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Global Existence and Uniqueness for a Thermomechanical Model for Shape Memory Alloys with Partition of the Strain

Laboratoire Lagrange, Dipartimento di Matematica "F. Casorati", Università di Pavia, Via Ferrata 1, 27100 Pavia, Italy

Michel Frémond

Laboratoire Lagrange, Laboratoire Central des Ponts et Chaussées, 58 boulevard Lefebvre, 75372 Paris Cedex 15, France

Christian Lexcellent

Laboratoire Lagrange, Laboratoire de Mécanique Appliquée, 24 rue de l’Epitaphe, 25000 Besançon Cedex, France

This paper investigates an initial and boundary value problem describing the thermomechanical behavior of shape memory alloys. In the strain tensor an elastic contribution is combined with a phase transformation term, for which only one of the phases turns out to be responsible. In particular, the solid-solid phase transition between the austenite phase and the martensites is described by two functionals, the free energy and the pseudo-potential of dissipation. A global existence and uniqueness result is stated by use of a fixed point argument and contracting estimates technique.

Key Words: shape memory alloys • thermomechanical models • partial differential equations • well-posedness results

Mathematics and Mechanics of Solids, Vol. 11, No. 3, 251-275 (2006)
DOI: 10.1177/1081286506040403


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