A finite deformation isogeometric finite element approach to fibre-reinforced composites with fibre bending stiffness

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dc.contributor.authorWitt, Carina
dc.contributor.authorKaiser, Tobias
dc.contributor.authorMenzel, Andreas
dc.date.accessioned2022-03-29T13:27:24Z
dc.date.available2022-03-29T13:27:24Z
dc.date.issued2021-05-28
dc.description.abstractIt is a common technique in many fields of engineering to reinforce materials with certain types of fibres in order to enhance the mechanical properties of the overall material. Specific simulation methods help to predict the behaviour of these composites in advance. In this regard, a widely established approach is the incorporation of the fibre direction vector as an additional argument of the energy function in order to capture the specific material properties in the fibre direction. While this model represents the transverse isotropy of a material, it cannot capture effects that result from a bending of the fibres and does not include any length scale that might allow the simulation of size effects. In this contribution, an enhanced approach is considered which relies on the introduction of higher-gradient contributions of the deformation map in the stored energy density function and which eventually allows accounting for fibre bending stiffness in simulations. The respective gradient fields are approximated by NURBS basis functions within an isogeometric finite element framework by taking advantage of their characteristic continuity properties. The isogeometric finite element approach that is presented in this contribution for fibre-reinforced composites with fibre bending stiffness accounts for finite deformations. It is shown that the proposed method is in accordance with semi-analytical solutions for a representative boundary value problem. In an additional example it is observed that the initial fibre orientation and the particular bending stiffness of the fibres influence the deformation as well as the stress response of the material.en
dc.identifier.urihttp://hdl.handle.net/2003/40834
dc.identifier.urihttp://dx.doi.org/10.17877/DE290R-22691
dc.language.isoende
dc.relation.ispartofseriesJournal of engineering mathematics;Vol. 128. 2021, Art. No: 15
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.subjectAnisotropic elasticityen
dc.subjectFibre bending stiffnessen
dc.subjectFibre curvatureen
dc.subjectFinite deformationsen
dc.subjectFibre stretch gradienten
dc.subjectGeneralised continuumen
dc.subjectIsogeometric analysisen
dc.subject.ddc620
dc.subject.ddc670
dc.subject.rswkFaserverbundwerkstoffde
dc.subject.rswkFinite-Elemente-Methodede
dc.subject.rswkBiegungde
dc.subject.rswkSteifigkeitde
dc.subject.rswkKrümmungde
dc.subject.rswkDeformationde
dc.subject.rswkDehnungde
dc.subject.rswkKontinuum <Mathematik>de
dc.subject.rswkIsogeometrische Analysede
dc.titleA finite deformation isogeometric finite element approach to fibre-reinforced composites with fibre bending stiffnessen
dc.typeTextde
dc.type.publicationtypearticlede
dcterms.accessRightsopen access
eldorado.secondarypublicationtruede
eldorado.secondarypublication.primarycitationJournal of engineering mathematics. Vol. 128. 2021, Art. No: 15en
eldorado.secondarypublication.primaryidentifierhttps://doi.org/10.1007/s10665-021-10117-3de

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