A Viscoelastic-Elastoplastic Finite Strain Framework for Modeling Polymers

Abstract

In this paper we present a new constitutive framework, the Parallel Rheological Framework (PRF), for modeling polymers that has been recently developed by the authors and implemented in the commercial finite element software Abaqus [1]. The framework is based on parallel finite-strain viscoelastic and elastoplastic networks. For each viscoelastic network a multiplicative split of the deformation gradient into elastic and viscous components is assumed. The evolution of the viscous component of the deformation gradient is governed by a flow rule obtained assuming the existence of a creep potential. The flow rule is expressed as a function of stress invariants and internal variables, and different evolution laws for the internal variables are allowed within the framework of the model. Similar to the viscoelastic networks, the deformation gradient in the elastoplastic network is decomposed into elastic and plastic components. The yield surface is defined assuming combined isotropic/kinematic hardening. The yield surface is a function of a scalar internal variable that describes isotropic hardening, and a tensorial internal variable (backstress) that describes the shift of the yield surface in the stress space. The evolution of the scalar variable is governed by associated flow rule, while the evolution of backstresses is determined by the Armstrong-Frederick law [2], which is extended to finite-strain deformations. Finally, stress softening is introduced into an elastoplastic network using a modified version of Ogden and Roxbourgh’s pseudo-elasticity model [3]. This paper presents an outline of the framework, including two recent enhancements: a new creep model (the power law model) and combined isotropic/kinematic hardening plasticity model. The framework is then applied to analyze numerically the uniaxial loading/unloading behaviors of filled natural rubber and an EPDM polymer. The results obtained using finite element simulations show very good correlation with experimental data.