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 ID | 765 |
| Article Category | Article |
| Authors | Melnik, Roderick V. N. (Author) and Roberts, A. J. (Author) |
| Journal Title | Journal of Applied Mathematics and Mechanics (ZAMM) |
| Journal of Applied Mathematics and Mechanics (ZAMM) (Zeitschrift fur Angewandte Mathematik und Mechanik (ZAMM)) | |
| Journal Citation | 83 (2), pp. 93-104 |
| Number of Pages | 12 |
| Year | 2003 |
| ISSN | 0044-2267 |
| 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. |
| Keywords | nonlinear thermoelasticity, shape-memory alloys, differential-algebraic solver, center manifold technique |
| ANZSRC Field of Research 2020 | 490303. Numerical solution of differential and integral equations |
| 401706. Numerical modelling and mechanical characterisation | |
| Public Notes | Files associated with this item cannot be displayed due to copyright restrictions. |
| Byline Affiliations | University of Southern Denmark, Denmark |
| Department of Mathematics and Computing |
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