On the propagation of maximally dissipative phase boundaries in solids

Abeyaratne, Rohan; Knowles, James K.

doi:10.1090/qam/1146630

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 $f = \varphi \left ( {\dot s} \right )$ relating the driving traction $f$ at a phase boundary to the phase boundary velocity $\dot s$ 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 $\varphi$ . Both kinetic relations are applied to the Riemann problem for longitudinal waves in the bar.

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