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Implications of Viscosity and Strain-Gradient Effects for the Kinetics of Propagating Phase Boundaries in Solids

Abeyaratne, Rohan and Knowles, James K. (1991) Implications of Viscosity and Strain-Gradient Effects for the Kinetics of Propagating Phase Boundaries in Solids. SIAM Journal on Applied Mathematics, 51 (5). pp. 1205-1221. ISSN 0036-1399. https://resolver.caltech.edu/CaltechAUTHORS:20141021-102900385

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Abstract

This paper is concerned with the propagation of phase boundaries in elastic bars. It is known that the Riemann problem for an elastic bar capable of undergoing isothermal phase transitions need not have a unique solution, even in the presence of the requirement that the entropy of any particle cannot decrease upon crossing a phase boundary. For a special class of elastic materials, the authors have shown elsewhere that if all phase boundaries move subsonically with respect to both phases, this lack of uniqueness can be resolved by imposing a nucleation criterion and a kinetic relation for the relevant phase transition. Others have singled out acceptable solutions on the basis of a theory that adds effects due to viscosity and second strain gradient to the elastic part of the stress. It is shown that, for phase boundaries that propagate subsonically, this approach is equivalent to the imposition of a particular kinetic relation at the interface between the phases.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1137/0151061 DOIArticle
http://epubs.siam.org/doi/abs/10.1137/0151061PublisherArticle
Additional Information:© 1991 Society for Industrial and Applied Mathematics. Received by the editors June 25, 1990; accepted for publication (in revised form) October 22, 1990. This research was supported by U.S. Office of Naval Research contract N00014-87-K-0117.
Funders:
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-87-K-0117
Subject Keywords:phase transitions, kinetics, Riemann problem
Issue or Number:5
Classification Code:AMS(MOS) subject classifications: 73, 35
Record Number:CaltechAUTHORS:20141021-102900385
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20141021-102900385
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:50604
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:21 Oct 2014 17:56
Last Modified:03 Oct 2019 07:25

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