Elastic–plastic contact analysis of an ellipsoid and a rigid flat

The work presents a finite element model (FEM) of the equivalent von-Mises stress and displacements that are formed for the different ellipticity contact of an ellipsoid with a rigid flat. The material is modeled as elastic perfectly plastic and follows the von-Mises yield criterion. The smaller the ellipticity of the ellipsoid is, the larger the depth of the first yield point from the ellipsoid tip happens. The FEM produces contours for the normalized normal and radial displacement as functions of the different interference depths. The evolution of plastic region in the asperity tip for a sphere (ke  =1) and an ellipsoid with different ellipticities (ke=12and15) is shown with increasing interferences. It is interesting to note the behavior of the evolution of the plastic region in the ellipsoid tip for different ellipticities, ke, is different. The developments of the plastic region on the contact surface are shown in more details in Fig. 7. When the dimensionless contact pressure is up to 2.5, the uniform contact pressure distribution is almost prevailing in the entire contact area. It can be observed clearly that the normalized contact pressure ascends slowly from the center to the edge of the contact area for a sphere (ke  =1), almost has uniform distribution prevailing the entire contact area for an ellipsoid (ke=12), and descends slowly from the center to the edge of the contact area for an ellipsoid (ke=15).