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

Melnik, R. V. N. and Roberts, A. J. and Thomas, K. A. (2000) Mathematical and numerical analysis of Falk-Konopka-type models for shape-memory alloys. International Journal of Differential Equations and Applications, 1A (3). pp. 291-300. ISSN 1311-2872

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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.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: This work is licensed under a Creative Commons Attribution 3.0 License.
Faculty / Department / School: Historic - Faculty of Sciences - Department of Maths and Computing
Date Deposited: 30 Nov 2007 11:47
Last Modified: 10 Jun 2014 23:47
Uncontrolled 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
Fields of Research : 09 Engineering > 0912 Materials Engineering > 091207 Metals and Alloy Materials
01 Mathematical Sciences > 0102 Applied Mathematics > 010207 Theoretical and Applied Mechanics
09 Engineering > 0913 Mechanical Engineering > 091307 Numerical Modelling and Mechanical Characterisation
Socio-Economic Objective: E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
URI: http://eprints.usq.edu.au/id/eprint/14109

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