Nicholas Davies edited intro.tex  over 7 years ago

Commit id: 1b496743ca6799c5f33e38ffb447e8b54ab20e75

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Over the last century or so there have been a number of suggested explanations for why trees grow with the observed TRP. The mechanical hypothesis which is investigated in this study, asserts that the TRP is a result of the tree needing to respond to different mechanical loadings from its environment as it grows. For a seedling, being highly flexible could be important in order to bend out of the path of animals and reduce wind and snow loads. However when the tree grows and a significant size is reached along with a large canopy greater stiffness could be an advantage in outerwood as bending becomes difficult due to the stem diameter. Note that there are other hypotheses, for a good review see \citet{meinzer_frederick_2011}. The purpose of this paper is to investigate the effect of the TRP of MFA and density on the ability to withstand wind loading.   Structural integrity of both greenwood and corewood have had little attention in literature at the scale of small cellular blocks. Investigating the TRP requires testing at scales small enough to separate corewood and outerwood. Classical mechanics theories have been used, sometimes in conjunction with experimental data from tree pulling and wind tunnel experiments --(Rudnicki et al., 2004; Peltola et al., 1999; Spatz and Bruechert, 2000)--. \citep{rudnicki_wind_2004, peltola_mechanistic_1999, spatz_basic_2000}.  Neither take into account changes in material properties within the stem. ---ref--- being the only known example where all nine orthotropic elastic material constants have been reported for core- and outerwood. Elastic deformation of a material occurs when the magnitude of loads applied to a sample are small enough that when released the sample returns to its original state --(Hibbeler, 2000)--. \citep{Hibbeler_mechanics_2000}.  Here we need to define some particular terminology and assumptions. The proportionality limit is the point at which the relationship between stress and strain stops being linear, although not necessarily elastic. The end of the elastic state is characterised by the yield point (elastic limit), after the yield point plastic (irreversible) deformation occurs, although this deformation does not necessarily result in a loss of stiffness --(Reiterer et al., 1999)--. \citep{reiterer_experimental_1999}.  It was assumed that the proportionality limit and the yield point are equal and the terms yield point, proportionality limit and failure point are used interchangeably to indicate what is strictly the proportionality limit. There is argument for and against the assumption that wood is a linear elastic material in literature --(Mackenzie-Helnwein et al., 2005a)--. \citep{mackenzie-helnwein_rate-independent_2005}.  Within this work models are restricted to the limit of proportionality in order to retain simplicity.