Abstract
In this report, a semi-analytical approach for three dimensional contact problem of two non-conformed, deformable bodies in contact under normal loading is presented. The contact surfaces could be rough or smooth. For plastic deformation, the perfect elasto-plasticity is assumed. Rough surfaces of different roughness profiles can be independently defined on each body surface. The numerical solution is based upon the analytical solution given by Boussinesq-Cerruti integral equations for an elastic half space [1]. Due to the geometry restriction, the bodies in contact are assumed as flat or nearly flat where the radii of curvature is very large as compared to the contact area size. The integral equations applied at each contact body are discretized on a rectangular grid defined at each contact surface and are evaluated by using multilevel and multi-summation technique (MLMS) [2]. In addition to the discretized integral equations, the contact condition and force balance equations in normal direction are imposed. Iterated conjugate gradient method (CGM) [2] is implement to find the displacement and tractions that satisfy the contact conditions. The surface displacement and tractions in normal direction, the real contact area, plastic contact area are obtained under the given conditions.
