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Article Dans Une Revue SIAM Journal on Mathematical Analysis Année : 2009

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

Résumé

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.
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Dates et versions

hal-00863759 , version 1 (06-03-2019)

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Alexander Mielke, Laetitia Paoli, Adrien Petrov. On existence and approximation for a 3D model of thermally-induced phase transformations in shape-memory alloys. SIAM Journal on Mathematical Analysis, 2009, 41 (4), pp.1388-1414. ⟨10.1137/080726215⟩. ⟨hal-00863759⟩
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