A stiffness derivative local hypercomplex-variable finite element method for computing the energy release rate

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dc.citation.journalTitleENGINEERING FRACTURE MECHANICS
dc.contributor.authorAguirre-Mesa A.M.
dc.contributor.authorRamirez-Tamayo D.
dc.contributor.authorGarcia M.J.
dc.contributor.authorMontoya A.
dc.contributor.authorMillwater H.
dc.contributor.researchgroupMecánica Aplicadaspa
dc.date.accessioned2021-04-16T20:10:42Z
dc.date.available2021-04-16T20:10:42Z
dc.date.issued2019-01-01
dc.description.abstractA “local” hypercomplex-variable finite element method, L-ZFEM, is proposed for the computation of the energy release rate (ERR) using the stiffness derivative equation. This approach is analogous to the stiffness derivative method proposed by Parks and Hellen but has superior numerical accuracy. In addition, this method is significantly more efficient than the previously published “global” hypercomplex-variable finite element method, ZFEM, in that the global hypercomplex system of FE equations is not assembled nor solved. Instead, the displacement field is computed using a traditional, real-valued finite element method, and the numerical derivative of the stiffness matrix at the element level is only computed for a group of local, surrounding elements to the crack tip by using a Taylor series expansion based on complex numbers or dual numbers. The ERR is then determined as a sum of the element contributions. Derivatives of the ERR with respect to an arbitrary model parameter such as a crack extension, material property, or geometric feature are also available using a combination of the global and local methods, GL-ZFEM. Both L-ZFEM and GL-ZFEM were implemented into the commercial finite element software Abaqus through user defined element subroutines. Numerical results show that the ERR obtained by L-ZFEM has the same accuracy as that estimated through the global ZFEM or the J-integral methods but exhibits superior computational efficiency. © 2019 Elsevier Ltdeng
dc.identifierhttps://eafit.fundanetsuite.com/Publicaciones/ProdCientif/PublicacionFrw.aspx?id=9854
dc.identifier.doi10.1016/j.engfracmech.2019.106581
dc.identifier.issn00137944
dc.identifier.issn18737315
dc.identifier.otherWOS;000483383200018
dc.identifier.otherSCOPUS;2-s2.0-85070621827
dc.identifier.urihttp://hdl.handle.net/10784/29221
dc.language.isoengeng
dc.publisherElsevier BV
dc.publisher.departmentUniversidad EAFIT. Departamento de Ingeniería Mecánicaspa
dc.relation.urihttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85070621827&doi=10.1016%2fj.engfracmech.2019.106581&partnerID=40&md5=9417c5bb20e1b91eb3be7d7dfc08986c
dc.rightshttps://v2.sherpa.ac.uk/id/publication/issn/0013-7944
dc.sourceENGINEERING FRACTURE MECHANICS
dc.subject.keywordABAQUSeng
dc.subject.keywordComputational efficiencyeng
dc.subject.keywordCrack tipseng
dc.subject.keywordEnergy release rateeng
dc.subject.keywordNumerical methodseng
dc.subject.keywordStiffnesseng
dc.subject.keywordStiffness matrixeng
dc.subject.keywordSubroutineseng
dc.subject.keywordTaylor serieseng
dc.subject.keywordComplex taylor series expansionseng
dc.subject.keywordComplex variable finite elementseng
dc.subject.keywordDerivative methodeng
dc.subject.keywordHypercomplexeng
dc.subject.keywordJ integraleng
dc.subject.keywordFinite element methodeng
dc.titleA stiffness derivative local hypercomplex-variable finite element method for computing the energy release rateeng
dc.typeinfo:eu-repo/semantics/articleeng
dc.typearticleeng
dc.typeinfo:eu-repo/semantics/publishedVersioneng
dc.typepublishedVersioneng
dc.type.localArtículospa

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