Abstract
The problem of contact between two elastic bodies is addressed computationally using the virtual element method (VEM). The use of the VEM allows the use of non-matching meshes for the two bodies, and hence obviates the need for node-to-node contact on the candidate contact interfaces. The contact constraint is imposed using either a Lagrange multiplier or penalty formulation. A number of numerical examples illustrate the robustness and accuracy of the algorithm.
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Acknowledgments
Special care had to be taken to obtain the smootheness of the displacement and contact tractions at the contact interface. In this context the authors would like to thank Prof. Franco Brezzi for pointing out a method for a special stabilization that enhanced the results considerably, see Sect. 3.2. The third author acknowledges the generous support of the Alexander von Humboldt Foundation, through a Georg Forster Research Award.
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Wriggers, P., Rust, W.T. & Reddy, B.D. A virtual element method for contact. Comput Mech 58, 1039–1050 (2016). https://doi.org/10.1007/s00466-016-1331-x
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DOI: https://doi.org/10.1007/s00466-016-1331-x