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On diffused-interface models of shape memory alloys

Pawłow I., Zajączkowski W. M.

Control and Cybernetics

2003

Vol. 32, no 3

629-658

The paper surveys mathematical models of thermo-mechanical evolution of shape memory alloys and related mathematical results. The survey is confined to so-called diffused-interface or phase-field models based on Landau-Ginzburg free energy as a ther-modynamic potential. It includes the well-known models due to Falk, Fremond and Fried-Gurtin. The focus is on a three-dimensional (3-D) generalization of Falk's model based on the linearized strain tensor, absolute temperature and strain tensor gradient. For such model the thermodynamical basis and the recent mathematical results on its well-posedness are presented.