Random composite media: homogenization, modeling, simulation, and material symmetry

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dc.contributor.advisorRostamian, Rouben
dc.contributor.advisorRathinam, Muruhan
dc.contributor.authorAlexanderian, Alen
dc.contributor.departmentMathematics and Statistics
dc.contributor.programMathematics, Applied
dc.date.accessioned2015-10-14T03:11:49Z
dc.date.available2015-10-14T03:11:49Z
dc.date.issued2010-01-01
dc.description.abstractWe present a systematic study of homogenization of diffusive and elastic random media with emphasis on tile-based random microstructures. We give detailed examples of several such media starting from their physical descriptions, then construct the associated probability spaces and verify their ergodicity. After a discussion of material symmetries of random media, we derive criteria for the isotropy of their homogenized limits. Furthermore, we study the periodization algorithm for the numerical approximation of the homogenized diffusion tensor and study the algorithm's rate of convergence. For one-dimensional tile-based media, we prove a central limit result, giving a concrete rate of convergence for periodization. We also provide numerical evidence for a similar central limit behavior in the case of two dimensional tile-based structures. Moreover, we study symmetries of elastic random media, and develop a theory for analyzing questions of isotropy; this allows us to derive minimal conditions on a symmetry group of a linearly elastic material that implies its isotropy. A natural setting for the formulation and analysis is provided by the group representation theory where the necessary and sufficient conditions for isotropy are expressed in terms of the irreducibility of certain group representations. Our approach allows for deriving isotropy results in contexts of hyperelastic, non-hyperelastic and polar media. Our theory also allows us to rederive several known results under a unified theory.
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dc.identifierdoi:10.13016/M2ZQ2B
dc.identifier.other10331
dc.identifier.urihttp://hdl.handle.net/11603/1020
dc.languageen
dc.relation.isAvailableAtThe University of Maryland, Baltimore County (UMBC)
dc.relation.ispartofUMBC Theses and Dissertations Collection
dc.relation.ispartofUMBC Graduate School Collection
dc.relation.ispartofUMBC Student Collection
dc.relation.ispartofUMBC Mathematics and Statistics Department Collection
dc.rightsThis item may be protected under Title 17 of the U.S. Copyright Law. It is made available by UMBC for non-commercial research and education. For permission to publish or reproduce, please see http://aok.lib.umbc.edu/specoll/repro.php or contact Special Collections at speccoll(at)umbc.edu.
dc.sourceOriginal File Name: Alexanderian_umbc_0434D_10331.pdf
dc.subjectGroup representation
dc.subjectHomogenization
dc.subjectIsotropy
dc.subjectMaterial symmetry
dc.subjectRandom media
dc.subjectSchur's Lemma
dc.titleRandom composite media: homogenization, modeling, simulation, and material symmetry
dc.typeText
dcterms.accessRightsAccess limited to the UMBC community. Item may possibly be obtained via Interlibrary Loan through a local library, pending author/copyright holder's permission.

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