In the sense of the stiffness matrix, it was assumed that no taper (ie 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 activating 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 that presented by --- gillis and hsu 1979 --- as can be seen in Figure ---- 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 xxxx and xxx. However at every point the value of the surface strain changes, ie the stress field is not axis-symmetric, and is instead governed by Equations xxx to xxx. --- describe how these equations work ---- 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 xxx shows some examples of surface strain values around the circumference of some theoretical samples.