Convex and non-convex energy in three-dimensional rate-type semilinear viscoelasticity (Q1181060)

The necessary and sufficient conditions imposed upon the constitutive functions of a rate-type viscoelastic equation are studied to ensure that a unique free energy function compatible with the second law of thermodynamics exists. The existence proof is given by an effective construction of the free energy function. The viscoelastic equation considered is semilinear, and the deformations considered are large. The necessary and sufficient conditions are also established for the free energy function to be non-negative and equivalent to (or to lie between) two Euclidean norms. The change in free energy that results from a change in the equilibrium hypersurface is also studied. All the conditions are expressed in terms of equilibrium hypersurface and the dynamic elastic moduli and may be tested in applications.