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In this work, we present an analytical solution for the contact problem of a rigid, loaded pin interacting with a circular hole in an infinite plane with microstructure, modelled by the couple-stress elastic theory, assuming frictionless contact with clearance under plane-strain conditions. The solution is constructed by employing the most general trigonometric series representations in polar coordinates for the stress, couple-stress, displacement, and rotation fields admitted by the theory of couple-stress elasticity. Enforcing the contact conditions yields a system of dual series equations for the unknown coefficients, which is subsequently reduced to an infinite linear algebraic system and solved by truncation, following established approaches in related literature. The influence of the material microstructure on the contact angle, as well as on the stress and couple-stress distributions along the hole boundary, is then examined. The results show that increasing the intrinsic material length scale leads to a stiffer mechanical response, thereby clearly highlighting the size-dependent behavior predicted by couple-stress theory. The convergence properties of the trigonometric series solution are also discussed.
Radi et al. (Thu,) studied this question.