Large strain viscoelastic constitutive models

This paper discusses a new continuum formulation for viscoelastic materials at finite strains. The model proposed is based on the multiplicative decomposition of the isochoric component of deformation gradient into elastic and viscous contribution and the generalized Maxwell rheological model. The inelastic or viscous components of the deformation gradient provide the internal variables required for the irreversible thermo-mechanical model. Nonlinear rate type of evolution equations are then proposed for the internal variables. These are based on a particular linear relaxation form of the generalized Maxwell model which leads to a viscoelastic formulation that can be seen as a particular case of a large strain viscoplastic model based on maximum plastic dissipation. In addition to the rate evolution equations, simple incremental stress update equations are proposed. These closely resemble the radial return algorithms used in von Mises plasticity. Finally a spatial form of the viscoelastic formulation is presented for isotropic materials. This formulation is based on principal directions and logarithmic stretches. Again incremental equations will be considered in order to permit subsequent computational implementations. (C) 2001 Elsevier Science Ltd. All rights reserved.