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Kinetic relations and the propagation of phase boundaries in solids

Abeyaratne, Rohan and Knowles, James K. (1991) Kinetic relations and the propagation of phase boundaries in solids. Archive for Rational Mechanics and Analysis, 114 (2). pp. 119-154. ISSN 0003-9527. doi:10.1007/BF00375400.

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This paper treats the dynamics of phase transformations in elastic bars. The specific issue studied is the compatibility of the field equations and jump conditions of the one-dimensional theory of such bars with two additional constitutive requirements: a kinetic relation controlling the rate at which the phase transition takes place and a nucleation criterion for the initiation of the phase transition. A special elastic material with a piecewise-linear, non-monotonic stress-strain relation is considered, and the Riemann problem for this material is analyzed. For a large class of initial data, it is found that the kinetic relation and the nucleation criterion together single out a unique solution to this problem from among the infinitely many solutions that satisfy the entropy jump condition at all strain discontinuities.

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Additional Information:© 1991 Springer-Verlag. Received June 21, 1990. We have had the benefit of comments and questions from Philip Holmes, Richard James, Quing Jiang, James Rice, Phoebus Rosakis, Stewart Silling and Lev Truskinovsky, to whom we express our thanks. The support of the Mechanics Branch of the Orifice of Naval Research through Contract N00014-87-K-0117 is gratefully acknowledged.
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Office of Naval Research (ONR)N00014-87-K-0117
Issue or Number:2
Record Number:CaltechAUTHORS:20141021-141408927
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:50629
Deposited By: Tony Diaz
Deposited On:21 Oct 2014 21:27
Last Modified:10 Nov 2021 18:58

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