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November  2010, 27(4): 1633-1659. doi: 10.3934/dcds.2010.27.1633

A model for shape memory alloys with the possibility of voids

Michel Frémond 1, and  Elisabetta Rocca 2,

1. 

Dipartimento di Ingegneria Civile, Università di Roma “Tor Vergata”, Via del Politecnico, 1, I-00133 Roma, Italy
2. 

WIAS Weierstrass Institute, Mohrenstr. 39, 10117 Berlin, Germany, Dipartimento di Matematica, Università di Milano, Via Saldini 50, 20133 Milano, Italy

Received  September 2009 Revised  January 2010 Published  March 2010

The paper is devoted to the study of a mathematical model for the thermomechanical evolution of metallic shape memory alloys. The main novelty of our approach consists in the fact that we include the possibility for these materials to exhibit voids during the phase change process. Indeed, in the engineering paper [60] has been recently proved that voids may appear when the mixture is produced by the aggregations of powder. Hence, the composition of the mixture varies (under either thermal or mechanical actions) in this way: the martensites and the austenite transform into one another whereas the voids volume fraction evolves. The first goal of this contribution is hence to state a PDE system capturing all these modelling aspects in order then to establish the well-posedness of the associated initial-boundary value problem.
Keywords: mixtures with voids, existence of solutions, nonlinear PDEs system, Shape memory alloys, initial-boundary value problem, continuous dependence result..
Mathematics Subject Classification: Primary: 80A22, 74D10; Secondary: 35A05, 35Q30, 35G2.
Citation: Michel Frémond, Elisabetta Rocca. A model for shape memory alloys with the possibility of voids. Discrete & Continuous Dynamical Systems, 2010, 27 (4) : 1633-1659. doi: 10.3934/dcds.2010.27.1633
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