Adhesion originated from van der Waals interactions becomes predominant over bulk properties of elastic solids at small length scales. A fundamental understanding of the mechanics of elastic contact and adhesion of rough surfaces is of paramount importance due to its wide applications in various engineering and biological fields from avoiding stiction failure of micro-electromechanical systems to achieving optimal adhesion capability of gecko-inspired micro-fibrillar adhesives. This dissertation focuses on several critical problems of frictionless adhesive elastic contact with particular emphasis on the interplay of surface roughness and adhesion. Based on the Maugis-Dugdale theory and Nayak's theory of rough surface, we propose a new mechanics model of adhesive elastic contact to study the depth-dependent hysteresis and energy loss during a contact cycle in the regime of large surface roughness. We develop an effective, nonlinear body force based approach to simulate adhesive elastic contact using the realistic molecular potential. It is shown that the surface roughness can either enhance or reduce the effective work of adhesion required to separate two contacting surfaces, depending on the magnitude of roughness. The continuum simulations reveal that the mechanism of adhesion enhancement and depth-dependent hysteresis observed in adhesive contact experiments is attributed to the small-scale surface imperfection induced mechanical instabilities. Through analyzing the quasi-static peeling of an elastic thin film from a rough substrate, we demonstrate that the effective work of adhesion can be significantly improved by surface roughness, resulting in an apparent interface toughening. Moreover, we examine the principle of contact splitting for biological fibrillar structures and investigate the effects of fibril's stiffness and surface's roughness and correlation length on adhesion of the fibrillar structure. We also present an analytical model of adhesive elastic contact that accounts for the effect of machine stiffness, which explains experimentally measured contact force-indentation depth curves better than the Johnson-Kendall-Roberts theory. These comprehensive results highlight the importance of surface topography and material properties in adhesive elastic contact and can guide future work on attuning effective adhesive and tribological properties through designing small-scale surface architectures.
