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A sharp interface model for the propagation of martensitic phase boundaries

Dondl, Patrick W. and Bhattacharya, Kaushik (2008) A sharp interface model for the propagation of martensitic phase boundaries. Technical Report. California Institute of Technology, Pasadena, CA. [CaltechSOLIDS:2008.003]

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Abstract

A model for the quasistatic evolution of martensitic phase boundaries is presented. The model is essentially the gradient flow of an energy that can contains 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 the coupling to the elasticity equation. We show existence of solutions under a technical convergence condition using an implicit time-discretization.

EPrint Type: Monograph (Technical Report)
Additional Information: This work draws from the doctoral thesis of Patrick Dondl at the California Institute of Technology <http://resolver.caltech.edu/CaltechETD:etd-05292007-211950>. We gratefully acknowledge the financial support of the National Science Foundation (ACI-0204932, DMS-0311788).
Uncontrolled Keywords: Martensitic phase boundaries, free boundary evolution, sets of finite perimeter, calculus of variations
ID Code: 21
Deposited By: Dr. Patrick W. Dondl
Deposited On: 26 November 2008
Record Number: CaltechSOLIDS:2008.003
Official Persistent URL: http://resolver.caltech.edu/CaltechSOLIDS:2008.003
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