Two stem and crown profiles were investigated. An open grown stem, assumed to have no light competition, at a stocking rate of one stem per hectare and a stem under competition at a stocking rate of 741 stems per hectare. Stems grown in the open tend to produce a lower taper and a wider crown which protrudes further to the base of the stem. The open grown stem and crown dimensions are extrapolated from measurements reported by \citet{waghorn_influence_2007}. These dimensions represent architecture for a stem grown at a stocking rate of 741 stems per hectare. The stocking rate of 741 stems per hectare was chosen as it is the stocking rate used to estimate crown density by \citet{Beets_1996}.

In order to ensure that the values being presented were realistic Equations \ref{eq:Mc} and \ref{eq:DMc} from \citet{papesch_mechanical_1997} were solved with \(h=15\) resulting in a maximum bending moment of \(42MP_{a}\) at a deflection of \(13\) degrees. Solving Equations \ref{eq:DC} through \ref{eq:T1} with wind speed \(\omega\) as the unknown, the wind speed at maximum bending moment (\(42MP_{a}\)) was calculated to be \(15.5m/s\). From these equations and the assumption that the maximum bending moment will occur at the lowest wind speed needed to surpass the proportional limit it is seen that at a stocking rate of 741 stems per hectare the FEM model predicts the stem with the radial profile \(LW\rightarrow HS\) will fail at approximately \(16m/s\), however the deflection angle is approximately \(21\) degrees at this point. The radial profiles at a stocking rate of \(741\) stems per hectare fall on either side of the \(13\) degree deflection at \(15.5m/s\) wind speed from Papesch et al. (1997). Open grown stems withstand higher wind speeds, however they break at lower deflection angles than stems at a stocking of \(741\). Open grown stems also fail at higher and lower wind speeds and deflections than the predictions from \citet{papesch_mechanical_1997}, with the radial profiles performing in a similar order as for the higher stocking rate. If growth stresses are not considered a reduction in the wind speeds to below the predicted value of \(15.5m/s\) is observed, for both stocking rates. The deflection angle at first failure is also reduced with radial profile \(LW\rightarrow HS\) to approximately \(14\) degrees (from \(21\) degrees). Radial profiles fall on either side of the prediction of \(13\) degrees from Papesch et al. (1997).

The stress profiles within the stems are fairly consistent regardless of the TRP used. All profiles show compression in the longitudinal direction and slight stresses in the other directions, when growth stresses are not considered. As the wind load increases, tension stresses start to become visible in the longitudinal direction on the windward side of the stem, along with compressive stresses on the leeward side. The largest of these appearing in the bottom third of the stem, with little appearing at the top. The longitudinal-tangential and longitudinal-radial shear planes also develop significant stresses, with the maximum magnitude usually occurring at similar heights in the stem as longitudinal stresses, as can be seen in Figure \ref{figure:lsLWHS}. Stress distributions within the stem don’t indicate points of failure because of the relationship between material directions, the change in strength with material direction and the change in strength of the material as the TRP evolves. To visualise when and where failure occurs Equations \ref{eq:SFten} and \ref{eq:SFcomp} were solved at each point in order to give a safety factor, with a value of less than one being before the point of failure and greater than one being after failure. Figure \ref{figure:sflLWHS} indicates that once a point breaks proportionality in one direction the same is likely to occur in other directions soon after. Typically failure occurs on the leeward side of the stem in the bottom half in multiple directions at a similar time. A horizontal slice is also taken through the stem at a height of \(3m\). The longitudinal stresses again dominate, being in compression from self weight at zero wind, as the wind increases the progression of tensile stresses from the windward side is visible moving from the outer edge of the stem toward the centre. The increase in compression at the leeward side of the stem is also visible following the same trend. Shear and normal stresses both increase with increasing wind speed, and the propagation can be seen in Figure \ref{figure:shLWHS}. Failure is also evident in the cross section shown in Figure \ref{figure:sfhLWHS}. Note the longitudinal-tangential and longitudinal-radial shear planes show slightly lower stresses in the centre of the stem than at the periphery the reason for this is unknown. These patterns vary but are typical for all TRPs, ages and stocking rates investigated.

