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. https://resolver.caltech.edu/CaltechAUTHORS:20141021-141408927
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Abstract
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.
| Item Type: | Article | |||||||||
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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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| Issue or Number: | 2 | |||||||||
| DOI: | 10.1007/BF00375400 | |||||||||
| Record Number: | CaltechAUTHORS:20141021-141408927 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20141021-141408927 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 50629 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Tony Diaz | |||||||||
| Deposited On: | 21 Oct 2014 21:27 | |||||||||
| Last Modified: | 10 Nov 2021 18:58 |
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