Two-dimensional finite element analysis of elastic adhesive contact of a rough surface.

Adhesive contact of a rigid flat surface with an elastic substrate having Weierstrass surface profile is numerically analyzed using the finite element method. In this work, we investigate the relationship between load and contact area spanning the limits of non-adhesive normal contact to adhesive contact for various substrate material properties, surface energy and roughness parameters. In the limit of non-adhesive normal contact, our results are consistent with published work. For the adhesive contact problem, we employ Lennard-Jones type local contact interaction model with numerical regularization to study the transition from partial to full contact including jump-to-contact instabilities as well as load-depth hysteresis. We have investigated evolution of bonded contact area and pull-off force for various surface roughness parameters, substrate material properties and surface energy. We have identified two non-dimensional parameters to adequately explain experimentally observed adhesion weakening and strengthening phenomena. A design chart of the relative pull-off force as function of non-dimensional parameters is also presented.

Stiffness of contacts between rough surfaces.

The effect of self-affine roughness on solid contact is examined with molecular dynamics and continuum calculations. The contact area and normal stiffness rise linearly with the applied load, and the load rises exponentially with decreasing separation between surfaces. Results for a wide range of roughness, system size, and Poisson ratio can be collapsed using Persson's contact theory for continuous elastic media. The compliance due to atomic-scale motion at the interface between solids has little effect on the area and normal stiffness, but can reduce the total transverse stiffness by orders of magnitude. The scaling of this effect with system size is discussed.