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A Concept for the Extension of the Assumed Stress Finite Element Method to Hyperelasticity

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Novel Finite Element Technologies for Solids and Structures

Part of the book series: CISM International Centre for Mechanical Sciences ((CISM,volume 597))

Abstract

The proposed work extends the well-known assumed stress elements to the framework of hyperelasticity. In order to obtain the constitutive relationship, a nonlinear set of equations is solved implicitly on element level. A numerical verification, where two assumed stress elements are compared to classical enhanced assumed strain elements, depicts the reliability and efficiency of the proposed concept. This work is closely related to the publication of Viebahn et al. (2019)

The financial support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) is gratefully acknowledged - 255432295.

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Author information

Authors and Affiliations

  1. Department of Civil Engineering, Faculty of Engineering, Institute of Mechanics, University of Duisburg-Essen, Essen, Germany

    Nils Viebahn & Jörg Schröder

  2. Faculty of Mechanical Engineering, Institute of Continuum Mechanics, Leibniz Universität Hannover, Hanover, Germany

    Peter Wriggers

Authors
  1. Nils Viebahn
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  2. Jörg Schröder
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  3. Peter Wriggers
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Correspondence to Nils Viebahn .

Editor information

Editors and Affiliations

  1. Faculty of Engineering, University of Duisburg-Essen, Essen, Germany

    Jörg Schröder

  2. Polytechnic School, University of São Paulo, São Paulo, Brazil

    Paulo de Mattos Pimenta

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Viebahn, N., Schröder, J., Wriggers, P. (2020). A Concept for the Extension of the Assumed Stress Finite Element Method to Hyperelasticity. In: Schröder, J., de Mattos Pimenta, P. (eds) Novel Finite Element Technologies for Solids and Structures. CISM International Centre for Mechanical Sciences, vol 597. Springer, Cham. https://doi.org/10.1007/978-3-030-33520-5_4

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  • DOI: https://doi.org/10.1007/978-3-030-33520-5_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-33519-9

  • Online ISBN: 978-3-030-33520-5

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