Paper

An aggregate (mosaic) model is proposed to represent the structure of paper and model the mechanical properties. The model treats paper as an aggregate of three subregions of characteristic materials, viz. bonded regions, unbonded regions (free fiber segments) and voids. A computer simulation based on the Monte Carlo method is performed to generate random and oriented paper sheets and input parameters for the aggregate model. The number of fiber crossings, total bonded area, average free fiber segment length and volume fractions of bonded material and free fiber segments and apparent sheet density are obtained from the statistical geometry description of the paper structure. The upper and lower bounds on the elastic moduli and moisture swelling coefficients of void-free paper are derived based on anisotropic elasticity theory and a fiber orientation distribution parameter. The finite element method is applied to generate effective elastic moduli and moisture swelling coefficients of the aggregate model consisting of fiber crossings and segments, but no voids. The elastic moduli of paper so obtained are corrected for the voids present in paper. The predictions are compared with previously published experimental results, and it is demonstrated that the results generally fall within the theoretical bounds. The mosaic model was shown to approximate the mechanical 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.