A comparison of finite strain viscoelastic models based on the multiplicative decomposition

Abstract

The constitutive equations of several finite strain viscoelastic models, based on the multiplicative decomposition of the deformation gradient tensor and formulated in a thermodynamically consistent framework, are reviewed to demonstrate their similarities and differences. The proposed analysis shows that dissipation formulations, which may appear different, are similar when expressed in the same configuration, enabling the definition of a unified general model. The ability of this general model to reproduce the main features of the behavior of rubbers is then explored. First, its responses are compared to those of finite linear viscoelastic models commonly implemented in commercial finite element codes. Cases of monotonic uniaxial tension and simple shear, relaxation, and sinusoidal simple shear are considered. Second, a comparison is made between a classic generalized Maxwell rheological scheme and a Zener one with a non-constant viscosity, exploring the relevance of both options within the general model’s constitutive equations.