Pin–hole contact with curvature-induced couple tractions in couple-stress elasticity

In this study, a curvature-compatible formulation is presented for the frictionless contact between a rigid pin and a circular hole in a microstructured elastic plane governed by constrained couple-stress theory under plane-strain conditions. Unlike the classical micro-free assumption, the present model allows transmission of couple tractions across the contact interface and imposes a uniform tangential curvature, consistent with the pin-hole geometry. The boundary value problem is expressed through trigonometric expansions in polar coordinates, yielding a coupled system of dual series equations that is reduced to an infinite algebraic system and solved by truncation. The effect of transmitted couple tractions on the contact half-angle and on the stress and couple-stress fields along the hole boundary is quantified. The results show that curvature compatibility significantly modifies the near boundary response and leads to a more uniform stress and couple-stress distribution compared with the microfree case. The formulation provides a consistent extension of pin-hole contact analysis in materials with intrinsic length-scale.