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 the phenomenological Souza-Auricchio model. 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. By recovering in this context a result by Rindler we prove the existence of optimal controls for a suitably large class of cost functionals and comment on their possible approximation.
Lussardi, L., Eleuteri, M., Stefanelli, U., Thermal control of the Souza-Auricchio model for shape memory alloys, <<DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S>>, 2013; 6 (Aprile): 369-386. [doi:10.3934/dcdss.2013.6.369] [http://hdl.handle.net/10807/39009]
Thermal control of the Souza-Auricchio model for shape memory alloys
Lussardi, Luca;Eleuteri, Michela;
2013
Abstract
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 the phenomenological Souza-Auricchio model. 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. By recovering in this context a result by Rindler we prove the existence of optimal controls for a suitably large class of cost functionals and comment on their possible approximation.
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