Constitutive modeling of viscoelastic solids at large strains based on the theory of evolving natural configurations

TL;DR

This paper develops a unified Lagrangian framework for viscoelastic solids at large strains using evolving natural configurations, modeling various standard solids, and validating with experimental data.

Contribution

It introduces a novel Lagrangian approach to model Maxwell, Kelvin-Voigt, Zener, and Poynting-Thompson solids within the theory of evolving natural configurations, including new integration algorithms.

Findings

The Poynting-Thompson model matches experimental data well.

Basic models are recoverable as limiting cases.

Models capture relaxation and rate effects accurately.

Abstract

The theory of evolving natural configurations is an effective technique to model dissipative processes. In this paper, we use this theory to revisit nonlinear constitutive models of viscoelastic solids. Particularly, a Maxwell and a Kelvin-Voigt model and their associated standard solids, viz., a Zener and a Poynting-Thompson solids respectively, have been modeled within a Lagrangian framework. We show that while a strain-space formulation of the evolving natural configurations is useful in modeling Maxwell-type materials, a stress-space formulation that incorporates a rate of dissipation function in terms of the relevant configurational forces is required for modeling the Kelvin-Voigt type materials. Furthermore, we also show that the basic Maxwell and Kelvin-Voigt models can be obtained as limiting cases from the derived standard solid models. Integration algorithms for the proposed models have been developed and numerical solutions for a relevant boundary value problem are obtained. The response of the developed models have been compared and benchmarked with experimental data. Specifically, the response of the novel Poynting-Thompson model is studied in details. This model shows a very good match with the existing experimental data obtained from a uniaxial stretching of polymers over a large extent of strain. The relaxation behavior and rate effects for the developed models have been studied.