Nonlinear Waves in Thermoelastic Solids Undergoing Phase Transitions

This paper is concerned with continuum modeling of the macroscopic dynamical response of one-dimensional thermoelastic bars undergoing phase transitions. The specific model considered involves a particular "two-well" Helmholtz free energy potential governing the bulk response of the material as well as a nucleation criterion and kinetic relation controlling the initiation and evolution of the phase transition. Inertia is taken into account, and the discussion is based on an adiabatic theory. In contrast to models in which the free energy involves only a single well, the entropy inequality at propagating strain discontinuities is not sufficient to assure the uniqueness of solutions to the boundary-initial value problems of interest: kinetics and nucleation must be imposed as well.