On the thermodynamic consistency of Quasi-Linear Viscoelastic models for soft solids

TL;DR

This paper examines the thermodynamic consistency of Fung's quasi-linear viscoelastic (QLV) model for soft solids, providing a thermodynamic formulation and analyzing its dissipative behavior.

Contribution

It introduces a thermodynamically consistent formulation of the QLV model with internal variables and compares it to existing internal-variable models.

Findings

The QLV model can be formulated consistently with thermodynamics.

The model's dissipative features are demonstrated in tension tests.

Structural similarities between QLV and Holzapfel-Simo models are highlighted.

Abstract

Originating in the field of biomechanics, Fung's model of quasi-linear viscoelasticity (QLV) is one of the most popular constitutive theories employed to compute the time-dependent relationship between stress and deformation in soft solids. It is one of the simplest models of nonlinear viscoelasticity, based on a time-domain integral formulation. In the present study, we consider the QLV model incorporating a single scalar relaxation function. We provide natural internal variables of state, as well as a consistent expression of the free energy to illustrate the thermodynamic consistency of this version of the QLV model. The thermodynamic formulation highlights striking similarities between QLV and the internal-variable models introduced by Holzapfel and Simo. Finally, the dissipative features of compressible QLV materials are illustrated in simple tension.