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Contact analysis without adhesion is still a challenging problem, mainlyowing to the multiscale and self-fractal characteristics of rough surfaces. Upto now, theories for analyzing contact behavior of rough surfaces in literaturecan be generally categorized into two groups: the asperity-based Hertz contactmodels initiated by Greenwood and Williamson (G-W model), which is shown moreaccurate under small indentation distance, and the magnification-based pressurediffusion theory initiated by Persson, which is shown to work well under fullcontact conditions. The aim of this paper is to propose a theoretical modelthat can effectively formulate the contact status of rough surfaces during theentire compression process. This is achieved by integrating the idea ofmagnification, or evolving resolution into an asperity representation of roughsurfaces, and a magnification-based multi-asperity model is thus established.In the derived model, the originally complex contact problem is decomposed intoa family of sub-problems each defined on a morphologically simpler contactislands. Benefiting from the explicit results given by Greenwood andWilliamson, the proposed method is relatively easy for numericalimplementation. Compared to other G-W type models, the proposed method hasespecially shown its strength in the computation of the contact area. Moreover,the G-W and Persson models are found well connected by the proposed method. Forits validation, the proposed model is well compared with existing numerical,theoretical and experimental results. In particular, the proposed model hasshown its excellency through comparison with representative theoretical,numerical and experimental data compiled in the contact challenge test byMueser et al.

A magnification-based multi-asperity (MBMA) model of rough contact where the Greenwood-Williamson and Persson theories meet