Modelling anisotropic maturation strains in wood in relation to fibre boundary conditions, microstructure and maturation kinetics

A generalisation of existing mechanical models is proposed to account for the relation between wood macroscopic properties and fibre microstructure and chemical composition. It is applied to understanding of the origin of anisotropic maturation strains measured at the outermost surface of the xylem. Various assumptions are considered for boundary conditions of the fibre during the progressive maturation process and are applied to experimental data from the literature. Assumptions that the fibre is fully restrained in displacement, or fully unrestrained or unrestrained in the transverse direction only are all incompatible with observations. Indeed, within the tree, the fibre is restrained in the longitudinal and tangential directions, but unrestrained in the radial direction towards the bark. Mixed boundary conditions must be introduced to correctly simulate both longitudinal and tangential maturation strains. In the context of an analytical axisymmetric model, this is estimated by considering a parameter of partial release of tangential stress during maturation. Consistence with data and with finite element computation in the case of a square fibre confirmed that, because of the unrestrained radial condition, a large part of the tangential maturation stress is released in situ.