Well-posedness and finite dimensional approximations of a mathematical model for the dynamics of shape-memory alloys

Ruben D. Spies

doi:10.1117/12.148432

22 July 1993 Well-posedness and finite dimensional approximations of a mathematical model for the dynamics of shape-memory alloys

Ruben D. Spies

Author Affiliations +

Proceedings Volume 1919, Smart Structures and Materials 1993: Mathematics in Smart Structures; (1993) https://doi.org/10.1117/12.148432
Event: 1993 North American Conference on Smart Structures and Materials, 1993, Albuquerque, NM, United States

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.

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Ruben D. Spies "Well-posedness and finite dimensional approximations of a mathematical model for the dynamics of shape-memory alloys", Proc. SPIE 1919, Smart Structures and Materials 1993: Mathematics in Smart Structures, (22 July 1993); https://doi.org/10.1117/12.148432

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