This work presents an analytical solution of a multi-scale contact model for nominally flat rough surfaces. Based on an extension of the multi-scale model of Jackson and Streator incorporating certain fractal properties, the model investigates the resolution-dependent contact area as a function of load. The progression of contact from full contact to clusters of contact regions, and from elastic to plastic asperity behavior is described in a concise, analytical formulation. Moreover, using an appropriately defined dimensionless scale number, this progression is found to be essentially independent of the roughness. The latter, however, determines how fast the progression is traversed. In a comparison with previous models, e.g. the Persson diffusion model, the present model is found to show good quantitative and qualitative agreement in spite of its more simplistic construction.

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