Frictionless Contact Procedure for Finite Cover Method using Nitsche’s Method

Abstract

The voxel-based FEM is an efficient numerical procedure to deal with complex geometries. It is difficult to analyze models containing contact conditions by this procedure, in which surfaces of objects are represented as stepwise shapes. In the voxel modeling based on the finite cover method (FCM), geometry is defined by using surface modeling procedures such as polyhedrons and the level set method instead of voxel representation and hence contact problems can be set more easily. In this paper, a contact algorithm for the FCM is proposed. The penalty method is widely used for contact constraint, and then a large penalty parameter, which needs to be employed to assure accuracy, may cause numerical instability. Moreover, in the FCM, it is difficult to manage positions of integration points for contact constraints and inaccurate distribution of contact stress may be obtained due to an over-constraint with concentration of integration points. In this paper, the Nitsche’s method is applied to contact constraint in the FCM in order to circumvent difficulties arising in the penalty method. To show effectiveness of our approach, we calculate several 2D frictionless contact problems.