|This work uses a finite element analysis and analytical equations to model elastic-plastic and fully plastic large deformations of spheres in contact with rigid flat surfaces. The case considered here is of a deformable sphere compressed by a rigid flat as opposed to the reverse case of a rigid spherical indenter penetrating a deformable surface. Most previous work only deals with elastic or elasto-plastic deformation at much smaller deformations. Based on an extensive literature survey, the work most related to plastic deformations of spherical surfaces are the papers by Noyan  and Chaudhri . Even existing finite element based models do not explain plastic deformations well. The current work theoretically explains the initiation and progression of plastic deformations throughout the sphere.
A model for predicting contact area, pressure and force for plastic deformations has been proposed based on the FEM simulations and analytical equations derived from volume conservation. The analytical volume conservation approach is similar to that used to model the barreling of compressed cylinders. The most important aspect of the model is the resulting equation relating the average pressure during fully plastic deformation to the yield strength. The model improves the current state-of-the art by providing equations relating contact force, area, pressure and interference much further into the fully plastic regime and for much larger deformations than the previous works. The results have been compared with existing models and with experimental data. All the results have been
simulated for three different sets of material properties to provide a model that is applicable to a wide range of materials.