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
Abstract
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.
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| Item Type: | Article (Commonwealth Reporting Category C) |
|---|---|
| Refereed: | Yes |
| Item Status: | Live Archive |
| Additional Information: | Author's version not held. |
| Faculty/School / Institute/Centre: | Historic - Faculty of Sciences - Department of Maths and Computing (Up to 30 Jun 2013) |
| Faculty/School / Institute/Centre: | Historic - Faculty of Sciences - Department of Maths and Computing (Up to 30 Jun 2013) |
| Date Deposited: | 20 Apr 2010 10:05 |
| Last Modified: | 02 Jul 2013 23:48 |
| Uncontrolled Keywords: | nonlinear thermoelasticity, shape-memory alloys, differential-algebraic solver, center manifold technique |
| Fields of Research (2008): | 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 |
| Fields of Research (2020): | 49 MATHEMATICAL SCIENCES > 4903 Numerical and computational mathematics > 490303 Numerical solution of differential and integral equations 40 ENGINEERING > 4017 Mechanical engineering > 401706 Numerical modelling and mechanical characterisation |
| Socio-Economic Objectives (2008): | E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences |
| Identification Number or DOI: | https://doi.org/10.1002/zamm.200310009 |
| URI: | http://eprints.usq.edu.au/id/eprint/7523 |
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