A novel approximate method to calculate the force applied on an elastic half space by a rigid sphere

Assume a rigid sphere that is slightly pushed towards an elastic half space. The applied force on the half space can be easily calculated using the basic theoretical tools provided by the Hertzian contact mechanics theory. It should be noted that the aforementioned analysis is valid under the condition that the deformation depth is significantly smaller compared to the sphere's radius (h MUCH LESS-THAN R). So, a significant question arises; what if the sphere is pushed deeper in the elastic half space (e.g. h > R)? In this paper, the aforementioned question is answered and a relative discussion regarding the application of the results is presented.

Automated summary

This paper discusses the calculation method of the applied force on an elastic half space when a rigid sphere is pushed towards it, under the condition that the deformation depth is significantly smaller compared to the sphere's radius. It also addresses the scenario when the deformation depth is larger and provides a relative discussion on the application of the results.