Orthotropic elastic constants of wood

Wood tracheids are essentially tubular structures but wood cross sections are characterized by large numbers of triple points or junctures of wall segments from three adjacent cells. A symmetric triple point is taken as an approximation to the basic unit of wood structure. This element is analysed as a linearly elastic, isotropic body. It is shown that bending effects enhance the deformations arising from simple strains so that the overall response of the element is anisotropic. The resulting stiffnesses are ordered $$E_L \user2{ > }E_R \user2{ > }G_{LR} \sim G_{LT} \user2{ > }E_T \user2{ > }G_{RT} $$ for what are considered to be fairly typical element geometries. It is shown that for all geometries the longitudinal Youngs modulus is proportional to the volume fraction of cell wall material.