Aspects of computational homogenization at finite deformations: a unifying review from Reuss' to Voigt's Bound

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dc.citation.issueNumber5en_US
dc.citation.volumeNumber68en_US
dc.contributor.authorSaeb, S.en_US
dc.contributor.authorSteinmann, P.en_US
dc.contributor.authorJavili, A.en_US
dc.date.accessioned2018-04-12T13:51:53Z
dc.date.available2018-04-12T13:51:53Z
dc.date.issued2016en_US
dc.departmentDepartment of Mechanical Engineeringen_US
dc.description.abstractThe objective of this contribution is to present a unifying review on strain-driven computational homogenization at finite strains, thereby elaborating on computational aspects of the finite element method. The underlying assumption of computational homogenization is separation of length scales, and hence, computing the material response at the macroscopic scale from averaging the microscopic behavior. In doing so, the energetic equivalence between the two scales, the Hill Mandel condition, is guaranteed via imposing proper boundary conditions such as linear displacement, periodic displacement and antiperiodic traction, and constant traction boundary conditions. Focus is given on the finite element implementation of these boundary conditions and their influence on the overall response of the material. Computational frameworks for all canonical boundary conditions are briefly formulated in order to demonstrate similarities and differences among the various boundary conditions. Furthermore, we detail on the computational aspects of the classical Reuss' and Voigt's bounds and their extensions to finite strains. A concise and clear formulation for computing the macroscopic tangent necessary for FE2 calculations is presented. The performances of the proposed schemes are illustrated via a series of two- and three-dimensional numerical examples. The numerical examples provide enough details to serve as benchmarks. © 2016 by ASME.en_US
dc.description.provenanceMade available in DSpace on 2018-04-12T13:51:53Z (GMT). No. of bitstreams: 1 bilkent-research-paper.pdf: 179475 bytes, checksum: ea0bedeb05ac9ccfb983c327e155f0c2 (MD5) Previous issue date: 2016en
dc.identifier.doi10.1115/1.4034024en_US
dc.identifier.issn0003-6900
dc.identifier.urihttp://hdl.handle.net/11693/38262
dc.language.isoEnglishen_US
dc.publisherAmerican Society of Mechanical Engineers (ASME)en_US
dc.relation.isversionofhttp://dx.doi.org/10.1115/1.4034024en_US
dc.source.titleApplied Mechanics Reviewsen_US
dc.subjectComputational homogenizationen_US
dc.subjectFE2en_US
dc.subjectFinite strainsen_US
dc.subjectMultiscaleen_US
dc.subjectRandom compositeen_US
dc.subjectBoundary conditionsen_US
dc.subjectHomogenization methoden_US
dc.subjectStrainen_US
dc.subjectComputational frameworken_US
dc.titleAspects of computational homogenization at finite deformations: a unifying review from Reuss' to Voigt's Bounden_US
dc.typeReviewen_US

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