A study of overall contact behavior of an elastic perfectly plastic hemisphere and a rigid plane

The overall contact behavior of an elastic perfectly plastic hemisphere against a rigid plane is presented. Based on volume conservation, the upper limit of overall contact area is derived. A finite element model for the overall contact behavior of a hemisphere and a rigid plane is studied. The material of the hemisphere is assumed to be elastic perfectly plastic. A series of materials with different yield stress to elasticity modulus ratios are studied in finite element analysis. The axial movement of the deformed hemisphere base is prevented. The radial deformable and radial rigid boundary conditions of the hemisphere bottom base are considered. Results show that the overall contact area gradually deviates from Hertz solution, and approaches the upper limit with the increase of interference. Material yield stress to elasticity modulus ratio mainly influences contact behaviors in the early contact stage, while the boundary condition of hemisphere bottom base affects the contact behaviors significantly for large contact interferences. By incorporating some existing models and fitting finite element results, a model for overall contact of a hemisphere against a rigid plane is obtained. This study covers the overall contact, which ranges from initial contact to the collapse of hemisphere. Comparisons of this study with several existing models and experimental data indicate that this study can predict the contact behaviors well in overall contact range.