Application of the Virtual Element Method to Non-Conforming Contact Interfaces

The main idea of the recently developed virtual element method is to find a single Ansatz function that can project the nodal values on the element area while being compatible with the interpolated values on the boundary. For this purpose a suitable polynomial function is chosen and then fitted to the continuum problem while the determining of the parameters is not done explicitly but during the calculation. The method gets its name from this virtually computed function.

Interpolating the values directly offers some great advantages over standard finite element formulations. The integration is executed in the physical domain and on the element boundary without the need of an isoparametric mapping. With this it is easily possible to discretize a geometry using convex or non-convex polygons with an arbitrary number of vertices. Additionally the method offers a simple formulation and the possibility to achieve higher continuity.

In the literature there are numerous formulations for classical contact and different discretization methods for the contact zone available. Widely used are the penalty and Lagrange multiplier method to enforce contact constraints in the finite element environment.

But especially non-conforming contact interfaces require a high effort in discretizing the contact surface in order to properly link the degrees of freedom. In this project the easy mesh adaption property of the virtual elements is used to obtain nodal contact enforcement. This allows for an easy and robust contact algorithm for non-conforming.

In this context also the general behaviour of the Virtual Elements regarding accuracy and stability are investigated and optimized.

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