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Modelling nonlinear dynamics of shape‐memory‐alloys with approximate models of coupled thermoelasticity
Author(s) -
Melnik R.V.N.,
Roberts A.J.
Publication year - 2003
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200310009
Subject(s) - representation (politics) , nonlinear system , computer science , manifold (fluid mechanics) , code (set theory) , dynamics (music) , function (biology) , scheme (mathematics) , mathematics , energy (signal processing) , algorithm , statistical physics , mathematical analysis , physics , mechanical engineering , statistics , set (abstract data type) , quantum mechanics , evolutionary biology , politics , political science , acoustics , law , biology , programming language , engineering
We present a general methodology for constructing approximate models describing shape memory alloys dynamics. We base our discussion on a general three‐dimensional model and the Falk‐Konopka representation for the free energy function. By considering a one‐dimensional counterpart of that model, we show that with little computational efforts we can reproduce successfully phase transition phenomena with our numerical scheme. The same scheme is applied in our code for the general case. Then, we describe a systematic approach to modelling SMA materials, and demonstrate that approach in deriving a centre‐manifold‐based low‐dimensional model from the general three‐dimensional model, preserving all main features of the dynamics. Computer algebra technique allows us to derive such models efficiently and with arbitrary degree of accuracy.