On the thermodynamic consistency of Quasi-linear viscoelastic models for soft solids

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 internalvariable models introduced by Holzapfel and Simo. Finally, the dissipative features of compressible QLV materials are illustrated in simple tension. (c) 2020 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )

Automated summary

Originating from biomechanics, Fung's model of quasi-linear viscoelasticity (QLV) is a popular constitutive theory used to compute the time-dependent relationship between stress and deformation in soft solids. This study discusses the thermodynamic consistency of the QLV model incorporating a single scalar relaxation function, highlighting similarities with other internal variable models. The dissipative features of compressible QLV materials are illustrated in simple tension.