# Mathematical and numerical analysis of Falk-Konopka-type models for shape-memory alloys

Article

*International Journal of Differential Equations and Applications.*1A (3), pp. 291-300.

Article Title | Mathematical and numerical analysis of Falk-Konopka-type models for shape-memory alloys |
---|---|

ERA Journal ID | 194 |

Article Category | Article |

Authors | Melnik, R. V. N. (Author), Roberts, A. J. (Author) and Thomas, K. A. (Author) |

Journal Title | International Journal of Differential Equations and Applications |

Journal Citation | 1A (3), pp. 291-300 |

Number of Pages | 10 |

Year | 2000 |

Place of Publication | Sofia, Bulgaria |

ISSN | 1311-2872 |

Abstract | This paper is devoted to the development of mathematical theory of thermomechanical phase transitions. A hierarchy of mathematical models for smart materials and structures technologies is discussed in the context of models describing shape memory alloy dynamics. The authors analyze mathematical models resulting from the Falk-Konopka generalization of the Landau theory to the meso-scale level. Using center manifold techniques, the authors derive a low-dimensional model obtained directly from the three-dimensional Falk-Konopka model. The results of the theoretical analysis are supported by computational experiments. |

Keywords | thermomechanical phase transitions; nonlinear dynamics; mathematical models for smart materials and stuctures technologies; multi-dimensional case; Landau theory; shape memory alloys (SMA); hyperbolic approximations of SMA dynamics; hysteresis and nonlinear phenomena; hierarchy of models; complex systems; systematic procedures for low dimensional reductions |

ANZSRC Field of Research 2020 | 401607. Metals and alloy materials |

490109. Theoretical and applied mechanics | |

401706. Numerical modelling and mechanical characterisation | |

Byline Affiliations | Commonwealth Scientific and Industrial Research Organisation (CSIRO), Australia |

Department of Mathematics and Computing | |

Institution of Origin | University of Southern Queensland |

https://research.usq.edu.au/item/q062v/mathematical-and-numerical-analysis-of-falk-konopka-type-models-for-shape-memory-alloys

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