Modelling nonlinear dynamics of shape-memory-alloys with approximate models of coupled thermoelasticity

Article


Melnik, Roderick V. N. and Roberts, A. J.. 2003. "Modelling nonlinear dynamics of shape-memory-alloys with approximate models of coupled thermoelasticity." Journal of Applied Mathematics and Mechanics (ZAMM). 83 (2), pp. 93-104. https://doi.org/10.1002/zamm.200310009
Article Title

Modelling nonlinear dynamics of shape-memory-alloys with approximate models of coupled thermoelasticity

ERA Journal ID765
Article CategoryArticle
AuthorsMelnik, Roderick V. N. (Author) and Roberts, A. J. (Author)
Journal TitleJournal of Applied Mathematics and Mechanics (ZAMM)
Journal of Applied Mathematics and Mechanics (ZAMM) (Zeitschrift fur Angewandte Mathematik und Mechanik (ZAMM))
Journal Citation83 (2), pp. 93-104
Number of Pages12
Year2003
ISSN0044-2267
1521-4001
Digital Object Identifier (DOI)https://doi.org/10.1002/zamm.200310009
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.

Keywordsnonlinear thermoelasticity, shape-memory alloys, differential-algebraic solver, center manifold technique
ANZSRC Field of Research 2020490303. Numerical solution of differential and integral equations
401706. Numerical modelling and mechanical characterisation
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Byline AffiliationsUniversity of Southern Denmark, Denmark
Department of Mathematics and Computing
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