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Advances in Computational Plasticity pp 417–434Cite as

Efficient Low Order Virtual Elements for Anisotropic Materials at Finite Strains

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Part of the book series: Computational Methods in Applied Sciences ((COMPUTMETHODS,volume 46))

Abstract

Virtual elements were introduced in the last decade and applied to problems in solid mechanics. The success of this methodology when applied to linear problems asks for an extension to the nonlinear regime. This work is concerned with the numerical simulation of structures made of anisotropic material undergoing large deformations. Especially problems with hyperelastic matrix materials and transversly isotropic behaviour will be investigated. The virtual element formulation is based on a low-order formulations for problems in two dimensions. The elements can be arbitrary polygons. The formulation considered relies on minimization of energy, with a novel construction of the stabilization energy and a mixed approximation for the fibers describing the anisotropic behaviour. The formulation is investigated through a several numerical examples, which demonstrate their efficiency, robustness, convergence properties, and locking-free behaviour.

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Acknowledgements

The paper is a contribution to honor Professor Roger Owen on behalf of his 75th birthday. The authors like to thank Roger Owen for his continuous support and friendship throughout the last four decades of research on finite element methods. The first author would like to thank for the support of the DFG within the priority program SPP 1748 1748 ‘Reliable simulation techniques in solid mechanics: Development of non-standard discretization methods, mechanical and mathematical analysis’ under the project WR 19/50-1.

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Authors and Affiliations

  1. Leibniz Universität Hannover, Hannover, Germany

    P. Wriggers & B. Hudobivnik

  2. University of Ljubljana, Ljubljana, Slovenia

    J. Korelc

Authors
  1. P. Wriggers
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  2. B. Hudobivnik
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  3. J. Korelc
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Corresponding author

Correspondence to P. Wriggers .

Editor information

Editors and Affiliations

  1. CIMNE, Universitat Politècnica de Catalunya, Barcelona, Spain

    Eugenio Oñate

  2. Swansea University, Swansea, United Kingdom

    Djordje Peric

  3. Swansea University, Swansea, United Kingdom

    Eduardo de Souza Neto

  4. CIMNE, Universitat Politècnica de Catalunya, Barcelona, Spain

    Michele Chiumenti

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Wriggers, P., Hudobivnik, B., Korelc, J. (2018). Efficient Low Order Virtual Elements for Anisotropic Materials at Finite Strains. In: Oñate, E., Peric, D., de Souza Neto, E., Chiumenti, M. (eds) Advances in Computational Plasticity. Computational Methods in Applied Sciences, vol 46. Springer, Cham. https://doi.org/10.1007/978-3-319-60885-3_20

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  • DOI: https://doi.org/10.1007/978-3-319-60885-3_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-60884-6

  • Online ISBN: 978-3-319-60885-3

  • eBook Packages: EngineeringEngineering (R0)

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