Cn continuous modelling of smooth contact surfaces using NURBS and application to 2D problems

This paper presents a strategy for the nite-element implementation of Cn continuous contact surfaces for deformable bodies undergoing nite deformations, whereby n represents an arbitrary level of continuity. The proposed novel approach avoids the non-physical oscillations of contact forces which are induced by the traditional enforcement of kinematic contact constraints via faceted surfaces discretizing the interacting boundaries. In particular, for certain problems, the level of continuity may in uence the rate of convergence signi cantly within a non-linear solution scheme. A hierarchical tree data structure is proposed for an e cient search algorithm to nd the neighbour elements on adaptively re ned meshes, which are involved in the smoothing process of a particular nite element. The same data structure is used for the automatic detection of the contact surfaces of a body. Three representative numerical examples demonstrate the increased rate of convergence, the ability to trace the actual surface more accurately and the prevention of pressure jumps of the proposed method