An elliptical pore model for the mechanical properties of paper

Abstract

A simple mechanical model for paper comprising only isotropic cell-wall cellulose and a single elliptical pore is presented. Finite element method analysis applied to this model produced two stress-strain curves equivalent to the anisotropy observed in machine-made paper. Nissan’s hydrogen-bond domination theory for cellwall material with a density of 1000 kg/m3 provided the stress-strain functionality to control the displacement of the mesh nodes. Experimental data were collected from a single roll of paper produced on a pilot machine run where formation was decreased in five steps. Fiber properties, sheet grammage, and density were held constant in the final paper. Regardless of the level of formation, all breaking stress and strain data fell into one of two stress-strain curves, a machine-direction curve and a cross-direction curve. The initial modulus of each stress-strain curve was used to estimate the shape of the elliptical pore used in the finite element method model. The results for the model matched the results from the experimental data.