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

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.


Statistics for USQ ePrint 2985
Statistics for this ePrint Item
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.
Depositing User: epEditor USQ
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 (FOR2008): 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 (SEO2008): E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
Identification Number or DOI: doi: 10.1007/s00466-002-0311-5
URI: http://eprints.usq.edu.au/id/eprint/2985

Actions (login required)

View Item Archive Repository Staff Only