Material properties derived from experiments such as in  \citet{Gon_alves_2013} exist in their native radial coordinate system and hence to be used in a Cartesian coordinate system as was required for some functions of modeling, a transformation between the two was needed. \citet{Davies2014} describes this transformation in Section 3.2.3 using Voigt (engineering) notation to convert the stiffness matrix from radial to Cartesian coordinates at any point in the domain. 
Within the stiffness matrix, it was assumed that no taper (i.e. that longitudinal stiffness exists parallel to the vertical axis regardless of the coordinate system), no spiral grain, knots, grain wobble etc. exist and that there is no change in material properties within the volume (i.e. the pith has the same 9 material constants that the periphery has). Further it was assumed that no external forces such as gravity were acting significantly on the simulated samples, the only forcing was the internal stress field. 
Traditionally the growth stress field is assumed to be axis-symmetric and follow a curve similar to those presented by \cite{Gillis1979,Archer_1987} etc. Here the stress field existing in a longitudinally ordinated plane from the pith to the periphery can be described by in the same way by Equations \ref{eq:Rcore} to \ref{eq:stress_gs}. However at every point the value of the surface strain changes, i.e. the stress field is not axis-symmetric is instead governed by Equation \ref{eq:stress_surface}. Further while the peaks and troughs of the surface strain are 90 degrees apart, their orientation with the splitting test is random and only by chance will peaks/troughs intersect with a cut. This was done as in real world experiments on straight stems it is not known where high or low surface stress is located and hence it can be reasonably assumed that the cut orientation will be randomly aligned with the surface stress pattern. Figure \ref{210238} shows some examples of surface strain values around the circumference of some theoretical samples.