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Purpose This paper aims to describe the application of the virtual element method (VEM) to contact problems between elastic bodies. Design/methodology/approach Polygonal elements with arbitrary shape allow a stable node-to-node contact enforcement. By adaptively adjusting the polygonal mesh, this methodology is extended to problems undergoing large frictional sliding. Findings The virtual element is well suited for large deformation contact problems. The issue of element stability for this specific application is discussed, and the capability of the method is demonstrated by means of numerical examples. Originality/value This work is completely new as this is the first time, as per the authors’ knowledge, the VEM is applied to large deformation contact.

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