Considering heterogeneity in a cylindrical section of a tree

Published values for the elastic coefficients of wood indicate that this material may be considered orthotropic with respect to the cylindrical coordinates. This indicates that simplifying the elasticity tensor to allow for the non-unique strains at r ¼ 0, is a simplification that may ignore important structural characteristics of a tree. The constitutive equations for a cylindrical section of a tree were posed in cylindrical coordinates as a linear function of the radial coordinate r. The constitutive equations were transformed to a Cartesian basis so that a solution to Saint-Venant’s Problem, proposed by Iesan (Lecture Notes in Mathematics (1987) 161) could be employed for a cylindrical section of a tree. From Iesan’s solution it was possible to determine that the auxiliary generalized plane strain stresses can only be a function of r, and that the total stresses (in cylindrical coordinates) in the plane of the transverse cross-section must be equal to zero