Thermal control of theSouza-Auricchio model for shape memory alloys

Michela Eleuteri; Luca Lussardi; Ulisse Stefanelli

doi:10.3934/dcdss.2013.6.369

Article Contents

2013, Volume 6, Issue 2: 369-386. Doi: 10.3934/dcdss.2013.6.369

This issue Previous Article An asymptotic analysis for a nonstandard Cahn-Hilliard system with viscosity Next Article A Cahn-Hilliard-Gurtin model with dynamic boundary conditions

Thermal control of the Souza-Auricchio model for shape memory alloys

1.
Università degli Studi di Milano, via Saldini 50, I-20133 Milano
2.
Università Cattolica del Sacro Cuore, via dei Musei 41, I-25121 Brescia
3.
Istituto di Matematica Applicata e Tecnologie Informatiche "E. Magenes" - CNR, via Ferrata 1, I-27100 Pavia

Received: July 2011

Revised: December 2011

Published: April 2013

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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 [6,53]. By assuming to be able to control the temperature of the body in time we determine the corresponding quasi-static evolution in the energeticsense. By recovering in this context a result by RINDLER [49,50] 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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Mathematics Subject Classification: 74C05, 49J20.

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