Adhesion at fractal interfaces: A theoretical framework for multiscale contact

Adhesive interactions at contact interfaces are strongly influenced by surface roughness spanning multiple length scales. In many contact-mode microsystems, the surface topography commonly exhibits fractal characteristics that are challenging to traditional models of contact and adhesion. This paper introduces a theoretical framework for analyzing adhesion at fractal interfaces that utilizes multiscale contact mechanics and surface physics. The analysis accounts for nominally flat, convex, and patterned surfaces, elastic and plastic deformation at the asperity level, and adhesion due to capillary and van der Waals forces. By incorporating fractal descriptors, such as fractal roughness and fractal dimension, the developed theoretical methodology captures the effect of contact geometric complexity on adhesive behavior. Simulation results illuminate how contact geometry, scale-invariant fractal topography parameters, elastic–plastic material properties, and mean surface separation affect the evolution of the real contact area and interfacial adhesive and repulsive forces. The present study reveals limitations of classical contact models of adhesion and provides useful guidance for the design and reliability assessment of microsystems where surface forces and multiscale deformation control reliability and performance.