Contact algorithm for non-linear elastic problems with large displacements and friction using the boundary element method Original Research Article

An efficient algorithm of contact is presented for the boundary element analysis of the static two-dimensional frictional contact problem between elastic solids. The algorithm guarantees equilibrium and compatibility at the nodes in the final deformed configuration and it allows us to deal with problems undergoing large displacements, with large slipping at the interface as the mismatching of contact nodes is allowed. The formulation is limited to elastic behaviour with small strains and a Coulomb’s friction law is assumed. The solution procedure, based on the Updated Lagrangian Approach, is incremental as the contact problem with friction is history-dependent. At least one load increment must be done for each node changing its boundary conditions during the loading process. Additional increments are necessary to record any relevant modifications of the geometry that might appear. Quadratic isoparametric boundary elements are used and the contact constraints are applied node-on-element, using the shape functions for distributing the geometry, displacements and tractions on each element at the contact zone. Some special attention is devoted to the frictional effects related to the type of interpolation used. Two representative examples are studied: a cylinder over a flat surface and a layer pressed against half-space. The computed results, when the displacements are small and friction is not considered, are found to agree well with the analytical solutions. When friction is taken into account, no analytical solution is available and the results are compared to the numerical solutions obtained by other authors. When in addition large displacements appear, the problem becomes highly non-linear and the most relevant aspects of those non-linearities will be shown in this paper.