Sliding friction contact problem from the perspective of the micropolar elasticity theory

In this study, the sliding friction contact problems associated with the indentation of an elastic half-plane by rigid cylindrical and flat punches were investigated within the context of the micropolar theory. The micropolar theory of elasticity introduces the characteristic material length and the dimensionless coupling number to describe the size effect. Coulomb’s friction law is satisfied by a punch when it is subjected to both normal and tangential forces. Using the Fourier integral transformation technique, these mixed-boundary value problems were reduced to singular integral equations of the second kind in which the unknown quantity is the contact stress on the contact surface. The collocation method was utilized to solve the integral equations numerically. An extensive parametric study was conducted to investigate the effects of the friction coefficient, the characteristic material length, and the dimensionless coupling number on the normal and in-plane stresses. The results show that the contact stress predicted by the micropolar theory differs significantly from those predicted by the couple stress theory and the classical elasticity theory.