Convergence behavior of 3D finite elements for Neo-Hookean material

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dc.identifier.uri http://dx.doi.org/10.15488/2721
dc.identifier.uri http://www.repo.uni-hannover.de/handle/123456789/2747
dc.contributor.author Stein, Erwin
dc.contributor.author Sagar, Gautam
dc.date.accessioned 2018-02-09T08:47:12Z
dc.date.available 2018-02-09T08:47:12Z
dc.date.issued 2008
dc.identifier.citation Stein, E.; Sagar, G.: Convergence behavior of 3D finite elements for Neo-Hookean material. In: Engineering Computations (Swansea, Wales) 25 (2008), Nr. 3, S. 220-232. DOI: https://doi.org/10.1108/02644400810857065
dc.description.abstract Purpose: The purpose of this paper is to examine quadratic convergence of finite element analysis for hyperelastic material at finite strains via Abaqus-UMAT as well as classification of the rates of convergence for iterative solutions in regular cases. Design/methodology/approach: Different formulations for stiffness - Hessian form of the free energy functionals - are systematically given for getting the rate-independent analytical tangent and the numerical tangent as well as rate-dependent tangents using the objective Jaumann rate of Kirchoff stress tensor as used in Abaqus. The convergence rates for available element types in Abaqus are computed and compared for simple but significant nonlinear elastic problems, such as using the 8-node linear brick (B-bar) element - also with hybrid pressure formulation and with incompatible modes - further the 20-node quadratic brick element with corresponding modifications as well as the 6-node linear triangular prism element and 4-node linear tetrahedral element with modifications. Findings: By using the Jaumann rate of Kirchoff stress tensor for both, rate dependent and rate independent problems, quadratic or nearly quadratic convergence is achieved for most of the used elements using Abaqus-UMAT interface. But in case of using rate independent analytical tangent for rate independent problems, even convergence at all is not assured for all elements and the considered problems. Originality/value: First time the convergence properties of 3D finite elements available in Abaqus sre systematically treated for elastic material at finite strain via Abaqus-UMAT. © Emerald Group Publishing Limited. eng
dc.language.iso eng
dc.publisher Bingley : Emerald Group Publishing Ltd.
dc.relation.ispartofseries Engineering Computations (Swansea, Wales) 25 (2008), Nr. 3
dc.rights Es gilt deutsches Urheberrecht. Das Dokument darf zum eigenen Gebrauch kostenfrei genutzt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. Dieser Beitrag ist aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich.
dc.subject Alloys eng
dc.subject Finite element analysis eng
dc.subject Kinematics eng
dc.subject ABAQUS eng
dc.subject Convergence of numerical methods eng
dc.subject Elasticity eng
dc.subject Finite element method eng
dc.subject Nonlinear equations eng
dc.subject Strain rate eng
dc.subject Hyperelastic materials eng
dc.subject Neo-Hookean material eng
dc.subject Nonlinear elastic problems eng
dc.subject Rate independent problems eng
dc.subject Materials science eng
dc.subject.ddc 620 | Ingenieurwissenschaften und Maschinenbau ger
dc.title Convergence behavior of 3D finite elements for Neo-Hookean material
dc.type article
dc.type Text
dc.relation.issn 0264-4401
dc.relation.doi https://doi.org/10.1108/02644400810857065
dc.bibliographicCitation.issue 3
dc.bibliographicCitation.volume 25
dc.bibliographicCitation.firstPage 220
dc.bibliographicCitation.lastPage 232
dc.description.version publishedVersion
tib.accessRights frei zug�nglich


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