  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.
