. The model is in general quite sensitive to parameter changes, which partly results from the location in the forest to which it was designed to apply (the stand edge). The predictions..., Cet article présente un modèle mécaniste permettant d'évaluer le risque de dommages causés par le vent et la neige pour des arbres individuels et des peuplements de pin sylvestre (Pinus sylvestris L.), d'épinette de Norvège (Picea abies (L.) Karst.) et de bouleau (Betula spp.). Le modèle prédit le moment de flexion critique et la vitesse du vent à laquelle les arbres à la lisière des forêts seront déracinés ou casseront. La résistance au renversement est prédite en utilisant des estimés du poids de la plaque formée par le sol et les racines pour dériver un moment de résistance, alors que la résistance de la tige à la rupture se base sur les valeurs de module de rupture pour les différentes espèces. Le modèle assume qu'un arbre sera déraciné si le moment de flexion total dépasse le support fourni par l'ancrage de la plaque de racines et de sol. De la même façon, on assume qu'un arbre cassera si la contrainte dans la tige dépasse la valeur critique du module de rupture. Le modèle est en général assez sensib...},  number = {6},  urldate = {2013-11-20},  journal = {Canadian Journal of Forest Research},  author = {Peltola, H and Kellomäki, S and Väisänen, H and Ikonen, V -P},  month = jun,  year = {1999},  pages = {647--661}  }  @article{moden_elastic_2008-1,  title = {Elastic deformation mechanisms of softwoods in radial tension – Cell wall bending or stretching?},  volume = {62},  url = {http://www.degruyter.com.ezproxy.canterbury.ac.nz/view/j/hfsg.2008.62.issue-5/hf.2008.082/hf.2008.082.xml},  abstract = {{AbstractRadial} softwood modulus E R is typically twice as high as the tangential modulus E T. The reason for this is unclear, although cell geometry is likely to contribute. The established hexagonal honeycomb model for prediction of E R is based on a cell wall bending mechanism only. If cell wall stretching also takes place, the dependence of E R on relative density will be different. If experimental data for E R as a function of relative density show deviations from cell wall bending predictions, this may indicate the presence of cell wall stretching. A {SilviScan} apparatus is used to measure density distribution. A procedure by means of digital speckle photography is then developed for measurements of local E R within the annual rings of spruce. Comparison is made between experimental data and the two expected density dependencies from cell wall bending and from stretching. The hypothesis of cell wall stretching as a contributing mechanism is supported based on the observed linear dependence of E R over a wide density range.},  number = {5},  urldate = {2013-11-13},  journal = {Holzforschung},  author = {Modén, Carl S. and Berglund, Lars A.},  month = sep,  year = {2008},  pages = {562--568}  }  @article{papesch_mechanical_1997,  title = {Mechanical stability of \textit{Pinus radiata} trees at {E}yrewell Forest Investigated using static tests},  volume = {27},  number = {2},  journal = {New Zealand Journal of Foresty Science},  author = {Papesch, {A.G.} and Moore, {J.R.} and Hawke, {A.E.}},  year = {1997},  pages = {188--204}  }  @article{watt_determining_2010,  title = {Determining the main and interactive effect of age and clone on wood density, microfibril angle, and modulus of elasticity for \textit{Pinus radiata}},  volume = {40},  issn = {0045-5067},  url = {http://www.nrcresearchpress.com.ezproxy.canterbury.ac.nz/doi/abs/10.1139/X10-095},  doi = {10.1139/X10-095},  abstract = {Detailed radial measurements of wood properties, taken at breast height, were obtained from control pollinated seedlings and a selection of 13 year old radiata pine (\textit{Pinus radiata D. Don}) clones. Using these data the key objectives of this study were to determine (i) the magnitude of mean clonal variation in modulus of elasticity ({MOE)} and properties affecting {MOE} (density and microfibril angle ({MFA))} and (ii) whether there is a significant age × clone interaction for these traits. All wood properties were significantly affected by the main and interactive effects of age and clone. There was a relatively linear increase in both {MOE} and density with tree age, while {MFA} declined linearly with tree age. Values of density and {MOE} diverged between the clonal extremes from age 3 to age 12. After diverging markedly up to age 6, differences in {MFA} between clonal extremes remained relatively constant to age 12. At age 12, values for density, {MFA}, and {MOE} varied between clonal extremes by, respectively, 194 kg·m–3 ..., Des mesures radiales détaillées des propriétés du bois ont été prises à hauteur de poitrine sur des semis issus d’une pollinisation contrôlée et sur des clones sélectionnés de pin radiata (Pinus radiata D. Don) {D.Don} âgés de 13 ans. À partir de ces données, les principaux objectifs de cette étude consistaient à déterminer (i) l’ampleur de la variation clonale moyenne du module d’élasticité ({MOE)} et des propriétés affectant le {MOE} (densité et angle des microfibrilles ({AMF))} et (ii) s’il y a une interaction âge × clone significative dans le cas de ces traits. Les effets principaux et l’interaction âge × clone étaient significatifs pour toutes les propriétés du bois. Le {MOE} et la densité augmentaient de façon relativement linéaire tandis que {l’AMF} diminuait linéairement en fonction de l’âge d’arbre. Entre 3 et 12 ans, les valeurs de densité et de {MOE} divergeaient entre les extrêmes clonaux. Après avoir divergé de façon marquée jusqu’à l’âge de 6 ans, les différences {d’AMF} entre les extrêmes clonaux demeuraie...},  number = {8},  urldate = {2013-11-13},  journal = {Canadian Journal of Forest Research},  author = {Watt, Michael S. and Sorensson, Charles and Cown, Dave J. and Dungey, Heidi S. and Evans, Robert},  month = jul,  year = {2010},  pages = {1550--1557}  }  @article{cave_modelling_1978-1,  title = {Modelling moisture-related mechanical properties of wood Part {II:} Computation of properties of a model of wood and comparison with experimental data},  volume = {12},  number = {1},  journal = {Wood Science and Technology},  author = {Cave, I. D.},  year = {1978},  keywords = {Agriculture, and Design, Ceramics, Characterization, Forestry, Glass, Leather, Materials Processing, Paper, Textiles, Wood, Wood Science \& Technology},  pages = {127--139}  }  @article{yamamoto_growth_2002,  title = {Growth stress controls negative gravitropism in woody plant stems},  volume = {216},  issn = {0032-0935},  shorttitle = {Growth stress controls negative gravitropism in woody plant stems},  url = {://000180037300011},  doi = {10.1007/s00425-002-0846-x},  abstract = {In the shoots of woody plant species, reaction-wood fibers are formed on the upper or lower side of the secondary xylem of a leaning trunk or branch wherever large, internal growth stress is generated. Negative gravitropic movement in woody plant stems is proposed to be the result of growth stress generated in the reaction-wood tissue. This study examines the interaction between bending moment due to increasing self-weight and recovery moment resulting from asymmetric growth stress, and tests a hypothesis that describes the relationship based on the structural mechanics beam theory. Simulations of observed tree branch morphology of Magnolia kobus {DC.}, Juniperits chinensis L., Abies saccharinensis Fr. Schum., and Prunus spachiana Kitamura f. spachiana cv. Plenarosea showed that (i) the growth stress generated in the reaction wood is sufficient to counteract the gravitropic response to increasing self-weight, and (ii) the specific directional angle of the shoot apex or preferred angle of the elongation zone plays an important role in controlling the spatial shape of the branch stem that is peculiar to plant species with large growth stress generated in the reaction-wood tissue.},  language = {English},  journal = {Planta},  author = {Yamamoto, H. and Yoshida, M. and Okuyama, T.},  month = dec,  year = {2002},  keywords = {{BRANCHES}, branch movement, cellulose microfibril, {CELL-WALLS}, Compression wood, {GENERATION} {PROCESS}, gravitropism, growth stress, {MATURATION}, mechanics, {PATTERNS}, Reaction, tension wood, {TISSUE} {STRESSES}, tree growth, Wood, woody plant shoots},  pages = {280--292}  }  @article{watt_modelling_2006,  title = {Modelling the influence of stand structural, edaphic and climatic influences on juvenile \textit{Pinus radiata} dynamic modulus of elasticity},  volume = {229},  issn = {0378-1127},  url = {http://dx.doi.org/10.1016/j.foreco.2006.03.016},  doi = {10.1016/j.foreco.2006.03.016},  number = {1-3},  journal = {Forest Ecology and Management},  author = {Watt, Michael S. and Moore, John R. and Façon, Jean-Philippe and Downes, Geoff M. and Clinton, Peter W. and Coker, Graham and Davis, Murray R. and Simcock, Robyn and Parfitt, Roger L. and Dando, John and Mason, E.G. and Bown, H.E.