Coupled viscoelastic-viscoplastic modeling of homogeneous and isotropic polymers: Numerical algorithm and analytical solutions

A coupled viscoelastic-viscoplastic (VE-VP) model is implemented and studied. The total strain is the sum of VE and VP parts, and the Cauchy stress is given by a linear YE model as a Boltzmann integral of the history of VE strains. The proposed computational algorithm features fully implicit integration, return mapping based on a two-step YE predictor/VP corrector strategy, and a consistent tangent operator. The algorithm is applied to J(2) VP coupled with VE. Very compact expressions are obtained which are form-identical to classical elasto-viscoplasticity (EVP) provided that the constant linear elastic shear and bulk moduli are replaced with incremental relaxation moduli which are appropriate functions of the time increment. Two different integration methods to obtain the incremental moduli are proposed and assessed. Closed-form solutions for uniaxial tension and simple shear are developed, based on an original solution method for integro-differential equations. The analytical results enable to illustrate the constitutive model and provide unambiguous benchmarks for numerical algorithms. Model predictions are compared with experimental data and reasonable correlation is obtained. (C) 2011 Elsevier B.V. All rights reserved.