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Numerical evaluation of discontinuous and nonconforming finite element methods in nonlinear solid mechanics

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Abstract

This work presents a systematic study of discontinuous and nonconforming finite element methods for linear elasticity, finite elasticity, and small strain plasticity. In particular, we consider new hybrid methods with additional degrees of freedom on the skeleton of the mesh and allowing for a local elimination of the element-wise degrees of freedom. We show that this process leads to a well-posed approximation scheme. The quality of the new methods with respect to locking and anisotropy is compared with standard and in addition locking-free conforming methods as well as established (non-) symmetric discontinuous Galerkin methods with interior penalty. For several benchmark configurations, we show that all methods converge asymptotically for fine meshes and that in many cases the hybrid methods are more accurate for a fixed size of the discrete system.

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Acknowledgements

The authors gratefully acknowledge the support of the Deutsche Forschungsgemeinschaft within the Priority Program 1748 “Reliable simulation techniques in solid mechanics. Development of non-standard discretization methods, mechanical and mathematical analysis” in the Projects RE 1057/30-1, WI 1430/8-1 and WO 671/15-1, and partially by WO 671/11-1.

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Authors and Affiliations

  1. Institute of Applied Mechanics, RWTH Aachen, Mies-van-der-Rohe-Str. 1, 52074, Aachen, Germany

    Hamid Reza Bayat, Stephan Wulfinghoff & Stefanie Reese

  2. Institute for Numerical Mathematics (M2), TU München, 85748, Garching b. München, Germany

    Linus Wunderlich & Barbara Wohlmuth

  3. Institute for Applied and Numerical Mathematics, KIT Karlsruhe, Englerstr. 2, 76131, Karlsruhe, Germany

    Julian Krämer & Christian Wieners

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  1. Hamid Reza Bayat
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  2. Julian Krämer
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  3. Linus Wunderlich
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  4. Stephan Wulfinghoff
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  6. Barbara Wohlmuth
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  7. Christian Wieners
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Correspondence to Hamid Reza Bayat.

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Bayat, H.R., Krämer, J., Wunderlich, L. et al. Numerical evaluation of discontinuous and nonconforming finite element methods in nonlinear solid mechanics. Comput Mech 62, 1413–1427 (2018). https://doi.org/10.1007/s00466-018-1571-z

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  • DOI: https://doi.org/10.1007/s00466-018-1571-z

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