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Rough surfaces are characterized by fractal geometry using a modified two-variable Weierstrass–Mandelbrot function. The developed algorithm yields three-dimensional fractal surface topographies representative of engineering rough surfaces. This surface model is incorporated into an elastic-plastic contact mechanics analysis of two approaching rough surfaces. Closed form solutions for the elastic and plastic components of the total normal force and real contact area are derived in terms of fractal parameters, material properties, and mean surface separation distance. The effects of surface topography parameters and material properties on the total deformation force are investigated by comparing results from two- and three-dimensional contact analyses and elastic and elastic-perfectly plastic material behaviors. For normal contact of elastic-perfectly plastic silica surfaces and range of surface interference examined, the interfacial force is predominantly elastic and the real contact area is approximately one percent of the apparent contact area or less, depending on the mean interfacial distance. The analysis can be easily modified to account for anisotropic fractal surfaces and different material behaviors.
Yan et al. (Thu,) studied this question.