Analysis of the influence of voids on the hygroelastic properties of paper

The influence of voids on the hygroelastic properties of paper has been investigated using analytical and numerical methods. Paper was modeled as a laminate made of cell-wall layers. A continuous fiber orientation distribution was introduced into the laminate model to derive the baseline properties of the papersheet. The voids in the papersheet were modeled as reinforcements with zero elastic properties. The reduction of elastic stiffnesses of isotropic materials containing different shapes and volume fractions of pores were analyzed using Voigt, Reuss, foam and combination models. Hashin's two-phase bounding model and Christensen's three-phase self-consistent models were also used to predict the elastic stiffnesses of isotropic porous materials. The influence of voids on the engineering constants of orthotropic materials was analyzed using 2-D and 3-D finite element models. The invariance of hygroexpansion in the presence of voids was demonstrated using analytical and numerical methods. The theoretical model predictions were correlated with previously published experimental results.