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.

弹性四分之一或八分之一空间的接触是在四分之一空间的侧面运动受到约束的情况下研究的：它可以沿侧面平面自由滑动，但其正常运动被阻止（对于例如，通过刚性墙）。通过向弹性半空间额外施加镜像载荷，可以轻松解决该接触问题。使用快速傅里叶变换（FFT）辅助边界元法对这种边界条件下刚性球体与弹性四分之一空间之间的非粘着接触和Johnson-Kendall-Roberts（JKR）型粘着接触进行了数值模拟（边界元法）。使用相同的想法研究弹性八分之一空间的接触。根据球体相对于侧边缘的位置，观察到不同的接触行为。在粘合接触的情况下，粘合力首先随着距四分之一空间边缘的距离的增加而增加，达到最大值，并在距边缘较大距离时进一步减小至 JKR 值。与半空间接触相比，粘附力的增强与边缘接触区域的钉扎有关。我们提供粘附力图及其解析近似值，以及接触平面和四分之一/八分之一空间内的压力分布。