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

H. Berjamin, W. J. Parnell, M. Destrade (2021). "On the thermodynamic consistency of Quasi-linear viscoelastic models for soft solids", Mechanics Research Communications 111, 103648. https://doi.org/10.1016/j.mechrescom.2020.103648

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.

Fung QLV, Thermodynamics, Nonlinear viscoelasticity, Soft solids, Biomechanics