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 SouzaAuricchio 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.
Thermal control of the souza-auricchio model for shape memory alloys / Eleuteri, Michela; Lussardi, Luca; Stefanelli, Ulisse. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S. - ISSN 1937-1632. - 6:2(2013), pp. 369-386. [10.3934/dcdss.2013.6.369]
Thermal control of the souza-auricchio model for shape memory alloys
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 SouzaAuricchio 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.Pubblicazioni consigliate
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