},  month = jul,  year = {2006},  keywords = {Environment, Euler buckling, Modulus of elasticity, \textit{Pinus radiata}, Stem slenderness, Taper, Temperature},  pages = {136--144}  }  @article{skatter_residual_2001,  title = {Residual stresses caused by growth stresses within a stem with radially varying spiral grain angle - two numerical solution approaches: 1) {f}inite element method and 2) {T}ransfer matrix method},  volume = {35},  issn = {0043-7719, 1432-5225},  shorttitle = {Residual stresses caused by growth stresses within a stem with radially varying spiral grain angle - two numerical solution approaches},  url = {http://link.springer.com.ezproxy.canterbury.ac.nz/article/10.1007/s002260000073},  doi = {10.1007/s002260000073},  abstract = {Two numerical methods, the Finite Element ({FE)} method and the Transfer Matrix ({TM)} method, have been applied to derive a solution for residual stresses in a stem. The source of stress is the maturation strains in new wood cells, which give rise to growth stresses. The methods are generally applicable to the case of spiral grain with a grain angle varying with radius, which often is the case in trees. Also, the methods allow for the elastic constants to vary with the radius, which is important to model, for example, juvenile wood. The numerical solutions are checked against an analytical solution in the case of a constant grain angle, and are found to coincide. In addition, the two methods are shown to independently produce the same stress distribution for one pattern of grain angle variation. This shows that the methods are reliable, and they will be used for obtaining a wider range of solutions in a subsequent paper.},  language = {en},  number = {1-2},  urldate = {2013-04-29},  journal = {Wood Science and Technology},  author = {Skatter, S. and Archer, R.},  month = apr,  year = {2001},  pages = {57--71}  }  @book{meinzer_frederick_2011,  series = {Tree Physiology},  title = {Size- and Age- Related Changes in Tree Structure and Function},  volume = {{F}our},  url = {http://www.springer.com/life+sciences/forestry/book/978-94-007-1241-6},  abstract = {Millions of trees live and grow all around us, and we all recognize the vital role they play in the world’s ecosystems. Publicity campaigns exhort us to plant yet more. Yet until recently comparatively little was known about the ...},  urldate = {2013-03-19},  publisher = {Springer},  author = {Meinzer, Frederick C. and Lachenbruch, Barbara and Dawson, Todd E.},  year = {2011},  keywords = {Plant Physiology, Size- and Age-Related Changes in Tree Structure and Function, Tree Biology}  }  @article{rudnicki_wind_2004,  title = {Wind tunnel measurements of crown streamlining and drag relationships for three conifer species},  volume = {34},  issn = {1208-6037},  url = {http://dx.doi.org/10.1139/x03-233},  doi = {10.1139/x03-233},  number = {3},  journal = {Canadian Journal of Forest Research},  author = {Rudnicki, Mark and Mitchell, Stephen J and Novak, Michael D},  month = mar,  year = {2004},  pages = {666--676}  }  @article{burgess_analysis_2004,  title = {Analysis of the structural efficiency of trees},  volume = {15},  url = {http://dx.doi.org/10.1080/09544820410001658517},  doi = {10.1080/09544820410001658517},  number = {2},  journal = {Journal of Engineering Design},  author = {Burgess, S. C. and Pasini, D.},  month = apr,  year = {2004},  pages = {177--193}  }  @article{mackenzie-helnwein_analysis_2005,  title = {Analysis of layered wooden shells using an orthotropic elasto-plastic model for multi-axial loading of clear spruce wood},  volume = {194},  issn = {0045-7825},  url = {http://www.sciencedirect.com/science/article/pii/S0045782504005511},  doi = {10.1016/j.cma.2004.07.051},  abstract = {The analysis of layered wooden shells requires a suitable constitutive model for multi-axially loaded wood. This paper presents a sophisticated model for softwood suitable for the description of inelastic deformations both in-plane and transverse to the shell surface. It incorporates micromechanical failure mechanisms in an orthotropic single-surface formulation by means of a non-associative hardening/softening law. The latter permits identification of active failure mechanisms and control over six distinct strength functions. These strength functions are used for the definition of a deformable elliptical state surface. Special issues concerning an effective numerical implementation of the proposed model are discussed. The return mapping algorithm is adopted for this purpose. It remains fully functional and effective for the orthotropic model with its non-conventional hardening/softening behavior. Moreover, the consistent tangent can be given as a closed form expression. Applicability of the model is verified by the finite element analysis of a layered cylindrical shell with one opening and stiffeners.},  number = {21--24},  urldate = {2013-11-13},  journal = {Computer Methods in Applied Mechanics and Engineering},  author = {Mackenzie-Helnwein, Peter and Müllner, Herbert W. and Eberhardsteiner, Josef and Mang, Herbert A.},  month = jun,  year = {2005},  keywords = {Layered, Layered shells, Multi-axial loading, Orthotropy, shells, Softwood, Strain softening},  pages = {2661--2685}  }  @article{xu_effects_2004,  title = {Effects of density and microfibril orientation on the vertical variation of low-stiffness wood in radiata pine butt logs},  volume = {58},  url = {http://www.degruyter.com.ezproxy.canterbury.ac.nz/view/j/hfsg.2004.58.issue-6/hf.2004.122/hf.2004.122.xml},  abstract = {{AbstractThe} roles of density and microfibril angle in causing low stiffness in radiata pine butt logs were studied in detail on a 17-year-old tree. Distributions of these variables were compared with stiffness variations in the vertical direction. Results supported the hypothesis that cell ultrastructure is responsible for the vertical variation in stiffness. The microfibril orientation in tangential wall is considered to be an important factor contributing to wood stiffness because of the smaller microfibril angles compared with radial microfibril angles, and also because of the larger decrease of the microfibril angles with the rapid increase of wood stiffness in vertical direction especially in corewood zone. The microfibrils in the S3 layer fall from over 80° to angles of 54° and 51° for radial and tangential cell walls at the top of the butt log. Further study is needed for fully understanding the characteristics of S3 layers.},  number = {6},  urldate = {2013-11-13},  journal = {Holzforschung},  author = {Xu, Ping and Donaldson, Lloyd and Walker, John and Evans, Robert and Downes, Geoffrey},  month = oct,  year = {2004},  pages = {673--677}  }  @book{gartner_plant_1995,  address = {San Diego},  title = {Plant Stems: Physiology and Functional Morphology},  publisher = {Academic Press.},  author = {Gartner, B. L},  year = {1995}  }  @book{mark_cell_1967,  title = {Cell wall mechanics of tracheids.},  address = {New Haven},  publisher = {Yale University Press},  abstract = {A review of fundamental knowledge on the structure of the cell-wall in relation to its behaviour under stress, supplemented by the author's experimental work and mathematical analysis. The 12 chapters deal with: mechanical testing; physical and chemical composition of the cell-wall; elastic constants of cell-wall components; theoretical strength of the structural framework; filament winding angles; molecular weight, distribution and crystallinity; strain behaviour of specimens; determination of stress distributions, and applications of cell-wall stress analysis. An extensive bibliography is given for each chapter, and author and subject indexes are included. {KEYWORDS:} wood anatomy {\textbackslash}textbackslashtextbackslash cell wall structure {\textbackslash}textbackslashtextbackslash wood anatomy {\textbackslash}textbackslashtextbackslash tracheids cell wall {\textbackslash}textbackslashtextbackslash wood anatomy {\textbackslash}textbackslashtextbackslash wood properties},  language = {English},  author = {Mark, R. E.},  year = {1967},  }  @article{kern_mechanical_2005,  title = {Mechanical perturbation affects conductivity, mechanical properties and aboveground biomass of hybrid poplars},  volume = {25},  url = {http://dx.doi.org/10.1093/treephys/25.10.1243},  doi = {10.1093/treephys/25.10.1243},  number = {10},  journal = {Tree Physiology},  author = {Kern, K. A. and Ewers, F. W. and Telewski, F. W. and Koehler, L.},  month = oct,  year = {2005},  pages = {1243--1251}  }  @article{gerhards_effect_1982,  title = {Effect of Moisture Content and Temperature on the Mechanical Properties of Wood: An Analysis of Immediate Effects},  volume = {14},  shorttitle = {Effect of Moisture Content and Temperature on the Mechanical Properties of Wood},  url = {http://swst.metapress.com/content/B08027N87757L339},  abstract = {Mechanical properties of wood increase as moisture content decreases below fiber saturation point, at least down to about 5\% {MC}, and as temperature decreases. This report summarizes the relevant studies reported in the literature on the immediate effects of moisture content and temperature on several mechanical properties of clear wood. Recommendations are made for future research.},  number = {1},  urldate = {2013-11-19},  journal = {Wood and Fiber Science},  author = {Gerhards, C.