M. Arndt, M. Griebel, and T. Roubíček.
Modelling and numerical simulation of martensitic transformation in
shape memory alloys.
Continuum Mechanics and Thermodynamics, 15(5):463-485, 2003.
Also as Preprint No. 26, SFB 611, University of Bonn.
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We consider the evolution of martensitic fine structures in shape memory alloys which undergo an isothermal phase-transformation. This process is modelled on a microscopical, continuum-mechanical level by partial differential equations. Here a homogeneous degree-1 dissipation potential is involved which can reflect specific energies needed for rate-independent phase transformations. An interface energy is incorporated by a nonlocal term, and hard-device loading is considered. After setting up the model and specifying its energy balance properties, three-dimensional numerical experiments for the cubic-to-tetragonal transformation in an InTl single crystal are presented which demonstrate geometrical/material interactions under tensile and shear loading.