Non-adhesive and adhesive contacts of an elastic quarter-or eighth-space with freely sliding sides

The contact of an elastic quarter- or eighth-space is studied under the condition that the movement of the side surface of the quarter-space is constrained: It can slide freely along the plane of the side surface but its normal movement is blocked (for example, by a rigid wall). The solution of this contact problem can be easily achieved by additionally applying a mirrored load to an elastic half-space. Non-adhesive contact and the Johnson-Kendall-Roberts (JKR)-type adhesive contact between a rigid sphere and an elastic quarter-space under such a boundary condition is numerically simulated using the fast Fourier transform (FFT)-assisted boundary element method (BEM). Contacts of an elastic eighth-space are investigated using the same idea. Depending on the position of the sphere relative to the side edge, different contact behavior is observed. In the case of adhesive contact, the force of adhesion first increases with increasing the distance from the edge of the quarter-space, achieves a maximum, and decreases further to the JKR-value in large distance from the edge. The enhancement of the force of adhesion compared to the half-space-contact is associated with the pinning of the contact area at the edge. We provide the maps of the force of adhesion and their analytical approximations, as well as pressure distributions in the contact plane and inside the quarter-/eighth-space.