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IMA Journal of Applied Mathematics Advance Access originally published online on September 24, 2007
IMA Journal of Applied Mathematics 2007 72(5):644-658; doi:10.1093/imamat/hxm035
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© The Author 2007. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

A model for temperature-induced phase transformations in finite-strain elasticity

Alexander Mielke{dagger}

Weierstraß–Institut für Angewandte Analysis und Stochastik, Mohrenstraße 39, 10117 Berlin, Germany and Institut für Mathematik, Humboldt-Universität zu Berlin, Rudower Chaussee 25, 12489 Berlin, Germany

{dagger} Email: mielke{at}wias-berlin.de

Received on September 1, 2006; Accepted on February 1, 2007

We propose a model for phase transformations that are driven by changes in the temperature. We consider the temperature as a prescribed quantity like an applied load. The model is based on the energetic formulation for rate-independent systems and thus allows for finite-strain elasticity. Time-dependent Dirichlet boundary conditions can be treated by decomposing the deformation as a composition of a given deformation satisfying the time-dependent boundary conditions and a part coinciding with the identity on the Dirichlet boundary.

Keywords: shape-memory materials; dissipation distance; energetic formulation; energetic solution; Lie group; multiplicative decomposition of strains.


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