Archive for Rational Mechanics and Analysis

, Volume 114, Issue 2, pp 119–154

Kinetic relations and the propagation of phase boundaries in solids

  • Rohan Abeyaratne
  • James K. Knowles
Article

DOI: 10.1007/BF00375400

Cite this article as:
Abeyaratne, R. & Knowles, J.K. Arch. Rational Mech. Anal. (1991) 114: 119. doi:10.1007/BF00375400

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.

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Rohan Abeyaratne
    • 1
    • 2
  • James K. Knowles
    • 1
    • 2
  1. 1.Department of Mechanical EngineeringMassachusetts Institute of TechnologyCambridge
  2. 2.Division of Engineering and Applied ScienceCalifornia Institute of TechnologyPasadena

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