On the propagation of maximally dissipative phase boundaries in solids

Authors:
Rohan Abeyaratne and James K. Knowles

Journal:
Quart. Appl. Math. **50** (1992), 149-172

MSC:
Primary 73B30

DOI:
https://doi.org/10.1090/qam/1146630

MathSciNet review:
MR1146630

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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 relating the driving traction at a phase boundary to the phase boundary velocity 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 . Both kinetic relations are applied to the Riemann problem for longitudinal waves in the bar.

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DOI:
https://doi.org/10.1090/qam/1146630

Article copyright:
© Copyright 1992
American Mathematical Society