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

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.

References in corpus (3)

• Mechanical Characterization of Brain Tissue in Compression at Dynamic Strain Rates
• Mechanical characterization of brain tissue in simple shear at dynamic strain rates
• Proper formulation of viscous dissipation for nonlinear waves in solids

Cited by in corpus (4)

• Acoustoelastic analysis of soft viscoelastic solids with application to pre-stressed phononic crystals
• Shear shock formation in incompressible viscoelastic solids
• A unified framework for linear thermo-visco-elastic wave propagation including the effects of stress-relaxation
• On the accuracy of one-way approximate models for nonlinear waves in soft solids