},  month = jan,  year = {1982},  pages = {4--36}  }  @book{rao_finite_1999,  Edition = {Third},  title = {The Finite Element Method in Engineering},  publisher = {Boston, Mass.; Oxford: Butterworth Heinemann},  author = {Rao, Singiresu},  year = {1999}  }  @article{ancelin_development_2004,  title = {Development of an individual tree-based mechanical model to predict wind damage within forest stands},  volume = {203},  issn = {0378-1127},  url = {http://www.sciencedirect.com/science/article/pii/S0378112704006395},  doi = {10.1016/j.foreco.2004.07.067},  abstract = {Models predicting forest stand wind-firmness are usually based on the calculation of a critical wind speed above which the mean tree of a stand is broken or uprooted. This approach is well adapted to regular stands, but in heterogeneous stands, not all the trees are necessarily damaged at the same time. Models used to analyse the distribution of damage within a population of trees can be a good alternative. In this perspective we developed {FOREOLE}, an individual-based mechanical model of tree response to wind. {FOREOLE} is based on a numerical description of tree structure allowing both wind and self-weight loads to be calculated at every level of the stem, as well as the bending moment at the tree base and mechanical stresses along the stem. We use a static approach to model wind forces in which the turbulent aspect of wind is taken into account through a gust factor. Stem breakage or uprooting is then predicted from comparisons to failure criteria, i.e. critical bending moment and critical compressive stress, respectively. Implemented in the software called {CAPSIS}, {FOREOLE} is compatible with a model of coniferous forest stand dynamics and allows wind-firmness to be simulated both in measured and virtual populations of trees. On individual trees, {FOREOLE} provided predictions of critical wind speed comparable to the existing models known as {GALES} and {HWIND}, despite differences in the method used to describe tree shape and to solve mechanics. These predictions appeared particularly sensitive to the gust factor and the drag coefficient. We then analysed the influence of stand structure, wind speed and individual tree characteristics on the type and amount of damage. From simulations in stands representing three different structures (regular, intermediate and selection stands), we showed that irregular stands experience scattered damage for a relatively wide range of wind speeds, whereas regular stands tend to collapse as a whole above a critical wind speed. Irregularity also increased the ratio between loss in volume of wood and loss in number of trees. Regarding tree characteristics, the highest and the slenderest subjects were the most sensitive, both to stem breakage and to overturning. Sensitivity to breakage was also increased by shorter crowns. In addition, statistical analysis of the simulation results also showed that wind speed remained the most significant variable in explaining wind damage.},  number = {1--3},  urldate = {2013-11-20},  journal = {Forest Ecology and Management},  author = {Ancelin, Philippe and Courbaud, Benoît and Fourcaud, Thierry},  month = dec,  year = {2004},  keywords = {Critical wind-speed, {FOREOLE}, transfer matrix method, Tree biomechanics, Tree stability, Wind-firmness},  pages = {101--121}  }  @article{halabe_nondestructive_1997,  title = {Nondestructive Evaluation of Green Wood Using Stress Wave and Transverse Vibration Techniques},  volume = {55},  number = {9},  journal = {Materials Evaluation},  author = {Halabe, Udaya B. and Bidigalu, Gangadhar M. and {GangaRao}, Hota {V.S.} and Ross, Robert J.},  year = {1997},  pages = {1013--1018}  }  @article{rosner_hydraulic_2011,  title = {Hydraulic efficiency compromises compression strength perpendicular to the grain in Norway spruce trunkwood},  volume = {25},  issn = {0931-1890, 1432-2285},  url = {http://link.springer.com.ezproxy.canterbury.ac.nz/article/10.1007/s00468-010-0505-y},  doi = {10.1007/s00468-010-0505-y},  abstract = {The aim of this study was to investigate bending stiffness and compression strength perpendicular to the grain of Norway spruce (Picea abies (L.) Karst.) trunkwood with different anatomical and hydraulic properties. Hydraulically less safe mature sapwood had bigger hydraulic lumen diameters and higher specific hydraulic conductivities than hydraulically safer juvenile wood. Bending stiffness ({MOE)} was higher, whereas radial compression strength lower in mature than in juvenile wood. A density-based tradeoff between {MOE} and hydraulic efficiency was apparent in mature wood only. Across cambial age, bending stiffness did not compromise hydraulic efficiency due to variation in latewood percent and because of the structural demands of the tree top (e.g. high flexibility). Radial compression strength compromised, however, hydraulic efficiency because it was extremely dependent on the characteristics of the “weakest” wood part, the highly conductive earlywood. An increase in conduit wall reinforcement of earlywood tracheids would be too costly for the tree. Increasing radial compression strength by modification of microfibril angles or ray cell number could result in a decrease of {MOE}, which would negatively affect the trunk’s capability to support the crown. We propose that radial compression strength could be an easily assessable and highly predictive parameter for the resistance against implosion or vulnerability to cavitation across conifer species, which should be topic of further studies.},  language = {en},  number = {2},  urldate = {2013-04-29},  journal = {Trees},  author = {Rosner, Sabine and Karlsson, Bo},  month = apr,  year = {2011},  keywords = {Agriculture, Compression strength perpendicular to the grain, Conduit wall reinforcement, Forestry, Hydraulic efficiency, Modulus of elasticity in bending, Norway spruce, Plant {Anatomy/Development}, Plant Pathology, Plant Physiology, Plant Sciences, Structure-function relationships, Vulnerability to cavitation, Wood shrinkage},  pages = {289--299}  }  @article{watt_influence_2011,  title = {Influence of stocking on radial and longitudinal variation in modulus of elasticity microfibril angle, and density in a 24-year-old \textit{Pinus radiata} thinning trial},  volume = {41},  issn = {1208-6037},  url = {http://dx.doi.org/10.1139/x11-070},  doi = {10.1139/x11-070},  number = {7},  journal = {Canadian Journal of Forest Research},  author = {Watt, Michael S. and Zoric, Branislav and Kimberley, Mark O. and Harrington, Jonathan},  month = jul,  year = {2011},  keywords = {{BAYESIAN} analysis, {LONGITUDINAL} method, {MICROFIBRILS}, Pinus radiata, {WOOD} – Quality},  pages = {1422--1431}  }  @article{d_anisotropic_1968,  title = {The anisotropic elasticity of the plant cell wall},  volume = {2},  issn = {1432-5225},  url = {http://dx.doi.org/10.1007/bf00350273},  doi = {10.1007/bf00350273},  number = {4},  journal = {Wood Science and Technology},  author = {D, Cave I.},  year = {1968},  keywords = {Agriculture, and Design, Ceramics, Characterization, Forestry, Glass, Leather, Materials Processing, Paper, Textiles, Wood, Wood Science \& Technology},  pages = {268--278}  }  @article{archer_origin_1987,  title = {On the origin of growth stresses in trees. {P}art {I:} {M}icro mechangics of the developing cambial cell wall},  volume = {21},  url = {http://dx.doi.org/10.1007/BF00376194},  doi = {10.1007/BF00376194},  number = {2},  journal = {Wood Science and Technology},  author = {Archer, R.},  year = {1987},  pages = {139--154}  }  @article{lasserre_influence_2009,  title = {Influence of initial planting spacing and genotype on microfibril angle, wood density, fibre properties and modulus of elasticity in \textit{Pinus radiata D. Don} corewood},  volume = {258},  issn = {0378-1127},  url = {http://www.sciencedirect.com/science/article/pii/S0378112709005088},  doi = {10.1016/j.foreco.2009.07.028},  abstract = {\textit{Pinus radiata D. Don} trees from six clones, grown at initial spacings of 2500 stems ha−1 and 833 stems ha−1 were destructively harvested. For these trees wood properties were measured on radial slices sampled at a height of 1.4 m above the ground. Relative to wide spacing, close initial stand spacing significantly reduced microfibril angle ({MFA)} and ring width and significantly increased dynamic modulus of elasticity ({MOE)}, fibre length, latewood percentage and cell wall thickness. Density and fibre width were not significantly different between spacing treatments. Examination of the influence of genetic population on wood properties indicated that genotype significantly influenced {MFA}, {MOE} and ring width. The key wood properties {MFA}, {MOE} and fibre length were regressed against tree diameter, height and stem slenderness. All three wood properties were most strongly correlated with stem slenderness. Multiple regression models developed for {MFA}, {MOE} and ring width accounted for respectively 62\%, 81\% and 58\% of the variation in these variables. The following changes occurred in sampled properties with increasing ring number: {MFA} and ring width declined markedly; {MOE} and fibre length increased markedly; latewood percentage and cell wall thickness increased slightly; and density and fibre width did not show any radial trend.},  number = {9},  urldate = {2013-11-12},  journal = {Forest Ecology and Management},  author = {Lasserre, Jean-Pierre and Mason, Euan G. and Watt, Michael S. and Moore, John R.