Various contact approaches for the finite cell method

Abstract

The finite cell method (FCM) provides a method for the computation of structures which can be described as a mixture of high-order FEM and a special integration technique. The method is one of the novel computational methods and is highly developed within the last decade. One of the major problems of FCM is the description of boundary conditions inside cells as well as in sub-cells. And a completely open problem is the description of contact. Therefore, the motivation of the current work is to develop a set of computational contact mechanics approaches which will be effective for the finite element cell method. Thus, for the FCM method we are developing and testing hereby focusing on the Hertz problem the following algorithms: direct integration in the cell method, allowing the fastest implementation, but suffering from numerical artifacts such as the "stamp effect"; the most efficient scheme concerning approximation properties the cell-surface-to-analytical-surface contact element designed for contact with rigid bodies leading to cell-wisely contact elements; and finally the discrete-cell-to-cell contact approach based on the finite discrete method. All developed methods are carefully verified with the analytical Hertz solution. The cell subdivisions, the order of the shape functions as well as the selection of the classes for shape functions are investigated for all developed contact approaches. This analysis allows to choose the most robust approach depending on the needs of the user such as correct representation of the stresses, or only satisfaction of geometrical non-penetration conditions.