On existence and approximation for a 3D model of thermally-induced phase transformations in shape-memory alloys
- Mielke, Alexander
- Paoli, Laetitia
- Petrov, Adrien
2010 Mathematics Subject Classification
- 49J40 74C05 74F05
- Shape-memory materials, rate-independent energetic formulation, temperature-induced phase transformation, differential inclusion, convergence for space-time discretization
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.
- SIAM J. Math. Anal., 41 (2009) pp. 1388--1414.