Receding contact problem involving large displacements using the BEM

Abstract

A new algorithm is presented for the boundary element analysis of the two-dimensional contact problem between elastic solids involving large displacements. The contact constraints are not applied node-on-node but node-on-element, using the element shape functions to distribute the geometry, displacements and tractions on each element in the contact zone. Thus, the discretizations performed along the two surfaces in contact need not necessarily be the same. The solution procedure is based on the updated Lagrangian approach and the resulting method is incremental. The algorithm guarantees equilibrium and compatibility at the nodes in the final deformed configuration and allows us to deal with problems undergoing large displacements without it being necessary to change the initial discretization of the boundary of the bodies. Only the frictionless static problem is dealt with, and the proposed algorithm is applied to the most representative receding contact problem: a layer pressed against an elastic foundation. The results obtained when the displacements are small are in good agreement with the analytical solution. When large displacements are considered, another nonlinearity appears and its influence will be shown in this paper.