Modelling unilateral frictionless contact using the null-space method and cubic B-Spline interpolation

The analysis of unilateral sliding contact in elasticity is equivalent to a minimisation problem subjected to a set of inequality constraints. However, the presence of boundary discontinuities, such as those stemming from the spatial discretisation, appears as a major problem to determine the set of active constraints. This work introduces a smoothing technique of the master surface resorting to cubic B-Spline interpolation, which is C1 continuous in contact situations between elastic and rigid bodies, and G1 continuous in elastic-elastic contact problems. The technique is applied in conjunction with the null-space method, where the solution is searched in an unconstrained manifold. The resulting formulation eases the contact transition along the master surface, and recovers the quadratic convergence of the iterative Newton-Raphson process. The robustness of the method is demonstrated using 2D and 3D examples.