Aspects of implementing constant traction boundary conditions in computational homogenization via semi-Dirichlet boundary conditions

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dc.citation.epage35en_US
dc.citation.issueNumber1en_US
dc.citation.spage21en_US
dc.citation.volumeNumber59en_US
dc.contributor.authorJavili, A.en_US
dc.contributor.authorSaeb, S.en_US
dc.contributor.authorSteinmann, P.en_US
dc.date.accessioned2018-04-12T10:37:44Z
dc.date.available2018-04-12T10:37:44Z
dc.date.issued2017en_US
dc.departmentDepartment of Mechanical Engineeringen_US
dc.description.abstractIn the past decades computational homogenization has proven to be a powerful strategy to compute the overall response of continua. Central to computational homogenization is the Hill–Mandel condition. The Hill–Mandel condition is fulfilled via imposing displacement boundary conditions (DBC), periodic boundary conditions (PBC) or traction boundary conditions (TBC) collectively referred to as canonical boundary conditions. While DBC and PBC are widely implemented, TBC remains poorly understood, with a few exceptions. The main issue with TBC is the singularity of the stiffness matrix due to rigid body motions. The objective of this manuscript is to propose a generic strategy to implement TBC in the context of computational homogenization at finite strains. To eliminate rigid body motions, we introduce the concept of semi-Dirichlet boundary conditions. Semi-Dirichlet boundary conditions are non-homogeneous Dirichlet-type constraints that simultaneously satisfy the Neumann-type conditions. A key feature of the proposed methodology is its applicability for both strain-driven as well as stress-driven homogenization. The performance of the proposed scheme is demonstrated via a series of numerical examples. © 2016, Springer-Verlag Berlin Heidelberg.en_US
dc.description.provenanceMade available in DSpace on 2018-04-12T10:37:44Z (GMT). No. of bitstreams: 1 bilkent-research-paper.pdf: 179475 bytes, checksum: ea0bedeb05ac9ccfb983c327e155f0c2 (MD5) Previous issue date: 2017en_US
dc.identifier.doi10.1007/s00466-016-1333-8en_US
dc.identifier.eissn1432-0924
dc.identifier.issn0178-7675
dc.identifier.urihttp://hdl.handle.net/11693/36370
dc.language.isoEnglishen_US
dc.publisherSpringer Verlagen_US
dc.relation.isversionofhttp://dx.doi.org/10.1007/s00466-016-1333-8en_US
dc.source.titleComputational Mechanicsen_US
dc.subjectComputational homogenizationen_US
dc.subjectConstant traction boundary conditionsen_US
dc.subjectFinite strainsen_US
dc.subjectSemi-Dirichlet boundary conditionsen_US
dc.titleAspects of implementing constant traction boundary conditions in computational homogenization via semi-Dirichlet boundary conditionsen_US
dc.typeArticleen_US

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