Mathematical modelling, finite dimensional approximations and sensitivity analysis for phase transitions in shape memory alloys

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dc.contributor.authorSpies, Ruben Danielen
dc.contributor.committeechairBurns, John A.en
dc.contributor.committeememberCliff, Eugene M.en
dc.contributor.committeememberHerdman, Terry L.en
dc.contributor.committeememberHannsgen, Kenneth B.en
dc.contributor.committeememberWheeler, Roberten
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T21:14:03Zen
dc.date.adate2008-06-06en
dc.date.available2014-03-14T21:14:03Zen
dc.date.issued1992en
dc.date.rdate2008-06-06en
dc.date.sdate2008-06-06en
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.description.degreePh. D.en
dc.format.extentiv, 159 leavesen
dc.format.mediumBTDen
dc.format.mimetypeapplication/pdfen
dc.identifier.otheretd-06062008-165948en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-06062008-165948/en
dc.identifier.urihttp://hdl.handle.net/10919/38367en
dc.language.isoenen
dc.publisherVirginia Techen
dc.relation.haspartLD5655.V856_1992.S672.pdfen
dc.relation.isformatofOCLC# 26650120en
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.type.dcmitypeTexten
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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