An Analytical Solution to an Archard-Type Fractal Rough Surface Contact Model

Due to the existence of multiple scales of features on surfaces, during the past two decades models have been developed that employ a fractal description of the rough surface profile. Most of these models use a truncation calculation to predict the contact area. The load corresponding to the truncated area of the fractal surface is then calculated using elastic and elastic–plastic asperity contact models. The current work instead uses a stacked asperity model that was first introduced by Archard to predict contact area as a function of load. From this the elastic contact of multiscale rough surfaces can be solved analytically, providing a closed-form solution for certain cases of surface profiles. The results of the model are then compared to a two-dimensional (2D) deterministic model of rough surface contact. Finally, the analytical relationships are used to create models for three-dimensional (3D) elastic and elastic–plastic contact of fractal/multiscale rough surfaces.