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Weak imposition of frictionless contact constraints on automatically recovered high-order, embedded interfaces using the finite cell method

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Abstract

The finite cell method (FCM) is a fictitious domain approach that greatly simplifies simulations involving complex structures. Recently, the FCM has been applied to contact problems. The current study continues in this field by extending the concept of weakly enforced boundary conditions to inequality constraints for frictionless contact. Furthermore, it formalizes an approach that automatically recovers high-order contact surfaces of (implicitly defined) embedded geometries by means of an extended Marching Cubes algorithm. To further improve the accuracy of the discretization, irregularities at the boundary of contact zones are treated with multi-level \(hp\)-refinements. Numerical results and a systematic study of h-, p- and hp-refinements show that the FCM can efficiently provide accurate results for problems involving contact.

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Notes

  1. We consider healing and simplification of geometries to be part of mesh generation as well.

  2. \(m_{\text {lim}}\) should not be chosen smaller than 1, since elements that contain a singularity might be skipped for refinement.

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Acknowledgements

The first and the last author gratefully acknowledge the financial support of the German Research Foundation under grants RA 624/15-2 and RA 624/22-1.

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Authors and Affiliations

  1. Chair for Computation in Engineering, Technische Universität München, Arcisstr. 21, 80333, Munich, Germany

    Tino Bog, Nils Zander, Stefan Kollmannsberger & Ernst Rank

  2. Institute for Advanced Study, Technische Universität München, Lichtenbergstr. 2a, 85748, Garching, Germany

    Ernst Rank

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  1. Tino Bog
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Correspondence to Tino Bog.

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Bog, T., Zander, N., Kollmannsberger, S. et al. Weak imposition of frictionless contact constraints on automatically recovered high-order, embedded interfaces using the finite cell method. Comput Mech 61, 385–407 (2018). https://doi.org/10.1007/s00466-017-1464-6

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