},  month = oct,  year = {2009},  keywords = {Density, Fibre length, Radiata pine, Stand density, Stem slenderness, Stiffness, Taper},  pages = {1924--1931}  }  @article{fourcaud_numerical_2003,  title = {Numerical modelling of shape regulation and growth stresses in trees},  volume = {17},  issn = {0931-1890, 1432-2285},  url = {http://link.springer.com.ezproxy.canterbury.ac.nz/article/10.1007/s00468-002-0203-5},  doi = {10.1007/s00468-002-0203-5},  abstract = {The main objective of this paper is to present the results of a study of the interactions between the growth and design of a tree with regards to biomechanical factors at the plant level. A numerical incremental model dedicated to the calculation of tree mechanical behaviour has been integrated in the plant architecture simulation software {AMAPpara.} At any stage of tree growth, a new equilibrium was calculated considering the weight increment applied on the structure, i.e. the mass of new wood layers and vegetative elements, as well as the biomechanical reaction caused by cell maturation strains in both normal and reaction wood. The resulting incremental displacements allowed the tree shape to be modified. The field of growth stresses was calculated within the stem, using a cumulative process taking into consideration the past history of each growth ring. The simulation results of trunk and branch shape, as well as internal stresses, were examined after consideration of different growth strategies. A block of trees was also simulated in order to show the influence of spatial competition on stem curvature and the variability in growth stress.},  language = {en},  number = {1},  urldate = {2013-04-14},  journal = {Trees},  author = {Fourcaud, Thierry and Blaise, Frederic and Lac, Patrick and Castera, Patrick and Reffye, {Philippe de}},  month = jan,  year = {2003},  keywords = {Biomechanics, Growth, Reaction, shape, simulation, stresses, Tree, Wood},  pages = {31--39}  }  @article{jaouen_how_2007,  title = {How to determine sapling buckling risk with only a few measurements},  volume = {94},  url = {http://dx.doi.org/10.3732/ajb.94.10.1583},  doi = {10.3732/ajb.94.10.1583},  number = {10},  journal = {American Journal of Botany},  author = {Jaouen, G. and Almeras, T. and Coutand, C. and Fournier, M.},  month = oct,  year = {2007},  pages = {1583--1593}  }  @book{walker_primary_2006,  address = {Dordrecht},  Edition = {Second},  title = {Primary wood processing. Principles and practice},  isbn = {978-1-4020-4392-5},  shorttitle = {Primary wood processing. Principles and practice},  abstract = {This book is primarily a general text covering the whole sweep of the forest industries. The over-riding emphasis is on a clear, simple interpretation of the underlying science, demonstrating how such principles apply to processing operations. The book considers the broad question what is wood? by looking at the biology, chemistry and physics of wood structure. Wood quality is examined, and explanations are offered on how and why wood quality varies and the implications for processing. Finally, various industrial processes are reviewed and interpreted. All chapters have been written by specialists, but the presentation targets a generalist audience. Written for: Students studying forestry, forest engineering and wood processing, cross-disciplinary postgraduate students whose programmes require such knowledge, managers employed in both forestry and primary processing industries with very diverse skills who start with no appreciation of the growing of trees, the properties of wood and the diversity of processing options},  publisher = {Springer},  author = {Walker, J.},  year = {2006}  }  @article{farruggia_microscopic_2000,  title = {Microscopic tensile tests in the transverse plane of earlywood and latewood parts of spruce},  volume = {34},  issn = {0043-7719, 1432-5225},  url = {http://link.springer.com.ezproxy.canterbury.ac.nz/article/10.1007/s002260000034},  doi = {10.1007/s002260000034},  abstract = {This paper presents a method which makes it possible to measure elastic properties of a small group of tracheids in the transverse plane. The method is based on tensile tests under microscope that are performed with the assistance of an image analysis system. The calculation of the strain field is based on a global comparison of the grey levels between each deformed image and the initial image. All tests were carried out within one annual ring of spruce: • radial and tangential Young's modulus and Poisson's ratio can be measured in earlywood with a good accuracy, • radial Young's modulus and Poisson's ratio of tracheids in latewood can be estimated with good confidence, • two tests of very thin samples allowed the evaluation of the tangential elastic modulus in latewood. The small size of the sample together with the local measurement of the strain field permitted us to perform several measurements along one single annual ring. Consequently, it was possible to reveal a good relationship between the mechanical properties and the local density determined by microdensitometry.},  language = {en},  number = {2},  urldate = {2013-11-13},  journal = {Wood Science and Technology},  author = {Farruggia, F. and Perré, P.},  month = jun,  year = {2000},  pages = {65--82}  }  @book{archer_growth_1986,  address = {Berlin; New York},  series = {Springer series in wood science},  title = {Growth stresses and strains in trees},  lccn = {QK 477.2 .S8 .A672},  publisher = {Springer-Verlag},  author = {Archer, Robert R.},  year = {1986},  keywords = {Effect of stress on, Growth, Plants, Trees, Wood}  }  @book{rao_meshfree_1999,  Edition = {Third},  title = {Meshfree methods: {M}oving beyond the finite element method},  isbn = {{075067072X}},  publisher = {Boston, Mass. Oxford: Butterworth Heinemann},  author = {Rao, S. S.},  year = {1999}  }  @article{gamstedt_mixed_2013,  title = {Mixed numerical-experimental methods in wood micromechanics},  volume = {47},  issn = {0043-7719},  url = {http://dx.doi.org/10.1007/s00226-012-0519-2},  doi = {10.1007/s00226-012-0519-2},  language = {English},  number = {1},  journal = {Wood Science and Technology},  author = {Gamstedt, {E.Kristofer} and Bader, {ThomasK.} and Borst, Karin},  year = {2013},  pages = {183--202}  }  @misc{contributors_gphoto2_2002,  title = {Gphoto2, Version 2.5.1},  notes = {http://www.gphoto.org/},  author = {Contributors, Various},  version = {2.5.1},  year = {2013}  }  @misc{barker_properties_1998,  title = {The properties of in-grade \textit{Pinus radiata} timber from peeler cores},  shorttitle = {The properties of in-grade \textit{Pinus radiata} timber from peeler cores},  author = {Barker, John},  year = {1998},  school{a dissertation submitted in partial fulfillment of a Bachelor of Forestry Science degree, at the University of Canterbury},  keywords = {Acoustic emission testing, Grading, Pinus radiata, Stress waves, Testing, Wood poles}  }  @article{spatz_basic_2000,  title = {Basic biomechanics of self-supporting plants: {W}ind loads and gravitational loads on a Norway spruce tree},  volume = {135},  url = {http://dx.doi.org/10.1016/S0378-1127(00)00296-6},  doi = {10.1016/S0378-1127(00)00296-6},  number = {1-3},  journal = {Forest Ecology and Management},  author = {Spatz, Hanns-Christof and Bruechert, Franka},  month = sep,  year = {2000},  pages = {33--44}  }  @article{dunham_crown_2000,  title = {Crown, stem and wood properties of wind-damaged and undamaged Sitka spruce},  volume = {135},  issn = {0378-1127},  url = {http://www.sciencedirect.com/science/article/pii/S0378112700002991},  doi = {10.1016/S0378-1127(00)00299-1},  abstract = {The study investigated the differences in slenderness ratio of all the snapped, overturned or undamaged trees within a wind-damaged stand of Sitka spruce containing areas of both, wet and dry soils. In addition, crown size, proportion of compression wood and mechanical properties of wood were investigated on 12 sets of trees of similar diameter that had snapped, overturned or remained undamaged from each of two further wind-damaged stands of Sitka spruce. No difference in stem diameter, height or slenderness ratio were found between the damaged and undamaged trees sampled from the dry part of the wind-damaged stand. On the wet part of the site, however, the snapped trees were found to be significantly taller and of greater diameter than the undamaged or overturned trees although slenderness ratios were similar for all trees. The experiment investigating matched sets of trees found that the snapped and overturned trees had significantly smaller crowns than the undamaged trees. Furthermore, the snapped trees had wood in the outer part of the stem that was less stiff, but of bending strength similar to that of similar wood taken from the undamaged and overturned trees. According to the results, high proportions of compression wood may be involved in the occurrence of storm damage. It is suggested that trees containing compression wood should be preferentially removed from the forest during thinning. Since it is not feasible to measure compression wood in standing trees, the presence of leaning stems or asymmetric crowns should be used to identify the trees to be removed. Furthermore, trees with small crowns should also be preferentially removed during thinning.