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Existence of solutions for a mathematical model of structural phase transitions in shape memory alloys
Author(s) -
Niezgódka Marek,
Sprekels Jürgen
Publication year - 1988
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.1670100302
Subject(s) - hysteresis , shape memory alloy , mathematics , phase transition , phase (matter) , partial differential equation , balance (ability) , statistical physics , mathematical analysis , classical mechanics , physics , thermodynamics , materials science , condensed matter physics , medicine , quantum mechanics , metallurgy , physical medicine and rehabilitation
In this paper a thermomechanical model for the dynamics of structural phase transitions in the so‐called ‘shape memory alloys’ is developed. These materials exhibit rather spectacular hysteresis phenomena. The resulting mathematical model consists of a coupled and highly non‐linear system of partial differential equations reflecting the balance laws of linear momentum and energy. For an appropriate weak formulation the local‐in‐time existence of weak solutions is shown.