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.
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. / Ph. D.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/38367 |
| Date | 06 June 2008 |
| Creators | Spies, Ruben Daniel |
| Contributors | Mathematics, Burns, John A., Cliff, Eugene M., Herdman, Terry L., Hannsgen, Kenneth B., Wheeler, Robert |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | English |
| Detected Language | English |
| Type | Dissertation, Text |
| Format | iv, 159 leaves, BTD, application/pdf, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | OCLC# 26650120, LD5655.V856_1992.S672.pdf |
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