The solution is found for the contact pressure and contact law when a rounded quarter plane is pressed onto an elastically similar half-plane, for the case when the interfacial coefficient of friction is sufficient to inhibit all slip away from the contact edge. The far field is specified by stress intensity factors as if the contacting pair were a monolithic wedge of internal angle 270 degrees. The solution found is used to investigate corner rounding for a simple contact between a square block and a half-plane, as an illustration of its use.
Fleury, R. M. N., Hills, D. A., & Barber, J. R. (2016). A corrective solution for finding the effects of edge-rounding on complete contact between elastically similar bodies. Part I: Contact law and normal contact considerations. International Journal of Solids and Structures, 85–86, 89–96. https://doi.org/10.1016/j.ijsolstr.2015.11.031