Coupled effects of surface elasticity, couple stresses, and adhesion in nanocontact mechanics

This paper investigates the adhesive nanocontact behavior of an elastic half-plane indented by a rigid cylindrical indenter, incorporating the simultaneous effects of surface elasticity, couple stresses, and adhesion. The free surface of the half-plane is modeled by the Steigmann-Ogden surface elasticity theory, while the bulk material behavior is described by the classical couple-stress elasticity theory. The adhesion at the contact interface is characterized by the Maugis-Dugdale (MD) adhesive contact model. Building on the fundamental nonclassical Flamant solution, the governing equations and boundary conditions of the nanocontact problem are reformulated into a system of triple integral equations. These equations are solved numerically by the Gauss-Chebyshev quadratures in combination with an iterative algorithm. The validation against the existing literature confirms the accuracy and robustness of the proposed solution methodology. Comprehensive parametric studies are performed to elucidate the critical roles of surface elasticity and couple stresses in adhesive nanocontact. The numerical results provide insights into the complex interactions among surface, couple-stress, and adhesive effects. Specifically, the interplay between the surface and adhesive effects is predominantly competitive, while the interaction between the couple stresses and adhesion exhibits an intricate nature. The findings highlight the necessity of simultaneously considering surface elasticity, couple stresses, and adhesion in nanoindentation analyses to achieve accurate predictions of material responses.