Spies, Ruben Daniel2014-03-142014-03-141992etd-06062008-165948http://hdl.handle.net/10919/38367Shape 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. A general one-dimensional dynamic mathematical model is presented which 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. Finally, an alternative approach to the stress-strain laws is presented which is able to capture the dependence on the strain history.iv, 159 leavesBTDapplication/pdfenIn CopyrightLD5655.V856 1992.S672Alloys -- Testing -- Mathematical modelsPhase transformations (Statistical physics)Shape memory effect -- Mathematical modelsDissertationhttp://scholar.lib.vt.edu/theses/available/etd-06062008-165948/