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arXiv · 2012.01811

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

Harold Berjamin·Michel Destrade·William J. Parnell
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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.

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Harold Berjamin, Michel Destrade, William J. Parnell. 2020-12-03. On the thermodynamic consistency of Quasi-Linear Viscoelastic models for soft solids. https://doi.org/10.1016/j.mechrescom.2020.103648

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