Bifurcation behavior of compressible elastic half-space under plane deformations

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buir.contributor.authorBakiler, A. Derya
buir.contributor.authorJavili, Ali
dc.citation.epage103553-13en_US
dc.citation.spage103553-1en_US
dc.citation.volumeNumber126en_US
dc.contributor.authorBakiler, A. Derya
dc.contributor.authorJavili, Ali
dc.date.accessioned2021-02-24T08:36:52Z
dc.date.available2021-02-24T08:36:52Z
dc.date.issued2020
dc.departmentDepartment of Mechanical Engineeringen_US
dc.description.abstractA finitely deformed elastic half-space subject to compressive stresses will experience a geometric instability at a critical level and exhibit bifurcation. While the bifurcation of an incompressible elastic half-space is commonly studied, the bifurcation behavior of a compressible elastic half-space remains elusive and poorly understood to date. The main objective of this manuscript is to study the bifurcation of a neo-Hookean compressible elastic half-space against the well-established incompressible case. The formulation of the problem requires a novel description for a non-linear Poisson’s ratio, since the commonly accepted definitions prove insufficient for the current analysis. To investigate the stability of the domain and the possibility of bifurcation, an incremental analysis is carried out. The incremental analysis describes a small departure from an equilibrium configuration at a finite deformation. It is shown that at the incompressibility limit, our results obtained for a compressible elastic half-space recover their incompressible counterparts. Another key feature of this contribution is that we verify the analytical solution of this problem with computational simulations using the finite element method via an eigenvalue analysis. The main outcome of this work is an analytical expression for the critical stretch where bifurcation arises. We demonstrate the utility of our model and its excellent agreement with the numerical results ranging from fully compressible to incompressible elasticity. Moving forward, this approach can be used to comprehend and harness the instabilities in bilayer systems, particularly for compressible ones.en_US
dc.embargo.release2022-11-01
dc.identifier.doi10.1016/j.ijnonlinmec.2020.103553en_US
dc.identifier.issn0020-7462
dc.identifier.urihttp://hdl.handle.net/11693/75549
dc.language.isoEnglishen_US
dc.publisherElsevieren_US
dc.relation.isversionofhttps://dx.doi.org/10.1016/j.ijnonlinmec.2020.103553en_US
dc.source.titleInternational Journal of Non-Linear Mechanicsen_US
dc.subjectInstabilitiesen_US
dc.subjectCompressible elasticityen_US
dc.subjectBifurcation of half-spaceen_US
dc.subjectNon-linear Poisson’s ratioen_US
dc.titleBifurcation behavior of compressible elastic half-space under plane deformationsen_US
dc.typeArticleen_US

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