},  number = {1--3},  urldate = {2013-11-20},  journal = {Forest Ecology and Management},  author = {Dunham, Roger A and Cameron, Andrew D},  month = sep,  year = {2000},  keywords = {Crown properties, Picea sitchensis, Stem properties, Wind damage, Wood properties},  pages = {73--81}  }  @article{gardiner_review_2008,  title = {A review of mechanistic modelling of wind damage risk to forests},  volume = {81},  url = {http://dx.doi.org/10.1093/forestry/cpn022},  doi = {10.1093/forestry/cpn022},  number = {3},  journal = {Forestry},  author = {Gardiner, B. and Byrne, K. and Hale, S. and Kamimura, K. and Mitchell, S. J. and Peltola, H. and Ruel, J.-C.},  month = aug,  year = {2008},  pages = {447--463}  }  @article{mishnaevsky_jr._micromechanical_2008,  title = {Micromechanical modelling of mechanical behaviour and strength of wood: State-of-the-art review},  volume = {44},  issn = {0927-0256},  shorttitle = {Micromechanical modelling of mechanical behaviour and strength of wood},  url = {http://www.sciencedirect.com/science/article/pii/S0927025608001882},  doi = {10.1016/j.commatsci.2008.03.043},  abstract = {An overview of the micromechanical theoretical and numerical models of wood is presented. Different methods of analysis of the effects of wood microstructures at different scale levels on the mechanical behaviour, deformation and strength of wood are discussed and compared. Micromechanical models of deformation and strength of wood are divided into three groups: cellular models (applied most often to the mesoscale or cell scale analysis of the wood deformation), continuum micromechanics and homogenization based methods, models which consider wood as a composite and are applied mainly to the analysis of wood at the microscale (cell wall scale) level and multiscale models. Lattice and composite models, which are used to analyze the damage and fracture of wood, are considered in a separate section. The areas of applicability and strong sides of each approach are discussed.},  number = {2},  urldate = {2013-03-19},  journal = {Computational Materials Science},  author = {Mishnaevsky Jr., Leon and Qing, Hai},  month = dec,  year = {2008},  keywords = {Cellular solids, composite, Lattice models, micromechanics, Natural materials, Wood},  pages = {363--370}  }  @article{tsai_general_1971,  title = {General Theory of Strength for Anisotropic Materials},  volume = {5},  journal = {Journal of Composite Materials},  author = {Tsai, Stephen W. and Wu, Edward M.},  year = {1971},  pages = {58--80}  }  @article{mattheck_shear_2006,  title = {Shear effects on failure of hollow trees},  volume = {20},  url = {http://dx.doi.org/10.1007/s00468-005-0044-0},  doi = {10.1007/s00468-005-0044-0},  number = {3},  journal = {Trees},  author = {Mattheck, C. and Bethge, K. and Tesari, I.},  month = may,  year = {2006},  pages = {329--333}  }  @article{d_longitudinal_1969,  title = {The longitudinal Young’s modulus of \textit{Pinus radiata}},  volume = {3},  issn = {1432-5225},  url = {http://dx.doi.org/10.1007/bf00349983},  doi = {10.1007/bf00349983},  number = {1},  journal = {Wood Science and Technology},  author = {D, Cave I.},  year = {1969},  pages = {40--48}  }  @misc{chris_eberl_robert_thompson_daniel_gianola_digital_2006,  title = {Digital Image Correlation and Tracking with Matlab},  url = {http://www.mathworks.com/matlabcentral/fileexchange/12413-digital-image-correlation-and-tracking},  author = {Chris Eberl, Robert Thompson, Daniel Gianola, Sven Bundschuh},  year = {2006--}  }  @article{holmberg_nonlinear_1999,  title = {Nonlinear mechanical behaviour and analysis of wood and fibre materials},  volume = {72},  issn = {0045-7949},  url = {http://www.sciencedirect.com/science/article/pii/S0045794998003319},  doi = {10.1016/S0045-7949(98)00331-9},  abstract = {The mechanical behaviour of wood was studied from a micro up to a macro level. Wood is a cellular material possessing a high degree of anisotropy. Like other cellular solids, it often exhibits a highly nonlinear stress-strain behaviour. In the present study the mechanical properties of the cellular structure of wood are characterized and modelled, the irregular cell shape, the anisotropic layered structure of the cell walls and the periodic variations in density being taken into account. The continuum properties were derived by use of a homogenization procedure and the finite element method. Stiffness and shrinkage properties determined by this procedure are presented and are compared with measured data. The constitutive properties thus determined at various structural levels can be used in numerical simulations of the behaviour of wood in different industrially related areas. One such area is that of the refining process in mechanical pulp manufacture. Simulations of the deformation and fracturing of wood specimens loaded under conditions similar to those found in the refining process are presented. The numerical and experimental results obtained are compared.},  number = {4-5},  urldate = {2013-03-19},  journal = {Computers \& Structures},  author = {Holmberg, Stefan and Persson, Kent and Petersson, Hans},  month = aug,  year = {1999},  keywords = {Cellular materials, Constitutive models, Defibration, finite element method, Homogenization, Mechanical behaviour, microstructure, Wood},  pages = {459--480}  }  @book{walker_primary_1993,  address = {Dordrecht},  Edition = {First},  title = {Primary wood processing. Principles and practice},  isbn = {978-1-4020-4392-5},  shorttitle = {Primary wood processing. Principles and practice},  abstract = {This book is primarily a general text covering the whole sweep of the forest industries. The over-riding emphasis is on a clear, simple interpretation of the underlying science, demonstrating how such principles apply to processing operations. The book considers the broad question what is wood? by looking at the biology, chemistry and physics of wood structure. Wood quality is examined, and explanations are offered on how and why wood quality varies and the implications for processing. Finally, various industrial processes are reviewed and interpreted. All chapters have been written by specialists, but the presentation targets a generalist audience. Written for: Students studying forestry, forest engineering and wood processing, cross-disciplinary postgraduate students whose programmes require such knowledge, managers employed in both forestry and primary processing industries with very diverse skills who start with no appreciation of the growing of trees, the properties of wood and the diversity of processing options},  publisher = {Springer},  author = {Walker, J.},  year = {1993}  }  @article{domec_age-_2002,  title = {Age- and position-related changes in hydraulic versus mechanical dysfunction of xylem: inferring the design criteria for Douglas-fir wood structure},  volume = {22},  issn = {0829-{318X}},  shorttitle = {Age- and position-related changes in hydraulic versus mechanical dysfunction of xylem},  abstract = {We do not know why trees exhibit changes in wood characteristics as a function of cambial age. In part, the answer may lie in the existence of a tradeoff between hydraulic properties and mechanical support. In conifers, longitudinal tracheids represent 92\% of the cells comprising the wood and are involved in both water transport and mechanical support. We used three hydraulic parameters to estimate hydraulic safety factors at several vertical and radial locations in the trunk and branches: vulnerability to cavitation; variation in xylem water potential (psi); and xylem relative water content. The hydraulic safety factors for 12 and 88 percent loss of conductivity (S(H12) and S(H88), representing the hydraulic safety factors for the air entry point and full embolism point, respectively) were determined. We also estimated the mechanical safety factor for maximum tree height and for buckling. We estimated the dimensionless hydraulic and mechanical safety factors for six seedlings (4 years old), six saplings (10 years old) and six mature trees ({\textbackslash}textbackslashtextgreater 110 years old) of Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco). Over the natural range of psi, S(H12) decreased linearly from treetop to a minimum of 0.95 at the tree base. Young and mature trees had S(H12) values 1.4 and 1.3 times higher, respectively, at their tips (juvenile wood) than at their bases (mature wood). Modeling analyses indicated that if trees were made entirely of mature wood, S(H12) at the stem base would be only 0.7. The mechanical safety factor was 1.2 times higher for the base of the tree than for the rest of the tree. The minimum mechanical safety factor-1.6 for the critical buckling height and 2.2 for the critical buckling load-occurred at the base of the live crown. Modeling analysis indicated that if trees were made only of mature wood, these values would increase to 1.7 and 2.3, respectively. Hydraulic safety factors had values that were less than half those for mechanical safety factors, suggesting that wood structure in Douglas-fir has evolved primarily as a result of selection for hydraulic safety rather than mechanical safety. The results suggest that forest managers must consider the role of juvenile wood in tree physiology to avoid producing plantations vulnerable to drought.