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

Michela Eleuteri; Luca Lussardi

doi:10.3934/eect.2014.3.411

Article Contents

2014, Volume 3, Issue 3: 411-427. Doi: 10.3934/eect.2014.3.411

This issue Previous Article Heat conduction with memory: A singular kernel problem Next Article Steady free fall of one-dimensional bodies in a hyperviscous fluid at low Reynolds number

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

Michela Eleuteri^1, and
Luca Lussardi^2,

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

Received: March 31, 2013

Revised: December 31, 2013

Published: August 2014

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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 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.

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Mathematics Subject Classification: 74C05, 49J20.

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