Effect of Defects, Inclusions and Inhomogeneities in Elastic Solids

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dc.contributor.advisorFederico, Salvatore
dc.contributor.authorAlhasadi, Mawafag F.
dc.contributor.committeememberEpstein, M.
dc.contributor.committeememberLi, Leping
dc.contributor.committeememberWan, Richard
dc.contributor.committeememberRu, Chongqing
dc.date2020-06
dc.date.accessioned2019-12-12T20:38:01Z
dc.date.available2019-12-12T20:38:01Z
dc.date.issued2019-12
dc.description.abstractThis thesis focusses on the theory of materials with defects introduced by John D. Eshelby in the 50s and the 60s, which today we call Configurational Mechanics or, in his honour, Eshelbian Mechanics. The thesis consists of four interconnected parts. The first part is dedicated to the relation between two of Eshelby’s developments: the energy momentum tensor (or Eshelby stress tensor), describing the net force on a defect, and the Eshelby fourth-order tensor, which relates the strain in an inclusion in an otherwise homogeneous and isotropic matrix to the virtual strain (transformation strain) defining the geometrical misfit between inclusion and matrix, within the theory of small deformations. The second part of the research was prompted by the fact that, although the relation between Eshelby’s inclusion problem (Eshelby, 1951, 1975) and Noether’s theorem has been mentioned in literature, no explicit relation has ever been given, to the best of our knowledge. In a framework based on modern differential geometry, it is shown that the application of Noether’s theorem allows for straightforwardly obtaining the classical results by (Eshelby, 1951, 1975). The third part of the thesis aims at investigating the work of Eshelby (1951, 1975) on configurational forces and of Noll (1967) on material uniformity within a general framework including thermo-elasticity, volumetric growth inertial effects, in which the divergence of the Eshelby stress is called the Eshelby force. A differential identity is obtained for the modified Eshelby stress, which includes, as a particular case, the identity found by Epstein and Maugin (1990). Moreover, a differential identity is obtained for what is called the modified Eshelby power, representing the time counterpart of the Eshelby force. Then, a relation between the modified Eshelby force and the modified Eshelby power is derived in the dynamical case. Finally, based on the results obtained in the previous parts of the research, a large-deformation counterpart is proposed of the imagined procedure that Eshelby (1957) used to investigate the theory of inclusions in the case of infinitesimal deformations. A mixed multiplicative decomposition of the deformation gradient, in terms of the Bilby-Kröner-Lee and the Noll-Epstein-Maugin decompositions allows for obtaining the large-deformation fourth-order Eshelby tensor, a novel result.en_US
dc.identifier.citationAlhasadi, M. F. (2019). Effect of Defects, Inclusions and Inhomogeneities in Elastic Solids (Doctoral thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca.en_US
dc.identifier.doihttp://dx.doi.org/10.11575/PRISM/37332
dc.identifier.urihttp://hdl.handle.net/1880/111336
dc.language.isoengen_US
dc.publisher.facultySchulich School of Engineeringen_US
dc.publisher.institutionUniversity of Calgaryen
dc.rightsUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.en_US
dc.subjectEllipsoidal inclusionen_US
dc.subjectEshelby stressen_US
dc.subjectEshelby fourth-order tensoren_US
dc.subjectMaterial uniformityen_US
dc.subjectNoether's theoremen_US
dc.subject.classificationApplied Mechanicsen_US
dc.subject.classificationEngineeringen_US
dc.subject.classificationEngineering--Mechanicalen_US
dc.titleEffect of Defects, Inclusions and Inhomogeneities in Elastic Solidsen_US
dc.typedoctoral thesisen_US
thesis.degree.disciplineEngineering – Mechanical & Manufacturingen_US
thesis.degree.grantorUniversity of Calgaryen_US
thesis.degree.nameDoctor of Philosophy (PhD)en_US
ucalgary.item.requestcopytrueen_US
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