A contact searching algorithm including bounding volume trees applied to finite sliding mortar formulations

Abstract

This paper presents a new contact searching algorithm for large deformation mortar-based contact formulations. In this algorithm, a bounding volume hierarchy, defined in the context of a binary tree, is built for each contact surface based on the geometry of the surface. A global contact searching procedure based on these 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 having contributions to the mortar integrals that define the contact formulation. The searching algorithm is shown to be very efficient and readily applicable to a variety of large sliding contact problems.

Transient three-dimensional contact problems: mortar method. Mixed methods and conserving integration

“…Note that the evaluation of the mortar integrals (28) by means of quadrature rules violates condition (36) in general. Inserting (36) in (35) yields…”

“…Two model problems have been taken from Yang and Lausen [36] and applied to the newly developed schemes.…”

An augmentation technique for large deformation frictional contact problems

“…we can rearrange the terms in (27) and obtain the rate of change of the convective coordinates (28) where A˛ˇdenotes the inverse of A˛ˇWD m˛ˇ g h˛ˇand h˛ˇD a˛ˇ n is the curvature of the surface. Replacing the velocity by the variation yields…”

“…Initial values and the material properties have been taken from Yang and Laursen [28]. The initial configuration is displayed in Figure 11.…”

Identification of the additional exposure zone for ensuring a complete contact of the two-layered system

“…In [7], on the basis of the domain decomposition method, contact interaction was studied by the method of penalty functions, which are the conditions for kinematic admissibility of displacements. In the case when large deformations are observed [8,9], a hierarchical algorithm for constructing a binary tree for the current state of the contact surface geometry is proposed. Two procedures are used -global, defining all pairs of candidates, and then local, defining elements with a weakened connection.…”