Numerical aspects associated with the implementation of a finite strain, elasto‐viscoelastic–viscoplastic constitutive theory in principal stretches

Abstract

Abstract This paper treats the numerical implementation of a finite strain, elasto‐viscoelastic–viscoplastic constitutive model for semi‐crystalline polymers, written in principal stretches. A parallel configuration of the three model elements is used that enables the decoupled algorithmic treatment of each response within a stress update numerical scheme. The numerical aspects associated with the use of principal stretch constitutive expressions in a tensor space numerical environment are initially developed for the general cases of any elastic or inelastic constitutive element. Included is the formulation of the closed‐form, consistent tangential modulus tensor. The principal space algorithmic treatments of the elastic, viscoelastic and viscoplastic elements are then used as specific examples. Of particular importance is the development of a principal space, closest point projection return mapping algorithm for viscoplasticity including isotropic strain hardening. Preliminary numerical examples are presented to illustrate the versatility of the model. Copyright © 2010 John Wiley & Sons, Ltd.