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A Sharp Interface Model for the Propagation of Martensitic Phase Boundaries

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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 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.

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Authors and Affiliations

  1. Hausdorff Center for Mathematics and Institute for Applied Mathematics, University Bonn, Endenicher Allee 60, 53115, Bonn, Germany

    Patrick W. Dondl

  2. Division of Engineering and Applied Science, MSC 104-44, California Institute of Technology, Pasadena, CA, 91125, USA

    Kaushik Bhattacharya

Authors
  1. Patrick W. Dondl
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  2. Kaushik Bhattacharya
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Correspondence to Kaushik Bhattacharya.

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Communicated by J. Ball and R. James

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Dondl, P.W., Bhattacharya, K. A Sharp Interface Model for the Propagation of Martensitic Phase Boundaries. Arch Rational Mech Anal 197, 599–617 (2010). https://doi.org/10.1007/s00205-009-0286-x

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  • DOI: https://doi.org/10.1007/s00205-009-0286-x

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