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Visco‐elasto‐plastic model for martensitic phase transformation in shape‐memory alloys
Author(s) -
Plecháč Petr,
Roubíček Tomáš
Publication year - 2002
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.335
Subject(s) - isothermal process , dissipation , martensite , hysteresis , shape memory alloy , homogeneous , mathematics , finite element method , transformation (genetics) , convergence (economics) , phase (matter) , thermodynamics , mathematical analysis , mechanics , materials science , physics , metallurgy , condensed matter physics , microstructure , chemistry , biochemistry , quantum mechanics , economic growth , gene , economics , combinatorics
Evolution of fine structure in martensite undergoing an isothermal process is modelled on a microscopic level by using a positive homogeneous dissipation potential which can reflect a specific energy needed for a phase transformation between different variants of martensite. The model thus naturally incorporates an activation phenomenon. Existence of a weak solution is proved together with convergence of finite‐element approximations. Numerical experiments showing the expected rate‐independent hysteresis response are also presented. Copyright © 2002 John Wiley & Sons, Ltd.