Micro-to-Meso Scale Limit for Shape-Memory-Alloy Models with Thermal Coupling

0380757 - ÚT 2013 RIV US eng J - Journal Article
Benešová, Barbora - Roubíček, Tomáš
Micro-to-Meso Scale Limit for Shape-Memory-Alloy Models with Thermal Coupling.
Multiscale Modeling and Simulation. Roč. 10, č. 3 (2012), s. 1059-1089. ISSN 1540-3459. E-ISSN 1540-3467
R&D Projects: GA ČR GAP201/10/0357
Institutional research plan: CEZ:AV0Z20760514
Keywords : martensitic transformation * relaxation * thermodynamics * gradient young measures
Subject RIV: BA - General Mathematics
Impact factor: 1.562, year: 2012
http://epubs.siam.org/doi/abs/10.1137/110852176

Modeling of shape-memory alloys represents a multiscale problem due to the occurrence of a martensite/austenite phase transformation and a microstructure in the deformation gradient typical for a martensitic phase. Inspired by relaxation in a static situation, a limit passage between two modeling scales, called micro- and mesoscales, is performed for the corresponding evolution variants while considering activated phase transformation and even thermodynamically consistent thermal coupling. The mesoscopic model captures possible fine spatial oscillations of the deformation gradient by means of gradient Young measures. In particular, the mesoscopic model is justified as a limit from the microscopic scale and existence of its solutions is proved.
Permanent Link: http://hdl.handle.net/11104/0211385