Loading and unloading of a power-law hardening spherical contact under stick contact condition

The loading and unloading process of a deformable sphere pressed by a rigid flat is a primary problem in contact mechanics. This work studies the contact of an elastic-plastic sphere with a rigid flat under stick condition during loading and unloading process by the finite element method. The sphere material is assumed isotropic with power-law hardening. The contact load and contact area are calculated at various Poisson's ratios and strain hardening exponents, with the sphere material properties varying from purely elastic to elastic-perfectly plastic. Analytical dimensionless expressions of the contact load, contact area and the residual interference after fully unloading for the power-law hardening materials in the elastic-plastic case are proposed for a wide range of interferences.