Smooth C~1-interpolations for two-dimensional frictional contact problems

摘要

Finite deformation contact problems are associated with large sliding in the contact area. Thus, in the discrete problem a slave node can slide over several master segments. Standard contact formulations of surfaces discretized by low order finite elements leads to sudden changes in the surface normal field. This can cause loss of convergence properties in the solution procedure and furthermore may initiate jumps in the velocity field in dynamic solutions. Furthermore non-smooth contact discretizations can lead to incorrect results in special cases where a good approximation of the contacting surfaces is needed. In this paper a smooth contact discretization is developed which circumvents most of the aforementioned problems. A smooth deformed surface with no slope discontinuities between segments is obtained by a C~1-continuous interpolation of the master surface. Different forms of discretizations are possible. Among these are Bezier, Hermitian or other types of spline interpolations. In this paper we compare two formulations which can be used to obtain smooth normal and tangent fields for frictional contact of deformable bodies. The formulation is developed for two-dimensional applications and includes finite deformation behaviour. Examples show the performance of the new discretization technique for contact.