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Published August 2010 | public
Journal Article

A Sharp Interface Model for the Propagation of Martensitic Phase Boundaries


A model for the quasistatic evolution of martensitic phase boundaries is presented. The model is essentially the gradient flow of an energy that can contain elastic energy due to the underlying change in crystal structure in the course of the phase transformation and surface energy penalizing the area of the phase boundary. This leads to a free boundary problem with a nonlocal velocity that arises from a coupling to the elasticity equation. We show existence of solutions under a technical convergence condition using an implicit time-discretization.

Additional Information

© 2009 Springer-Verlag. Received January 21, 2009. Accepted September 28, 2009. Published online December 22, 2009. Communicated by J. Ball and R. James. This work draws from the doctoral thesis of Patrick Dondl at the California Institute of Technology. We gratefully acknowledge the financial support of the National Science Foundation (ACI-0204932, DMS-0311788).

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