On the modelling of smooth contact surfaces using cubic splines

In this paper, a new strategy for the smooth representation of 2D contact surfaces is developed and imple- mented. The contact surfaces are modelled using cubic splines which interpolate the nite element nodes. These splines provide a unique surface normal vector and do not require prior knowledge of surface tan- gents and normals. C2-continuous cubic splines are suitable for representing rigid contact surfaces, while C1-continuous Overhauser splines are shown to be most suitable for representing exible contact surfaces. A consistent linearization of the kinematic contact constraints, based on the spline interpolation, is derived. The new spline-based contact surface interpolation scheme does not in uence the element calculations. Conse- quently, it can be easily implemented in standard FE codes. Several numerical examples are used to illustrate the advantages of the proposed smooth representation of contact surfaces. The results show a signi cant improvement in accuracy compared to traditional piecewise element-based surface interpolation. The pre- dicted contact stresses are also less sensitive to the mismatch in the meshes of the di erent contacting bodies. This property is useful for problems where the contact area is unknown a priori and when there is signi cant tangential slip