The growth stress implementation described by Equations \ref{eq:rcore} to \ref{eq:stress_gs}, provides similar surfaces strains to that reported for Pinus taeda \citep{timell_compression_1986-3}. However the assumptions around the implementation are untested and caution should be applied when interpreting these results. In particular the growth stress profile is added into the stress vector as a constant state, only implemented in longitudinal direction and not accumulative. Not accumulating the growth stresses through successive growth steps, instead reapplying them at each time step results in stems of all ages having the same growth stress profile (as magnitude only varies by wood properties). It may not be the case that young trees (eg 5 years old) have the same growth stresses as their 15 year old counterparts. The growth stress profile causes some points to break proportionality in the core of the stem, the structural affect is assumed to be negligible, instead the point at which the proportion of failed points starts to increase is taken as the start of structure breakdown. The progression of points passing the proportional limit can be seen in Figures \ref{figure:sflLWHSgs} and \ref{figure:sfhLWHSgs}. Note the tension at the periphery of the stem and compression in the centre caused by the growth stresses. Figures \ref{figure:slLWHSgs} and \ref{figure:shLWHSgs} show how the implementation of growth stresses effects the stress in the different material directions.

Figure \ref{figure:contrasting15} is a plot of two samples, (\(LW\rightarrow HS\) and \(HW\rightarrow LS\)), with and without growth stresses, at a wind speed of \(20m/s\). The plot shows the failure criterion value for each point separated by their height. The two samples were chosen to show contrast between TRPs. Although the samples LW and HS show the largest contrast in material properties, they both exhibit similar strength properties, HW and LS show lower strengths in most directions. In general samples which more closely follow the natural TRP show a more constant variation in the number of failed points with height. The implementation of growth stresses appears to cause the differences between the TRPs to become more accentuated in this respect. TRPs which perform better tend to have more constant failure profiles in the lower half to two thirds of the stem, both with and without growth stresses.

The implementation of growth stresses clusters the average height of first failure when compared to stems without growth stresses, as can be seen in Figure \ref{figure:failure}. In stems with observed radial profiles, the wind speeds at which the first points break proportionality increase substantially more than stems with unnatural profiles when growth stresses are implemented. Younger stems gain the most strength from having growth stresses, although younger trees may produce lower growth stresses than larger older ones, which was not considered, all stems have the same growth stress profiles governed by the martial properties of the wood within the stem.

Including growth stresses causes a marked increase in tensile failure and decrease in compressive failure for the longitudinal direction. The effect is strongest for young trees, and is less pronounced at higher stockings in older stems, although still evident, and shown in Figures \ref{figure:df741} and \ref{figure:df741gs}. Even with the increase in tensile failure, most stems still fail in longitudinal compression and/or various shear planes. In TRPs which perform best longitudinal tensile failure is nearly as common as compressive failure, by contrast in the poorer performing TRPs (with the exception of the low density high stiffness profile) there is a much larger gap.

The environment a tree experiences is largely effected by its surroundings, trees inside forests experience lower wind loads than those grown on open plains. For this reason the two scenarios were considered and it can be seen in Figures \ref{figure:npf741gs} and \ref{figure:npf1gs} that while stocking rate effects at what wind speed stems will fail, the order TRPs failure remains fairly constant. Stems at a stocking of 741 stems per hectare fail significantly earlier than the open grown trees, even though their crowns are smaller. The change in slenderness ratio from 97 to 124 caused a reduction in wind speed at first failure from \(20\) to \(16m/s\) for the TRP \(LW\rightarrow HS\) (at age 15). By comparison, for the open grown stem removing growth stresses causes a reduction from \(20\) to \(15m/s\) and from \(16\) to \(12m/s\) for a stocking of 741. The TRP still has the most influence with a spread of up to \(10m/s\) at 15 years.

Throughout a trees lifetime its structure changes as it grows and adapts to its current environmental setting. The simulation was run for a tree at ages 5, 10 and 15 years old. TRPs which perform well (have a low proportion of failed points at a given wind speed) at one time perform well at all other times. Table \ref{table:trp_ranking} categorises the TRPs into the groups of how well they performed over all time. Note that the top four TRPs consists of every permutation of the HS and LW samples while the bottom six TRPs contains all permutations of LS and HW. When the TRP is split into its stress direction constituents the tendency to fail in longitudinal compression is evident for a number of TRPs, and is often accompanied or closely followed by a number of other directions. For younger stems the spread in deflection is much lower, this could be contributed to the lower radial variation between samples as only the first third of the TRP is used in the five year old stems because of the lower radius.