Mortar-Finite Element Methods for Frictional Contact

Figure 1: Click for Movie

In the area of computational contact mechanics, it can be said that most prevalent approaches in use today employ a traditional node-to-surface implementation of contact interaction, whereby contact constraints are enforced in terms of contact nodal positions with respect to opposing element surfaces. Such approaches suffer from several shortcomings, particularly in the case where both contacting bodies are deformable. Recently, in a series of articles (see below), we have described a set of new mortar-based surface to surface contact algorithms, possessing unprecedented robustness in the simulation of large deformation solid-to-solid contact. The movie to the right provides an example of the type of simulation we now perform routinely: the frictional interaction of two bodies, subject to finite deformations and bulk plasticity.

Current efforts are focused on the development of efficient search algorithms for multi-body contact and extensions to dynamics.

Contact Searching with Bounding Volume Hierarchies

Figure 2: Click to view movie

A new contact searching algorithm for large deformation mortar-based contact formulations is implemented. In this algorithm, a bounding volume hierarchy, which is a binary tree, is built for each contact surface based on the geometry and mesh connectivities of the discretized surface. Each node of the tree saves the bounding volume of the corresponding subsurface. The bounding volumes are defined with k-th discrete orientation polytopes(k-DOPs) which can be efficiently computed and updated, and the intersection between two k-DOPs can be quickly detected. A novel technology is proposed to inflate the bounding volumes to improve the performance, i.e. robustness and efficiency, of the searching algorithm. A global contact searching procedure based on the bounding volume trees is first performed to find all candidate contact element pairs, and then a local searching procedure is done to find all the mortar segments on which we compute the mortar integrals.

This algorithm is extended to self-contact problems by applying a curvature criterion with a new algorithm to detect subsurface adjacency. To define the mortar traction fields on contiguous surface patches, a novel technique, called a facet sorting algorithm, is proposed based on element connectivity of self-contact element pairs as identified by the searching algorithm. In several numerical examples featuring large deformations and sliding, in both two and three dimensions, the algorithm is shown to be very efficient, robust and applicable to general contact problems.


  1. Yang B, Laursen TA A contact searching algorithm including bounding volume trees applied to finite sliding mortar formulations COMPUTATIONAL MECHANICS, in press, 2006
  2. Yang B, Laursen TA, Meng XN Two dimensional mortar contact methods for large deformation frictional sliding INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 62 (9): 1183-1225 MAR 7 2005
  3. Puso MA, Laursen TA A mortar segment-to-segment frictional contact method for large deformations COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING 193 (45-47): 4891-4913 2004