Instantaneous and equilibrium Grüneisen parameters for a nonlinear viscoelastic polymer

Abstract

In studying the propagation of shock waves in nonlinear viscoelastic solids, it is useful to characterize the mechanical response of the material in terms of instantaneous and equilibrium stress-strain functions. A natural extension of this concept to include thermodynamic influences leads to the consideration of instantaneous and equilibrium thermodynamic response functions for the stress and internal energy. An important factor in the thermoviscoelastic behavior concerns the stress/energy response as characterized by the Grüneisen parameter, or in the present context, an instantaneous and equilibrium parameter. An example of these parameters and their temperature dependence is given for the solid polymer, polymethyl methacrylate, based on a thermoviscoelastic constitutive model developed for predicting steady shock wave propagation.