# American Institute of Mathematical Sciences

April  2013, 6(2): 277-291. doi: 10.3934/dcdss.2013.6.277

## A new "flexible" 3D macroscopic model for shape memory alloys

 1 Dipartimento di Meccanica Strutturale, Università di Pavia, via Ferrata 1, 27100 Pavia, Italy 2 Dipartimento di Matematica, Università di Pavia, via Ferrata 1, 27100 Pavia

Received  November 2011 Revised  January 2012 Published  November 2012

In this paper we introduce a 3D phenomenological model for shape memory behavior, accounting for: martensite reorientation, asymmetric response of the material to tension/compression, different kinetics between forward and reverse phase transformation. We combine two modeling approaches using scalar and tensorial internal variables. Indeed, we use volume proportions of different configurations of the crystal lattice (austenite and two variants of martensite) as scalar internal variables and the preferred direction of stress-induced martensite as tensorial internal variable. Then, we derive evolution equations by a generalization of the principle of virtual powers, including microforces and micromovements responsible for phase transformations. In addition, we prescribe an evolution law for phase proportions ensuring different kinetics during forward and reverse transformation of the oriented martensite.
Citation: Ferdinando Auricchio, Elena Bonetti. A new "flexible" 3D macroscopic model for shape memory alloys. Discrete & Continuous Dynamical Systems - S, 2013, 6 (2) : 277-291. doi: 10.3934/dcdss.2013.6.277
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