An adaptive NS/ES-FEM approach for 2D contact problems using triangular elements

An adaptive contact analysis approach is presented for 2D solid mechanics problems using only triangular elements and the subdomain parametric variational principle (SPVP). The present approach is implemented for the node-based smoothed FEM (or NS-FEM), the edge-based smoothed FEM (ES-FEM) and the standard FEM models with automatically adaptive refinement scheme. A modified Coulomb frictional contact model and its corresponding discrete equations are introduced. The global discretized system equations are then formulated in an incremental form with the aid of the basic boundary value equations for friction contact and the subdomain parametric variational principle. A simple adaptive refining scheme is presented, and the Voronoi vertices are taken as candidate points to become new nodes because of duality property between the Voronoi diagrams and Delaunay triangulation. The present adaptive approach can properly simulate variable behaviors of a contact interface such as bonding/debonding, contacting/departing, and sticking/slipping. Several examples are presented to numerically validate the proposed approach via the comparison with reference solutions obtained by ABAQUS®, and to investigate the effects of the various parameters used in the computations on the response of the contact system. The numerical results have demonstrated that the present adaptive contact analysis approach using the ES-FEM has higher accuracy and convergence rate in the strain energy than that using FEM and NS-FEM. However, the latter two methods can provide the lower and upper bound solution for the system strain energy, respectively.