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

Please always quote using this URN:urn:nbn:de:0296-matheon-5198
  • 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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Metadaten
Author:Alexander Mielke, Laetitia Paoli, Adrien Petrov
URN:urn:nbn:de:0296-matheon-5198
Referee:Carsten Carstensen
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2008/10/27
Release Date:2008/04/07
Tag:
Institute:Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
MSC-Classification:49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Jxx Existence theories / 49J40 Variational methods including variational inequalities [See also 47J20]
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Cxx Plastic materials, materials of stress-rate and internal-variable type / 74C05 Small-strain, rate-independent theories (including rigid-plastic and elasto-plastic materials)
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Fxx Coupling of solid mechanics with other effects / 74F05 Thermal effects
Preprint Number:526
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