# Phase transitions in shape memory alloys with hyperbolic heat conduction and differential-algebraic models

Article

*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 |

https://research.usq.edu.au/item/9y539/phase-transitions-in-shape-memory-alloys-with-hyperbolic-heat-conduction-and-differential-algebraic-models

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