Phase transitions in shape memory alloys with hyperbolic heat conduction and differential-algebraic models
Article
Melnik, R. V. N., Roberts, A. J. and Thomas, K. A.. 2002. "Phase transitions in shape memory alloys with hyperbolic heat conduction and differential-algebraic models." Computational Mechanics. 29 (1), pp. 16-26. https://doi.org/10.1007/s00466-002-0311-5
| Article Title | Phase transitions in shape memory alloys with hyperbolic heat conduction and differential-algebraic models |
|---|---|
| ERA Journal ID | 3732 |
| Article Category | Article |
| Authors | Melnik, R. V. N. (Author), Roberts, A. J. (Author) and Thomas, K. A. (Author) |
| Journal Title | Computational Mechanics |
| Journal Citation | 29 (1), pp. 16-26 |
| Number of Pages | 11 |
| Year | 2002 |
| Place of Publication | Berlin, Germany |
| ISSN | 0178-7675 |
| 1432-0924 | |
| Digital Object Identifier (DOI) | https://doi.org/10.1007/s00466-002-0311-5 |
| Web Address (URL) | http://biophysics.asu.edu/banf_files/melnik/landau_free_energy.pdf |
| Abstract | The dynamics of phase transitions and hysteresis phenomena in materials with memory are described by a strongly nonlinear coupled system of partial differential equations which, in its generality, can be solved only numerically. Following principles of extended thermodynamics, in this paper we construct a new model for the description of this dynamics based on the Cattaneo-Vernotte law for heat conduction. Models based on the Fourier law follow from this general consideration as special cases. We develop a general procedure for the solution of the resulting systems by their reduction to differential-algebraic systems. Finally, a computational code for the numerical implementation of this procedure is explained in detail, and representative numerical examples are given. |
| Keywords | phase transitions; shape memory alloys; hyperbolic heat conduction; Cattaneo Vernotte law; differential algebraic systems; Fourier law; hyperbolic heat conduction; solid phase transformations |
| ANZSRC Field of Research 2020 | 490406. Lie groups, harmonic and Fourier analysis |
| 401607. Metals and alloy materials | |
| 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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