Energy estimates in three-dimensional rate-type semilinear viscoelasticity with non-convex free energy

Abstract

One uses the free energy function, constructed in [3] for three-dimensional rate-type semilinear viscoelastic constitutive equations, in order to obtain energetic estimates for the solution of a non-isolated body problem with prescribed boundary motion. We consider both small and large deformation theories. The results involve viscoelastic models with non-monotone equilibrium hypersurfaces (i.e. With non-convex free energy). A viscoelastic approach to non-linear and non-monotone hyperelasticity by means of a Maxwell's type viscosity is discussed. Thus, materials presenting softening, like iron for instance, geomaterials with post-failure behaviour and also a rate-type approach to phase transitions in continuum thermodynamics may be included.