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|Title:||Phase transitions in shape memory alloys with hyperbolic heat conduction and differential-algebraic models|
|Citation:||Computational Mechanics, 2002; 29(1):16-26|
|R. V. N. Melnik, A. J. Roberts, K. A. Thomas|
|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 low 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.|
Shape memory alloys
Hyperbolic heat conduction
|Appears in Collections:||Aurora harvest|
Mathematical Sciences publications
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