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.
Author: | Alexander Mielke, Laetitia Paoli, Adrien Petrov |
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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 |