# American Institute of Mathematical Sciences

September  2014, 3(3): 411-427. doi: 10.3934/eect.2014.3.411

## Thermal control of a rate-independent model for permanent inelastic effects in shape memory materials

 1 Dipartimento di Matematica e Informatica, Università di Firenze, viale Morgagni 67/a, I-50134 Firenze, Italy 2 Dipartimento di Matematica e Fisica "N.Tartaglia", Università Cattolica del Sacro Cuore, Via dei Musei 41, I-25121 Brescia, Italy

Received  April 2013 Revised  January 2014 Published  August 2014

We address the thermal control of the quasi-static evolution of a polycrystalline shape memory alloy specimen. The thermomechanical evolution of the body is described by means of an extension of the phenomenological Souza-Auricchio model [6,7,8,57] accounting also for permanent inelastic effects [9,11,27]. By assuming to be able to control the temperature of the body in time we determine the corresponding quasi-static evolution in the energetic sense. In a similar way as in [28], using results by Rindler [49,50] we prove the existence of optimal controls for a suitably large class of cost functionals.
Citation: Michela Eleuteri, Luca Lussardi. Thermal control of a rate-independent model for permanent inelastic effects in shape memory materials. Evolution Equations & Control Theory, 2014, 3 (3) : 411-427. doi: 10.3934/eect.2014.3.411
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##### References:
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