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

Abstract

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 mechanical energy after either an energy minimal quasi-static motion or a maximally dissipative quasi-static motion.

On the encounter of an acoustic shear pulse with a phase boundary in an elastic material: reflection and transmission behavior

“…Energetic considerations in both a quasi-static and fully dynamical sense have recently received a great deal of study with a view toward a full or partial resolution to the uniqueness issue. These results will be presented in a subsequent communication which extends the results presented here [36].…”

On the propagation of maximally dissipative phase boundaries in solids

“…Among such selection criteria, perhaps the two that are most often encountered in applications are the "viscosity-capillarity condition" studied by Shearer [10,11], Slemrod [12,13], Truskinovsky [14,15], and others, and variants of the "entropy rate admissibility criterion" proposed by Dafermos [16,17] and investigated in connection with phase transitions by Hattori [18,19], James [20], and Pence [21], For the trilinear elastic bar, the relation between a selection criterion of the viscosity-capillarity type and the kinetics of phase transitions was recently explored in [22], where it was shown that imposing this selection criterion is equivalent to the prescription of a kinetic relation / = (p{s) with a particular choice of (p . In the present paper, we show-again for the trilinear material-that the "entropy rate shock admissibility criterion" stated by Dafermos in [17], if suitably modified, is also equivalent to a kinetic relation of the form f = (p(s).…”

Reflection and Transmission of Waves from an Interface with a Phase-Transforming Solid

“…The only work of which we are aware that is related to the specific problem under discussion here is that of Pence [4,5]. In [4], Pence studies the reflection and transmission of an acoustic shear wave from an initially stationary phase boundary in an elastic solid. The analysis in [5] is concerned with the structure of the fields in two elastic bars, one of which (the impactor) is composed of a single-phase material, while the other (the target) is made of a material capable of sustaining a phase transformation.…”