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Proceedings Paper

Well-posedness and finite dimensional approximations of a mathematical model for the dynamics of shape-memory alloys
Author(s): Ruben D. Spies
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Paper Abstract

Shape Memory Alloys (SMA's) are intermetallic materials (chemical compounds of two or more elements) that are able to sustain a residual deformation after the application of a large stress, but they 'remember' the original shape to which they creep back, without the application of any external force, after they are heated above a certain critical temperature. We present here a general one-dimensional dynamic mathematical model which reflects the balance laws for linear momentum and energy. The system accounts for thermal coupling, time-dependent distributed and boundary inputs and internal variables. Well-posedness is obtained using an abstract formulation in an appropriate Hilbert space and explicit decay rates for the associated linear semigroup are derived. Numerical experiments using finite- dimensional approximations are performed for the case in which the thermodynamic potential is given in the Landau-Devonshire form. The sensitivity of the solutions with respect to the model parameters is studied.

Paper Details

Date Published: 22 July 1993
PDF: 13 pages
Proc. SPIE 1919, Smart Structures and Materials 1993: Mathematics in Smart Structures, (22 July 1993); doi: 10.1117/12.148432
Show Author Affiliations
Ruben D. Spies, Univ. of Minnesota/Twin Cities (Argentina)

Published in SPIE Proceedings Vol. 1919:
Smart Structures and Materials 1993: Mathematics in Smart Structures
H. Thomas Banks, Editor(s)

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