Modelling and numerical simulation of martensitic transformation in shape memory alloys |
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Authors: | Email author" target="_blank">M?ArndtEmail author M?Griebel T?Roubícek |
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Institution: | (1) Institut für Angewandte Mathematik, Rheinische Friedrich-Wilhelms-Universität Bonn, Wegeler Straße 6, 53115 Bonn, Germany;(2) Mathematical Institute, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic;(3) Institute of Information Theory and Automation, Academy of Sciences, Pod vodárenskou vezí 4, 182 08, Czech Republic |
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Abstract: | 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.Received: 27 June 2002, Accepted: 18 March 2003, Published online: 27 June 2003PACS:
81.30Kf |
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Keywords: | shape-memory material solid/solid phase transformation multiwell stored energy plastic-like dissipation computer simulation |
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