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

Melnik, R. V. N. and 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. ISSN 0178-7675


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.

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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Awaiting Author's version. Deposited in accordance with the copyright policy of the publisher.
Faculty / Department / School: Historic - Faculty of Sciences - Department of Maths and Computing
Date Deposited: 11 Oct 2007 01:18
Last Modified: 06 Nov 2013 04:41
Uncontrolled Keywords: phase transitions; shape memory alloys; hyperbolic heat conduction; Cattaneo Vernotte law; differential algebraic systems; Fourier law; hyperbolic heat conduction; solid phase transformations
Fields of Research : 01 Mathematical Sciences > 0101 Pure Mathematics > 010106 Lie Groups, Harmonic and Fourier Analysis
09 Engineering > 0912 Materials Engineering > 091207 Metals and Alloy Materials
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
Identification Number or DOI: 10.1007/s00466-002-0311-5

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