Surface-To-Surface Contact – Various Aspects for Implementations within the Finite Element Method

Abstract

The current Chapter is devoted to the finite implementation of various algorithms for Surface-To-Surface contact pair. Newton iterative scheme is the main solution method for the most algorithms. Thus, the result of linearization developed in Sect. 7.1 is directly employed to construct the tangent matrices. Diversity of contact approaches leading to the corresponding contact elements are depending on the type of approximation involved into the discretization within the finite element method. First, the standard Node-To-Surface (NTS) approach for non-frictional and frictional problems are considered. Implementation of the Mortar method within the Segment-To-Segment (STS) type of contact element together with integration by subdivision is shown to be effective to satisfy the Contact Patch Test . The simplest smoothing technique for contact surfaces is shown as the implementation of the Segment-To-Segment type of contact element – this technique is the basis for the isogeometric implementation. A special Segment-To-Analytical Surface (STAS) contact approach is illustrated for the contact with rigid surfaces described analytically. The Large Penetration algorithm is presented as additional technique to accelerate the global solution. It is shown to be effective for some problems where the large penetration and as a result large load steps are applicable. Finally, two versions of implementation of the Nitsche method are shown.