Coupled modeling of moisture and mechanical behavior of wood using thermo-mechanics

Wood is a moisture sensitive material regarding durability (wood rot, mould growth) and also the mechanical behavior is highly influenced by variations in moisture content. Examples are the hygroscopic behavior of wood, the important swelling and shrinkage, especially in radial and tangential directions, and the decrease of stiffness and strength with moisture content. It is also believed that due to the swelling of wood, the moisture capacity of wood increases and that moisture transport properties change. It is found that the moisture sensitivity most importantly is limited to the range below the fiber saturation point, which indicates the saturation of the cell walls. Determining the dynamic stiffness on wood while loaded in compression, showed that the stiffness increases with the stress level (stiffening effect) and thus depends nonlinearly on the stress or strain level. In conclusion, wood exhibits a strong coupling between moisture and mechanical behavior and behaves fundamentally nonlinearly. In this paper, we propose a new material model for wood, based on a thermo-mechanical formulation of the changes in energy when a material is mechanically or hygroscopically loaded. The energy formulation includes the mechanical energy of the solid, the energy due to adsorption of the fluid and the energy due to fluid-solid interactions in the porous material. Traditionally, these energies include second order terms in the basic variables, strain and moisture content. Using the Clausius Duhem equation, incremental constitutive equations and material properties can be obtained by second order differentiation of the energy equation. The material properties include the stiffness, the moisture capacity and a coupling coefficient, and generally depend on strain and moisture content. In second order energy formulations, the nonlinearity of the material properties has to be determined from experiments. In this paper, we present a new higher order formulation of the energy, leading to nonlinear equations for the material properties on strain and moisture content. The advantage of a higher order energy formulation is that the nonlinear dependence of the material properties is inherently taking into account, leading to consistent formulations of the dependence of the material properties on strain and moisture content. However, these formulations lead to material properties in undrained conditions (sealed specimen with no change in moisture content). In reality, material testing on wood is generally executed in drained conditions, meaning equilibrium between vapor pressure of the environment and moisture content of the wood sample. Using a Legendre transformation, the constitutive equations and material properties can be formulated dependent on stress and capillary pressure (or chemical potential). This formulation leads to adequate nonlinear equations for the material properties, which can be determined from experiments. The model is applied to reproduce adequately free swelling due to moisture uptake and strain-stress relations for different moisture contents. The model can also explain the changes in internal stresses of a wood specimen exposed to varying relative humidity conditions.