},  number = {2-3},  journal = {Tree physiology},  author = {Domec, J C and Gartner, B L},  month = feb,  year = {2002},  keywords = {Oregon, Plant Leaves, Plant Stems, Pseudotsuga, water, Wood},  pages = {91--104}  }  @article{fourcaud_biomechanics_2011,  title = {Biomechanics of Growing Trees: Mathematical Model, Numerical Resolution and Perspectives},  volume = {1389},  issn = {{0094243X}},  shorttitle = {Biomechanics of Growing Trees},  url = {http://proceedings.aip.org/resource/2/apcpcs/1389/1/734_1?isAuthorized=no},  doi = {doi:10.1063/1.3636836},  abstract = {The growth of trees is characterized by the elongation and thickening of its axes. New cells are formed at the periphery of the existing body, the properties of the older inner material being unchanged. The calculation of the progressive deflection of a growing stem is not a classical problem in mechanics for three main reasons: 1‐ the hypothesis of mass conservation is not valid; 2‐ the new material added at the periphery of the existing and deformed structure does not participate retroactively to the total equilibrium and tends to “fix” the actual shape; 3‐ an initial reference configuration corresponding to the unloaded structure cannot be classically defined to formulate the equilibrium equations. This paper proposes a theoretical framework that allows bypassing these difficulties. Equations adapted from the beam theory and considering the strong dependencies between space and time are given. A numerical scheme based on the finite element method is proposed to solve these equations. The model opens new research perspectives both in mathematics and plant biology.},  number = {1},  urldate = {2013-03-19},  journal = {{AIP} Conference Proceedings},  author = {Fourcaud, Thierry and Guillon, Thomas and Dumont, Yves},  month = sep,  year = {2011},  pages = {734--737}  }  @book{butterfield_three-dimensional_1980,  address = {London},  Edition = {Second},  title = {Three-dimensional structure of wood},  isbn = {0412163209},  shorttitle = {Three-dimensional structure of wood},  publisher = {Chapman and Hall},  author = {Butterfield, B. and Meylan, B. A.},  year = {1980}  }  @book{mattheck_trees:_1991,  address = {Berlin},  title = {Trees: the mechanical design},  isbn = {3540542760},  shorttitle = {Trees: the mechanical design},  publisher = {Springer Verlag},  author = {Mattheck, C.},  year = {1991}  }  @article{gillis_elastic_1979,  title = {An elastic plastic theory of longitudinal growth stresses},  volume = {13},  url = {http://dx.doi.org/10.1007/BF00368603},  doi = {10.1007/BF00368603},  number = {2},  journal = {Wood Science and Technology},  author = {Gillis, P. P. and Hsu, C. H.},  year = {1979},  pages = {97--115}  }  @article{yeh_elasto-plastic_1992,  title = {Elasto-Plastic Fracture Mechanics of Wood using the J-Intergral Method},  volume = {24},  number = {3},  journal = {Wood and Fiber Science},  author = {Yeh, B. and Schniewind, A.},  year = {1992},  pages = {364--376}  }  @article{archer_distribution_1974,  title = {On the distribution of tree growth stresses. {P}art {I}: An anisotropic plane strain theory},  volume = {8},  issn = {0043-7719, 1432-5225},  shorttitle = {On the distribution of tree growth stresses},  url = {http://link.springer.com.ezproxy.canterbury.ac.nz/content/pdf/10.1007%2FBF00352022},  doi = {10.1007/BF00352022},  number = {3},  urldate = {2013-04-15},  journal = {Wood Science and Technology},  author = {Archer, R. and Byrnes, F. E.},  year = {1974},  pages = {184--196}  }  @article{tsai_general_1971-1,  title = {A General Theory of Strength for Anisotropic Materials},  volume = {5},  url = {http://dx.doi.org/10.1177/002199837100500106},  doi = {10.1177/002199837100500106},  number = {1},  journal = {Journal of Composite Materials},  author = {Tsai, S. W. and Wu, E. M.},  month = jan,  year = {1971},  pages = {58--80}  }  @article{peltola_mechanical_2006,  title = {Mechanical stability of trees under static loads},  volume = {93},  url = {http://dx.doi.org/10.3732/ajb.93.10.1501},  doi = {10.3732/ajb.93.10.1501},  number = {10},  journal = {American Journal of Botany},  author = {Peltola, H. M.},  month = oct,  year = {2006},  pages = {1501--1511}  }  @book{campbell_n._a.and_reece_biology_2005,  address = {San Francisco, Boston, New York},  Edition = {International 7th Edition},  title = {Biology},  publisher = {Pearson Education},  author = {Campbell, N. A.and Reece, J. B.},  year = {2005}  }  @phdthesis{persson_micromechanical_2000,  address = {Lund, Sweeden},  type = {Structural Mechanics},  title = {Micromechanical Modelling of Wood and Fibre Properties},  school = {Lund University},  author = {Persson, Kent},  year = {2000}  }  @article{henrik_three_2013,  title = {A three dimensional plasticity model for perpendicular to grain cohesive fracture in wood},  volume = {98},  issn = {0013-7944},  url = {http://dx.doi.org/10.1016/j.engfracmech.2012.12.008},  doi = {10.1016/j.engfracmech.2012.12.008},  journal = {Engineering Fracture Mechanics},  author = {Henrik, Danielsson and Gustafsson, Per Johan},  month = jan,  year = {2013},  pages = {137--152}  }  @book{barkas_swelling_1949,  title = {The swelling of wood under stress: a discussion of its hygroscopic, elastic and plastic properties, based on a course of lectures given at Svenska traforskningsinstitutet, Stockholm, Sweden, March 1948},  shorttitle = {The swelling of wood under stress},  language = {en},  publisher = {H. M. Stationery Off.},  author = {Barkas, Wilfred W.},  year = {1949},  keywords = {Wood}  }  @book{aus/nzs_characterization_2010,  title = {Characterization of structural timber - Test methods, {AS/NZS} 4063.1:2010},  url = {http://shop.standards.co.nz/catalog/4063.1%3A2010%28AS|NZS%29/view},  publisher = {Standards New Zealand},  author = {{AUS/NZS}},  month = jul,  year = {2010}  }  @phdthesis{riyanto_comparative_1996,  address = {Oregon, United States of America},  title = {Comparative Test Methods for Evaluating Shear Strength of Structural Lumber},  school = {Oregon State Univeristy},  author = {Riyanto, Djoko Sukrisno},  year = {1996}  }  @article{tabarsa_stress-strain_2000,  title = {Stress-Strain Response of Wood Under Radial Compression. {P}art {I}: Test Method and Influences of Cellular Properties},  volume = {32},  url = {http://swst.metapress.com/content/A216474577485QQ6},  abstract = {A new test system was developed for real-time microscopic observation of wood cell-wall deformation and stress-strain relationship under transverse compression. The system consists of a small compression device, a stereo-microscope, a video microscaler, a videocassette recorder and a computer-based data logger. The significance of this system is that it allows the influence of cellular structure of wood on its stress-strain behavior and the cell-wall collapse mechanism to be studied. This test system was used in a research program aimed at generating some basic understanding of microstructural behavior of wood under transverse compression. Tests were conducted on white spruce specimens to evaluate the proposed test procedure and system, and the influences of some microscopic and macroscopic features such as wood density, cell-wall thickness, and earlywood/latewood ratio. End-matched specimens were tested using the test system at three levels of magnification. Gross and individual ring behaviors were observed and measured by testing at a low magnification ({12X).} Earlywood and latewood behaviors were measured separately using a medium level of magnification ({32X).} Finally the mechanism of cell-wall collapse was observed using the highest magnification ({160X).} Test results show that earlywood and latewood have varying degrees of influence on the various segments of the gross stress-strain curve in radial compression. First collapse of cellular structure occurs at a location with minimum cell-wall thickness and density. Initiation of cell-wall collapse and its gradual progression are clearly visible using the apparatus, thereby verifying the capability of the proposed method.},  number = {2},  urldate = {2013-11-13},  journal = {Wood and Fiber Science},  author = {Tabarsa, Taghi and Chui, Ying},  month = apr,  year = {2000},  pages = {144--152}  }  @article{hofstetter_hierarchical_2008,  title = {Hierarchical modelling of microstructural effects on mechanical properties of wood. A review},  volume = {63},  url = {http://eprints.gla.ac.uk/62740/},  abstract = {Wood exhibits a hierarchical architecture. Its macroscopic properties are determined by microstructural features at different scales of observation. Recent developments of experimental micro-characterisation techniques have delivered further insight into the appearance and the behaviour of wood at smaller length scales. The improved knowledge and the availability of increasingly powerful micromechanical modelling techniques and homogenisation methods have stimulated rather comprehensive research on multiscale modelling of wood. Linking microstructural properties to macroscopic characteristics is expected to improve the knowledge of the mechanical behaviour of wood and to serve as the basis for the development of innovative wood-based products and for biomimetic material design. Moreover, understanding fundamental aspects of wood machining requires multiscale approaches which can take into account the heterogeneity, anisotropy and hierarchies of wood and wood composites. In this review, recent developments in the field of hierarchical modelling of the hygroelastic behaviour of wood are discussed, and a short outline of the theoretical background is given. Much focus is placed on composite micromechanical models for the wood cell wall and on multiscale models for wood resting upon hierarchical finite element models and on the application of continuum micromechanics, respectively. These models generally lead to the specification of equivalent homogeneous continua with effective material properties. Finally, current deficiencies and limitations of hierarchical models are sketched and possible future research directions are specified.