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Novel Finite Elements - Mixed, Hybrid and Virtual Element Formulations at Finite Strains for 3D Applications

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Non-standard Discretisation Methods in Solid Mechanics

Part of the book series: Lecture Notes in Applied and Computational Mechanics ((LNACM,volume 98))

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Abstract

The main goal of this research project is to develop new finite-element formulations as a suitable basis for the stable calculation of modern isotropic and anisotropic materials with a complex nonlinear material behavior. New ideas are pursued in a strict variational framework, based either on a mixed or virtual FE approach. A novel extension of the classical Hellinger-Reissner formulation to non-linear applications is developed. Herein, the constitutive relation of the interpolated stresses and strains is determined with help of an iterative procedure. The extension of the promising virtual finite element method (VEM) is part of the further investigation. Particularly, different stabilization methods are investigated in detail, needed in the framework of complex nonlinear constitutive behavior. Furthermore the interpolation functions for the VEM is extended from linear to quadratic functions to obtain better convergence rates. Especially in this application the flexibility of the VEM regarding the mesh generation will constitute a huge benefit. As a common software development platform the AceGen environment is applied providing a flexible tool for the generation of efficient finite element code.

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Acknowledgements

The authors gratefully acknowledge the support by the Deutsche Forschungsgemeinschaft in the Priority Program 1748 “Reliable Simulation Techniques in Solid Mechanics, Development of Non-standard Discretization Methods, Mechanical and Mathematical Analysis” for the project “Novel finite elements for anisotropic media at finite strain” (Project number: 255432295, IDs: WR 19/50-1, SCHR 570/23-1).

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Authors and Affiliations

  1. Institute of Mechanics, University Duisburg-Essen, Duisburg, Germany

    Jörg Schröder & Nils Viebahn

  2. Institute of Continuum Mechanics, Leibniz Universität Hannover, Hannover, Germany

    Peter Wriggers & Alex Kraus

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  1. Jörg Schröder
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  2. Peter Wriggers
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  3. Alex Kraus
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  4. Nils Viebahn
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Correspondence to Jörg Schröder .

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Editors and Affiliations

  1. Institute of Mechanics, University of Duisburg-Essen, Essen, Germany

    Jörg Schröder

  2. Institute of Continuum Mechanics, Leibniz Universität Hannover, Hannover, Germany

    Peter Wriggers

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Schröder, J., Wriggers, P., Kraus, A., Viebahn, N. (2022). Novel Finite Elements - Mixed, Hybrid and Virtual Element Formulations at Finite Strains for 3D Applications. In: Schröder, J., Wriggers, P. (eds) Non-standard Discretisation Methods in Solid Mechanics. Lecture Notes in Applied and Computational Mechanics, vol 98. Springer, Cham. https://doi.org/10.1007/978-3-030-92672-4_2

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  • DOI: https://doi.org/10.1007/978-3-030-92672-4_2

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