A Microstructurally-based Orthotropic Elasto-plastic Model for Paper and Paperboard

Abstract

This report describes the formulation of a microstructurally-based orthotropic elastic-plastic continuum model for paper and paperboard. The model consists of two constitutive components: an elastic component developed from the finite deformation theory of elasticity, and a plastic component with a modified Tsai-Wu yield criteria and a nonlinear hardening function. Fiber orientation distribution underlying the paper structure is captured using a structural tensor. The model is implemented in a user-defined subroutine (UMAT) of a finite element software ABAQUS. Structural parameters of the model were measured from a selected set of papers using image analysis technique; other parameters were obtained from fitting the simulation results to the corresponding experimental data. Good agreements between the model predictions and the mechanical response of corrugated paperboard created from the selected set of papers confirm model validity.