},  number = {2},  journal = {Holzforschung},  author = {Hofstetter, K. and Gamstedt, E. K.},  month = dec,  year = {2008},  pages = {130--138}  }  @article{niklas_wind-induced_2000,  title = {Wind-induced stresses in cherry trees: {E}vidence against the hypothesis of constant stress levels},  volume = {14},  issn = {0931-1890, 1432-2285},  shorttitle = {Wind-induced stresses in cherry trees},  url = {http://link.springer.com/article/10.1007/s004680050008},  doi = {10.1007/s004680050008},  abstract = {We calculated the wind-induced bending moments and stresses generated in the stems of five Prunus serotina conspecifics differing in height and canopy shape and size (based on detailed measurements of stem projected area and location with respect to ground level) to test the hypothesis that wind-loads generate uniform and constant stress levels along the lengths of tree twigs, branches, and trunks. These calculations were performed using five different wind speed profiles to evaluate the relative importance of the shape of wind speed profiles versus the ’geometry’ of tree shape on stem stress distributions and magnitudes. Additionally, we evaluated the effect of absolute tree size and stem taper on wind- induced stresses by scaling the size of smaller conspecifics to the absolute height of the largest of the five trees yet retaining the original stem proportions (i.e., diameter relative to stem length) for each plant. Finally, we also determined how the factor of safety for wind-loading (i.e., the quotient of stem yield stress and wind-load stress) changed as a function of tree size (and, presumably, age). Our results indicate that wind-load stress levels (1) vary along stem length even for the same wind speed profile and the same maximum wind speed; (2) would increase to dangerous levels with increasing tree height if it were not for ontogenetic changes in stem taper and canopy shape that reduce stress intensities to manageable levels; (3) tend to be more dependent on stem taper and canopy shape and size than on the shape of the wind speed profile; and (4) the factor of safety against wind-induced mechanical failure decreases as trees get larger, but varies along the length of large trees such that preferential stem failure is likely and functionally adaptive. We thus (1) reject the hypothesis of constant wind-induced stress levels; (2) support the view that size-dependent changes in stem taper are required to maintain wind-load mechanical reliability; and (3) suggest that certain portions of mature trees are ’designed’ to fail under high winds speeds, thereby reducing drag and the bending moments and stresses experienced by trunks.},  language = {en},  number = {4},  urldate = {2013-03-19},  journal = {Trees},  author = {Niklas, K. J. and Spatz, H.-C.},  month = feb,  year = {2000},  keywords = {Constant stress, Drag forces, Key words Biomechanics, Prunus serotina, Stem taper},  pages = {230--237}  }  @article{kenneth_general_2001,  title = {A {GENERAL} {THEORY} {FOR} {THE} {ORIGIN} {OF} {GROWTH} {STRESSES} {IN} {REACTION} {WOOD:} {HOW} {TREES} {STAY} {UPRIGHT}},  volume = {22},  url = {http://dx.doi.org/10.1163/22941932-90000279},  doi = {10.1163/22941932-90000279},  number = {3},  journal = {{IAWA} Journal},  author = {Kenneth, Bamber Richard},  month = jan,  year = {2001},  pages = {205--212}  }  @article{hanhijarvi_computational_2003,  title = {Computational Analysis of Quality Reduction during Drying of Lumber due to Irrecoverable Deformation. {I:} Orthotropic Viscoelastic-Mechanosorptive-Plastic Material Model for the Transverse Plane of Wood},  volume = {129},  issn = {0733-9399},  shorttitle = {Computational Analysis of Quality Reduction during Drying of Lumber due to Irrecoverable Deformation. I},  url = {http://ascelibrary.org/doi/abs/10.1061/%28ASCE%290733-9399%282003%29129%3A9%28996%29},  doi = {10.1061/(ASCE)0733-9399(2003)129:9(996)},  abstract = {This paper presents the development of an orthotropic material model for the mechanical analysis of wood in the plane perpendicular to the growth direction. It is based on an earlier uniaxial development and experimental verification. The novel features are the biaxial extension and the description of partially irrecoverable creep deformation by enhancing a viscoelastic-mechanosorptive creep model by coupling it with orthotropic plasticity. The mathematical description of both the equations of state and the evolution laws are formulated on a thermodynamical basis. A semianalytical solution algorithm is derived for the obtained nonlinear system of differential equations. The model is applicable over a wide range of temperature as well as moisture content ({20–120°C;} nearly 0\% moisture content to fiber saturation), which is achieved through application of the time-temperature-moisture superposition principle and the introduction of a moisture-change-temperature superposition principle. A set of material parameters suitable for this range of conditions is given for Pinus silvestris.},  number = {9},  urldate = {2013-11-19},  journal = {Journal of Engineering Mechanics},  author = {Hanhijärvi, A. and Mackenzie-Helnwein, P.},  year = {2003},  pages = {996--1005}  }  @article{schniewind_wood_1972,  title = {Wood as a linear orthotropic viscoelastic material},  volume = {6},  url = {http://dx.doi.org/10.1007/BF00351807},  doi = {10.1007/BF00351807},  number = {1},  journal = {Wood Science and Technology},  author = {Schniewind, A. P. and Barrett, J. D.},  year = {1972},  pages = {43--57}  }  @article{reiterer_experimental_1999,  title = {Experimental evidence for a mechanical function of the cellulose microfibril angle in wood cell walls},  volume = {79},  shorttitle = {Experimental evidence for a mechanical function of the cellulose microfibril angle in wood cell walls},  url = {://000082665100008},  abstract = {Wood is a natural fibre composite with a hierarchical cellular structure of a specific strength and a specific modulus of elasticity that can be compared with those of other common construction materials. Each wood cell is typically built of cellulose fibrils spiralling around the macroscopic fibre direction. While it is natural to assume a relation between the microfibril angle ({MFA)} and the mechanical properties, a good correlation has up to now only been established for single fibres, where a larger extensibility was found for fibres with larger {MFA.} In the present paper, we show for the first time that this relation even exists for thin (200 mu m) sections of wood: which provides strong evidence for the fact that the {MFA} optimizes the extensibility of wood. In a combination of tensile tests with structural investigations by small angle X- ray scattering on the same sample of Picea abies, we found a remarkable increase in maximum strain with increasing {MFA}, and also a change in the elastic moduli.},  journal = {Philosophical Magazine a-Physics of Condensed Matter Structure Defects and Mechanical Properties},  author = {Reiterer, A. and Lichtenegger, H. and Tschegg, S. and Fratzl, P.},  month = sep,  year = {1999},  keywords = {fibrils, picea-abies, x-ray-scattering},  pages = {2173--2184}  }  @article{morgan_structural_1987,  title = {Structural analysis of tree trunks and branches: tapered cantilever beams subject to large deflections under complex loading},  volume = {3},  url = {http://dx.doi.org/10.1093/treephys/3.4.365},  doi = {10.1093/treephys/3.4.365},  number = {4},  journal = {Tree Physiology},  author = {Morgan, J. and Cannell, M. G. R.},  month = dec,  year = {1987},  pages = {365--374}  }  @article{james_dynamic_2003,  title = {Dynamic loading of trees},  volume = {29},  issn = {1935-5297},  number = {3},  journal = {Arboriculture and urban forestry},  author = {James, K.