Melnik, Roderick V. N. and Roberts, A. J. (2003) Modelling nonlinear dynamics of shape-memory-alloys with approximate models of coupled thermoelasticity. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 83 (2). pp. 93-104. ISSN 0044-2267
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Official URL: http://dx.doi.org/10.1002/zamm.200310009
Identification Number or DOI: doi: 10.1002/zamm.200310009
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.
|Item Type:||Article (Commonwealth Reporting Category C)|
|Additional Information:||Author's version not held.|
|Uncontrolled Keywords:||nonlinear thermoelasticity, shape-memory alloys, differential-algebraic solver, center manifold technique|
|Fields of Research (FOR2008):||01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations|
09 Engineering > 0913 Mechanical Engineering > 091307 Numerical Modelling and Mechanical Characterisation
|Socio-Economic Objective (SEO2008):||E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences|
|Deposited On:||20 Apr 2010 20:05|
|Last Modified:||16 Aug 2010 13:39|
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