Continuous modelling of single layer 2D carbonnanostructures based on a modified Cauchy–Born rule

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dc.date.accessioned2023-11-01T14:41:53Z
dc.date.available2023-11-01T14:41:53Z
dc.date.issued2023-09-08
dc.description.sponsorshipGefördert im Rahmen des Projekts DEALger
dc.identifierdoi:10.17170/kobra-202311018935
dc.identifier.urihttp://hdl.handle.net/123456789/15139
dc.language.isoengger
dc.relation.doidoi:10.1002/pamm.202300197
dc.rightsNamensnennung-Nicht-kommerziell 4.0 International*
dc.rights.urihttp://creativecommons.org/licenses/by-nc/4.0/*
dc.subjectCauchy–Born hypothesiseng
dc.subjectextension Cauchy–Born hypothesiseng
dc.subjectgraphene-based nanostructureseng
dc.subjecthomogenisationeng
dc.subjectReissner–Mindlin shell elementeng
dc.subject.ddc510
dc.subject.swdFestkörpermechanikger
dc.subject.swdKristallgitterger
dc.subject.swdMindlin-Reissner plate theoryger
dc.subject.swdNanostrukturger
dc.titleContinuous modelling of single layer 2D carbonnanostructures based on a modified Cauchy–Born ruleeng
dc.typeAufsatz
dc.type.versionpublishedVersion
dcterms.abstractGraphene is the thinnest known structure. It consists of a single layer of carbon atoms and has unique mechanical properties. The carbon atoms form bonds with neighbouring atoms that can be described by interatomic potentials. A simulation of molecular mechanical processes can be performed by applying the formalism of the finite element method to the interatomic potentials. Neglecting local effects, a continuum formulation is an efficient alternative to a discrete model. The continuum formulation requires a connection between the discrete atomic lattice and the continuum. One way of doing this is to use the Cauchy–Born rule. This paper reviews the extensions of the Cauchy–Born rule, in particular, the exponential Cauchy–Born rule, and adds an alternative approach. It is shown that all contributions dealing with the exponential Cauchy–Born rule inevitably lead to shell models with Kirchhoff–Love kinematics. The approach presented here instead uses a shell model with Reissner–Mindlin kinematics, which has the major advantage of a much simpler mesh generation and a simpler application of the boundary condition.eng
dcterms.accessRightsopen access
dcterms.creatorOchs, Julian
dcterms.creatorWackerfuß, Jens
dcterms.extent9 Seiten
dcterms.source.articlenumbere202300197
dcterms.source.identifiereissn:1617-7061
dcterms.source.issueIssue 2
dcterms.source.journalProceedings in applied mathematics and mechanics : PAMMeng
dcterms.source.volumeVolume 23
kup.iskupfalse

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