Boundary element method for two-dimensional frictional contact problems of anisotropic elastic solids

Abstract

The conventional boundary element method solving for the problems of two-dimensional anisotropic elastic solids with prescribed traction and/or prescribed displacement boundary conditions is extended to the frictional contact problems. A complete system of linear equations is constructed by boundary integral equations and contact constraint relations. The contact solutions are obtained by using an efficient, iterative and fully incremental loading technique. By using this technique, the nonlinearity raised by unknown contact region and unknown slip direction of frictional contact can be approximated by the accumulation of linear increments. The incremental load is determined by using the load extrapolation technique that allows only one or two node pairs come into contact in each iteration. The slip direction of frictional contact is decided by referring to the relative tangential slip in the frictionless state. To avoid reassembling the whole system equations in each iteration, a suitable arrangement of the equation system is made and a fast solver is adopted to get the solution without resolving the entire system of equations. When the contact bodies contain holes, cracks or inclusions, we use a special boundary element whose fundamental solution satisfies the boundary condition along the hole/crack/inclusion boundary. The validation of the proposed method is demonstrated through several numerical examples, which further lead to the discussion of the effects of friction coefficient, material anisotropy, holes, cracks and inclusions on contact.