THE RELATIVE FREE-ENERGY AND ENERGY ESTIMATES IN MODELING PHASE-TRANSITIONS BY RATE-TYPE CONSTITUTIVE-EQUATIONS

The properties of a simplified viscoelastic piecewise linear model with non-monotone equilibrium curve are further studied in this paper. This model, in contrast to the elastic one, can describe the way the deviation from the equilibrium takes place. A notion of relative free energy to an equilibrium state is introduced. It is shown that the relative free energy to equilibrium states outside Maxwell's interval is always positive and it provides bounds in terms of input data for the solutions of the viscoelastic problem. The mean square pressure (stress) deviation from the equilibrium is estimated in terms of the relative free energy. For an impact problem of a semi-infinite body one can conclude that the wave structure for the viscoelastic model approaches the wave structure for the elastic model when the Maxwell's type viscosity coefficient is large or, equivalently, when the relaxation time is small.