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

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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

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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.
License of this version: 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.
Document Type: article
Publishing status: publishedVersion
Issue Date: 2008
Appears in Collections:Fakultät für Maschinenbau

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1 image of flag of Germany Germany 75 51.02%
2 image of flag of Korea, Republic of Korea, Republic of 13 8.84%
3 image of flag of United States United States 9 6.12%
4 image of flag of China China 8 5.44%
5 image of flag of India India 6 4.08%
6 image of flag of France France 6 4.08%
7 image of flag of United Kingdom United Kingdom 5 3.40%
8 image of flag of Japan Japan 4 2.72%
9 image of flag of Czech Republic Czech Republic 3 2.04%
10 image of flag of Netherlands Netherlands 2 1.36%
    other countries 16 10.88%

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