Numerical methods for contact between two joined quarter spaces and a rigid sphere

Quarter space problems have many useful applications wherever an edge is involved, and solution to the related contact problem requires extension to the classical Hertz theory. However, theoretical exploration of such a problem is limited, due to the complexity of the involved boundary conditions. The present study proposes a novel numerical approach to compute the elastic field of two quarter spaces, joined so that their top surfaces occupy the same plane, and indented by a rigid sphere with friction. In view of the equivalent inclusion method, the joined quarter spaces may be converted to a homogeneous half space with properly established eigenstrains, which are analyzed by our recent half space-inclusion solution using a three-dimensional fast Fourier transform algorithm. Benchmarked with finite element analysis the present method of solution demonstrates both accuracy and efficiency. A number of interesting parametric studies are also provided to illustrate the effects of material combinations, contact location and friction coefficient showing the deviation of the solution from Hertz theory.