Where \(tol_{z}\) is the tolerance required to select all points at the boundary between the base of the stem and the ground, and where \(tol\) is the tolerance sufficient to select only the points at the boundary between the base of the stem and the ground for the initial seedling’s radius.

By solving Equation \ref{eq:F_new} for displacement \(\boldsymbol{u}\) subject to the boundary conditions (Equations \ref{eq:BC1} and \ref{eq:BC2}) and internal and external loadings (Equations \ref{eq:Bs}, \ref{eq:Bc1}, \ref{eq:Tw} and \ref{eq:GS}) the displacement field was obtained. Hooks law (Equation \ref{eq:hooks}) was used to find the stress. Solving of the system is achieved through the FEM.

Failure surfaces were created using Tsai and Wu’s failure criterion \citep{tsai_general_1971} and calculated for every point in the stem for all wind speeds. Each point is evaluated for its safety factor, where a factor of one is on the failure surface, with a lower than one factor being before the limit of proportionality and higher than one factor after the limit. The values are the observed stress over the proportional limit stress given the other five stress states. Due to the dependence of each direction of failure on the other directions, all but the variable in question are held constant at their modelled values. Once passed the proportional limit the linear stress strain curves were still assumed, this is not physically accurate. The proportional limit stresses were calculated from the linear interpolation described by Equation \ref{eq:constants}

From the experimental work presented in \citet{Davies_2016} and the relationships presented in Equation \ref{eq:constants} proportional limit surfaces for each point were calculated using \citet{tsai_general_1971}’s criterion. Because the proportional limit surfaces are defined in the local \(rtl\) coordinate system and the stresses provided by the model are in the global \(xyz\) system Equation \ref{eq:stress_tans} was used to convert each stress vector into the local system at its given global location. The failure criterion was applied through Equation \ref{eq:tw_app} and the maximum and minimum stress values which could be obtained without failure calculated for each point assuming all other stresses stay fixed (Equations \ref{eq:tw_opt_max} and \ref{eq:tw_opt_min}). With the maximum tensile and compressive stresses a safety factor was calculated as per Equations \ref{eq:SFten} and \ref{eq:SFcomp}. The stress bounds can be used to investigate how much redundant strength is available at failure by both position in the stem and direction of stress.