Poromechanical modeling of moisture induced swelling anisotropy in cellular tissues of softwoods

Abstract

Experimental studies reveal that softwoods exhibit different swelling patterns at the cellular scale depending on the position of the tracheid cells within the growth ring. Thin-walled earlywood cells show anisotropic swelling behavior while the swelling of thick-walled bulky latewood cells is generally isotropic. A poromechanical model is developed to explore the anisotropic swelling behavior of softwoods at the cellular scale. The general description for the macroscopically observable free swelling strain of cellular tissues is derived by upscaling the constitutive equations of a double porosity medium which is found to be dependent on stiffness, Biot coefficient, Biot modulus and the geometry of the cells. The effective poroelastic constants of earlywood and latewood cells are computed from a periodic honeycomb unit cell by means of an efficient finite-element-based computational upscaling scheme. The estimated swelling coefficients compare well with experimental measurements. It is found that the anisotropy in swelling behavior of wood cells can be related to the anisotropy of elastic properties at the cell wall level and the geometry of the cells. The proposed poromechanical model provides a physically relevant description of swelling behavior which originates from the coupled interaction of water and solid phases within the porous cell walls of softwoods.