The Impact of Surface Higher Order Differentiability in Two-dimensional Contact Elements

The aim of this work is to propose new contact elements of higher order of differentiability for analysing two-dimensional frictionless contact problems. Several methods were proposed in the literature to solve the problem caused by the lack of continuity resulting from the discretization. Among them are Bézier interpolation, Hermitian interpolation and splines. One of the difficulties in using Hermitian interpolation is to verify the partition of unity. Therefore, new elements that satisfy the C1 and C2 continuity at the interface are presented in this paper. These new contact elements are based on Hermitian polynomials for ensuring a higher order of continuity. The advantage is that this approach can be easily developed not only for linear elements but also for quadratic elements with higher order of differentiability. The performance of different surface representations is assessed through a comparison with a C0 surface discretization. Some numerical examples are used for assessing the accuracy and the convergence behaviour