WIAS Preprint No. 1330, (2008)

On existence and approximation for a 3D model of thermally-induced phase transformations in shape-memory alloys



Authors

  • Mielke, Alexander
    ORCID: 0000-0002-4583-3888
  • Paoli, Laetitia
  • Petrov, Adrien

2010 Mathematics Subject Classification

  • 49J40 74C05 74F05

Keywords

  • Shape-memory materials, rate-independent energetic formulation, temperature-induced phase transformation, differential inclusion, convergence for space-time discretization

Abstract

This paper deals with a three-dimensional model for thermal stress-induced transformations in shape-memory materials. Microstructure, like twined martensites, is described mesoscopically by a vector of internal variables containing the volume fractions of each phase. We assume that the temperature variations are prescribed. The problem is formulated mathematically within the energetic framework of rate-independent processes. An existence result is proved and temporal regularity is obtained in case of uniform convexity. We study also space-time discretizations and establish convergence of these approximations.

Appeared in

  • SIAM J. Math. Anal., 41 (2009) pp. 1388--1414.

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