A magnification-based multi-asperity (MBMA) model of rough contact without adhesion

Contact analysis without adhesion is still a challenging issue, mainly owing to the multiscale and self-fractal characteristics of rough surfaces. One of the most widely used theories for analyzing contact behavior of rough surfaces is the asperity-based Hertz contact models initiated by Greenwood and Williamson. Due to its single-scaled nature, however, G-W models generally output less accurate predictions when indentation is deep. This article aims for proposing a new theoretical model that effectively formulates the contact status of rough surfaces throughout the entire compression process. This is achieved by integrating the idea of magnification, or evolving resolution into the G-W model, and a magnification-based multi-asperity model is thus established where the multiscale nature of rough surface is taken into account properly. In the derived model, the originally complex contact problem is decomposed into a family of sub-problems each defined on a morphologically simpler contact islands, and a number of explicit formulations from existing multi-asperity models can thus be used. The present model not only effectively reproduces the results of G-W models for short indentation distance, but is also shown that when indentation is sufficiently deep, the present model smoothly transits to the regime of elastic interaction between smooth surfaces governed by Hookean-law formulation. Compared to other G-W type models, the proposed framework has also shown its strength in the computation of actual contact area. The proposed model is then compared with existing molecular dynamics simulation and experimental results for validation. (C) 2019 Elsevier Ltd. All rights reserved.