Introduction of a segment-to-segment penalty contact formulation

Abstract

The modeling of contact problems in solid mechanics using the finite element method is a challenging and complicated task. Stable, efficient and accurate algorithms are required for finding an effective solution for general contact problems. This thesis introduces a transition from a node-to-segment penalty contact formulation to an effective segment-to-segment penalty contact formulation.

The main issues of the node-to-segment approach are convergence problems and inaccurate results in case of nonconforming meshes. These disadvantages are caused by the fact that the contact constraints are satisfied only at the nodal locations. The relatively new segment-to-segment formulations provide a way to apply the constraint conditions along the entire boundary in a weak integral sense. This usually results in better stability and accuracy.

Several different discretization schemes for the proposed segment-to-segment formulation are presented. Moreover, additional complexities caused by the new formulation are discussed and the solutions for these problems are introduced. The different discretization schemes are compared by simple examples as well as big and complicated real models. Additionally, the widely accepted numerical benchmark test known as “patch test” is conducted to compare the results given by the different contact implementations.

The results obtained by the comparisons support the expected outcome of the segment-to-segment approach. The advantages of the segment-to-segment formulations become clear and a much better contact algorithm is introduced into an open source finite element analysis program.