A model for multiphase moisture and heat transport below and above the saturation point of deformable and swelling wood fibers-II: Hygro-mechanical response

Abstract

A non-linear elastic constitutive model for a swelling/shrinking orthotropic wood matrix is proposed. The model is thermodynamically consistent, derived based on the principles of continuum mechanics and the hybrid mixture theory. Moisture induced strains are introduced considering finite deformations by assuming a multiplicative split of the deformation gradient tensor into a swelling and an elastic part. Novel definitions of the Cauchy stress tensor and the moisture-dependent elastic material tangent matrix are obtained. The model is coupled to a multi-phase transient mass and heat transport model developed in Part I of this work. In this part of the work 2-D and 3-D test examples are used to describe the ability of the model to simulate moisture-induced distortions when drying wood within the hygroscopic and also from the over-hygroscopic moisture ranges. Despite deriving the model considering wood, the obtained constitutive relations can be suitably adopted to other orthotropic porous materials displaying properties similar to that of wood.