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Existence and approximation for a 3D model of thermally‐induced phase transformations in shape‐memory alloys
Author(s) -
Mielke Alexander,
Paoli Laetitia,
Petrov Adrien
Publication year - 2008
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200810395
Subject(s) - shape memory alloy , microstructure , convergence (economics) , thermal , phase (matter) , space (punctuation) , rate of convergence , materials science , mathematics , volume (thermodynamics) , statistical physics , thermodynamics , physics , metallurgy , computer science , economics , quantum mechanics , computer network , channel (broadcasting) , economic growth , operating system
This note deals with a three–dimensional model for thermal stress–induced transformations in shape–memory materials. Microstructure, like twined martensites, is described mesoscopically by a vector of internal variables containing the volume fractions of each phase. The problem is formulated mathematically within the energetic framework of rate–independent processes. An existence result is proved and we study space–time discretizations and establish convergence of these approximations. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)