On virtual element solutions of unilateral contact problems

This contribution investigates the capabilities of an arbitrary order virtual element approach to solve a special class of contact problems, i.e. the unilateral contact between a two-dimensional elastic body and a rigid frictionless foundation of arbitrary shape, which is known as the Signorini problem. In order to account for the presence of the rigid obstacle, the virtual element formulation has been coupled to a Projected Successive Over-Relaxation (PSOR) algorithm. Due to its unique features, the Virtual Element Method (VEM) proves to be very versatile when dealing with the need of inserting new nodes on the contact surface and when a higher order interpolation field along element edges is required. The salient features of the method have been illustrated through a simple but insightful numerical example.