},  year = {2003},  pages = {165--171}  }  @book{skaar_springer_1988,  title = {Wood-Water Relations},  series = {Springer Series in Wood Science},  url = {http://dx.doi.org/10.1007/978-3-642-73683-4},  publisher = {Springer-Verlag},  author = {Skaar, Christen},  editor = {Timell, T. {E.Editor}},  year = {1988}  }  @article{yamamoto_generation_1998,  title = {Generation mechanism of growth stresses in wood cell walls: {R}oles of lignin deposition and cellulose microfibril during cell wall maturation},  volume = {32},  issn = {0043-7719, 1432-5225},  shorttitle = {Generation mechanism of growth stresses in wood cell walls},  url = {http://link.springer.com.ezproxy.canterbury.ac.nz/article/10.1007/BF00704840},  doi = {10.1007/BF00704840},  abstract = {To explain the generation mechanism of tree growth stresses in relation to time and location inhomogeneity in the secondary wall lignification, we made a theoretical discussion by using an analytical model. In this analysis, time dependence, which has not been explicitly considered in a conventional model, was introduced. This made us possible to simulate the generation process of the growth stresses as a time dependent phenomenon attendant upon the secondary wall maturation. Analysis well explained the experimental results quantitatively on the assumption that a tensile stress originates in the cellulose microfibril as a bundle and a compressive stress are generated in the matrix skeleton during the secondary wall lignification. This verifies the propriety of “the unified hypothesis” proposed by Okuyama et al. quantitatively.},  language = {en},  number = {3},  urldate = {2013-04-29},  journal = {Wood Science and Technology},  author = {Yamamoto, H.},  month = jun,  year = {1998},  keywords = {Agriculture, Ceramics, Characterization and Evaluation Materials, Composites, Forestry, Glass, Natural Methods, Wood Science \& Technology},  pages = {171--182}  }  @article{astley_modelling_1998,  title = {Modelling the elastic properties of softwood},  volume = {56},  url = {http://dx.doi.org/10.1007/s001070050262},  doi = {10.1007/s001070050262},  number = {1},  journal = {Holz als Roh- und Werkstoff},  author = {Astley, R. J. and Stol, K. A. and Harrington, J. J.},  month = jan,  year = {1998},  pages = {43--50}  }  @article{mattheck_engineering_1990,  title = {Engineering Components grow like trees},  volume = {21},  url = {http://dx.doi.org/10.1002/mawe.19900210403},  doi = {10.1002/mawe.19900210403},  number = {4},  journal = {Materialwissenschaft und Werkstofftechnik},  author = {Mattheck, C.},  month = apr,  year = {1990},  pages = {143--168}  }  @book{austin_situation_2012,  title = {Situation and outlook for primary industries 2012},  publisher = {M. f. P. Industries. Wellington, Ministry for Primary Industries},  author = {Austin, Forbes},  year = {2012}  }  @article{larson_changes_1966,  title = {Changes in the chemical composition of wood cell walls associated with age in Pinus resinosa},  volume = {16},  language = {English},  journal = {Forest Products Journal},  author = {Larson, {PR}},  year = {1966},  pages = {37--45}  }  @book{coutts_wind_1995,  address = {Cambridge; New York},  title = {Wind and trees},  isbn = {0521460379},  lccn = {SD390.7.W56 W55 1995},  publisher = {Cambridge University Press},  author = {Coutts, M. P. and Grace, J.},  year = {1995},  keywords = {Effect of wind on Congresses, Forest ecology, Physiology, Plants, Trees},  annote = {Selected papers from a conference held at Heriot-Watt University, Edinburgh, July 1993}  }  @article{pang_modelling_2000,  title = {Modelling of Stress Development During Drying and Relief During Steaming in \textit{Pinus Radiata} Lumber},  volume = {18},  issn = {0737-3937},  url = {http://www.tandfonline.com/doi/abs/10.1080/07373930008917806},  doi = {10.1080/07373930008917806},  abstract = {{ABSTRACT} A one-dimensional stress model was proposed for drying of radiata pine lumber, which has considered wood moisture shrinkage, instantaneous stress-strain relationships, mechano-sorptive creep, time-induced creep and temperature effects. In addition, wood hardening behaviour in the plastic region and differences between stress increase and decrease have been taken into account. The proposed Stress model can predict stress development and relief in a drying cycle once the required wood mechanical and Theological properties have been quantified. Drying experiments were performed to dry Pinus radiata sap wood boards of 100×40×590 mm in a tunnel dryer. In the experiment, wood temperature, moisture content gradient and residual stress through board thickness were measured. The drying cycle included {HT} drying, cooling and final steam conditioning. The measured stress patterns were in agreement with the model predictions. However, more accurate calculations will be made once the detailed experimental data for radiata pine wood mechanical and rheological properties are available.},  number = {8},  urldate = {2013-11-19},  journal = {Drying Technology},  author = {Pang, S.},  year = {2000},  pages = {1677--1696}  }  @article{waghorn_influence_2007,  title = {Influence of tree morphology genetics, and initial stand density on outerwood modulus of elasticity of 17-year-old \textit{Pinus radiata}},  volume = {244},  issn = {0378-1127},  url = {http://dx.doi.org/10.1016/j.foreco.2007.03.057},  doi = {10.1016/j.foreco.2007.03.057},  number = {1-3},  journal = {Forest Ecology and Management},  author = {Waghorn, Matthew J. and Watt, Michael S. and Mason, Euan G.},  month = jun,  year = {2007},  keywords = {Euler buckling, Initial stand density, Modulus of elasticity, Path analysis, Pinus radiata, Stem slenderness, Stiffness, Taper, Tree breeding},  pages = {86--92}  }  @book{anders_logg_about_2013,  title = {About the {FEniCS} Project - {FEniCS} Project},  url = {http://fenicsproject.org/about/},  urldate = {2013-04-14},  author = {Anders Logg, Kent-Andre Mardal and Wells, Garth N.},  year = {2013}  }  @article{ormarsson_numerical_2010,  title = {Numerical study of how creep and progressive stiffening affect the growth stress formation in trees},  volume = {24},  issn = {0931-1890, 1432-2285},  url = {http://link.springer.com.ezproxy.canterbury.ac.nz/article/10.1007/s00468-009-0383-3},  doi = {10.1007/s00468-009-0383-3},  abstract = {It is not fully understood how much growth stresses affect the final quality of solid timber products in terms of, e.g. shape stability. It is, for example, difficult to predict the internal growth stress field within the tree stem. Growth stresses are progressively generated during the tree growth and they are highly influenced by climate, biologic and material-related factors. To increase the knowledge of the stress formation, a finite element model was created to study how the growth stresses develop during the tree growth. The model is an axisymmetric general plane strain model where material for all new annual rings is progressively added to the tree during the analysis. The material model used is based on the theory of small strains (where strains refer to the undeformed configuration which is good approximation for strains less than 4\%) where so-called biological maturation strains (growth-related strains that form in the wood fibres during their maturation) are used as a driver for the stress generation. It is formulated as an incremental material model that takes into account elastic strain, maturation strain, viscoelastic strain and progressive stiffening of the wood material. The results clearly show how the growth stresses are progressively generated during the tree growth. The inner core becomes more and more compressed, whereas the outer sapwood is subjected to slightly increased tension. The parametric study shows that the growth stresses are highly influenced by the creep behaviour and evolution of parameters such as modulus of elasticity, micro-fibril angle and maturation strain.},  language = {en},  number = {1},  urldate = {2013-04-14},  journal = {Trees},  author = {Ormarsson, Sigurdur and Dahlblom, Ola and Johansson, Marie},  month = feb,  year = {2010},  keywords = {Agriculture, Creep, Distortions, Finite element simulations, Forestry, Growth stresses, Plant {Anatomy/Development}, Plant Pathology, Plant Physiology, Plant Sciences, Trees, Wood},  pages = {105--115}  }  @article{gerhards_effect_1982-1,  title = {Effect of Mooisture Content and Temperature on teh Mechanical Properties of Wood: An Analysis of Immediate Effects},  volume = {18},  number = {1},  journal = {Wood and Fiber},  author = {Gerhards, C. C.},  year = {1982},  pages = {4--36}  }  @article{chaffey_why_2002,  title = {Why is there so little research into the cell biology of the secondary vascular system of trees?},  volume = {153},  shorttitle = {Why is there so little research into the cell biology of the secondary vascular system of trees?},  url = {://000173715400004},  abstract = {Despite new techniques for studying the cell biology of plant development in recent years, the secondary vascular system has been neglected. Why is this? Here it is argued that some of the barriers that have prevented more widespread study of the tree secondary vascular system are no longer valid. Some of the more intriguing aspects of the secondary vascular system include the recent discovery of a putative plant muscle and identification of a cytoskeleton-facilitated three-dimensional symplasmic transport pathway that permeates the tree. There are great merits in the recently adopted model tree species, poplar, and a new model system - wood formation in Arabidopsis. The time is now right for much greater exploitation of the possibilities that exist for study of the secondary vascular system of trees.},  journal = {New Phytologist},  author = {Chaffey, N.},  month = feb,  year = {2002},  note = {2},  pages = {213--223}  }