On the encounter of an acoustic shear pulse with a phase boundary in an elastic material: energy and dissipation

The fully dynamical motion of a phase boundary is examined for a specific class of elastic materials whose stress-strain relation in simple shear is nonmonotone. Previous work has shown that a preexisting stationary phase boundary in such a material can be set in motion by a finite amplitude shear pulse and that an infinity of solutions is possible according to the present theory. In this work, these solutions are examined in detail from the perspective of energy and dissipation. It is shown that there exists at most two solutions which involve no dissipation (corresponding to conservation of mechanical energy). It is also shown that there exists one solution that maximizes the mechanical energy dissipation rate. The total mechanical energy remaining in the dynamical fields after one such pulse-phase boundary encounter is shown to exceed the total methanical energy after either an energy minimal quasi-static motion or a maximally dissipative quasi-static motion.