A Boundary Element Approach For Initial Receding Contact Problem Involving Large Displacements

Abstract

An algorithm based on the Boundary Element Method is utilised for the frictionless and frictional loading process in the specific case of receding contact problem. The formulation is limited to elastic behaviour of the materials involved and a Coulomb Type of friction is assumed. The contact constraints are applied node on element using quadratic shape functions to distribute the geometry, tractions and displacements at the contact zone. Therefore, the usual way of imposing the contact conditions (node-pair) is abandoned. That allows us to deal with the large displacement problem using an incremental procedure (Updated Lagrangian Approach). At least one increment of load must be done for each node changing its contact condition and additional increments could be necessary to note any relevant alterations of the geometry. The algorithm guarantees compatibility and equilibrium at the nodes in the final deformed configuration and special attention is devoted to the frictional effect. The proposed procedure is applied to the most representative two-dimensional receding contact problem- a layer pressed against an elastic foundation. The results obtained, when the displacements are small and friction is not considered, are in good agreement with the analytical solution. When friction is taken into account and large displacements appear, the problem is highly non-linear and the influence of those non-linearities is going to be shown.