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dc.contributor.authorSpies, Ruben Danielen
dc.date.accessioned2014-03-14T21:14:03Zen
dc.date.available2014-03-14T21:14:03Zen
dc.date.issued1992en
dc.identifier.otheretd-06062008-165948en
dc.identifier.urihttp://hdl.handle.net/10919/38367en
dc.description.abstractShape 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.en
dc.format.extentiv, 159 leavesen
dc.format.mediumBTDen
dc.format.mimetypeapplication/pdfen
dc.language.isoenen
dc.publisherVirginia Techen
dc.relation.isformatofOCLC# 26650120en
dc.relation.haspartLD5655.V856_1992.S672.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.lccLD5655.V856 1992.S672en
dc.subject.lcshAlloys -- Testing -- Mathematical modelsen
dc.subject.lcshPhase transformations (Statistical physics)en
dc.subject.lcshShape memory effect -- Mathematical modelsen
dc.titleMathematical modelling, finite dimensional approximations and sensitivity analysis for phase transitions in shape memory alloysen
dc.typeDissertationen
dc.contributor.departmentMathematicsen
dc.description.degreePh. D.en
thesis.degree.namePh. D.en
thesis.degree.leveldoctoralen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.disciplineMathematicsen
dc.type.dcmitypeTexten
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-06062008-165948/en
dc.date.sdate2008-06-06en
dc.date.rdate2008-06-06en
dc.date.adate2008-06-06en


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