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22 July 1993 Well-posedness and finite dimensional approximations of a mathematical model for the dynamics of shape-memory alloys
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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.
© (1993) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
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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