On the propagation of maximally dissipative phase boundaries in solids

Abstract

This paper is concerned with the kinetics of propagating phase boundaries in a bar made of a special nonlinearly elastic material. First, it is shown that there is a kinetic law of the form f = φ ( s ˙ ) f = \varphi \left ( {\dot s} \right ) relating the driving traction f f at a phase boundary to the phase boundary velocity s ˙ \dot s that corresponds to a notion of maximum dissipation analogous to the concept of maximum plastic work. Second, it is shown that a modified version of the entropy rate admissibility criterion can be described by a kinetic relation of the above form, but with a different φ \varphi . Both kinetic relations are applied to the Riemann problem for longitudinal waves in the bar.