A numerical model for the deterministic analysis of adhesive rough contacts down to the nano-scale

A numerical model based on the Multi-Level Multi-Integration technique has been developed to study the adhesion between two surfaces. The model provides a self-consistent solution of surface separation and contact pressure throughout an arbitrary surface contact (including random surface roughness) with the adhesive interactions governed by the Lennard-Jones potential. Using this approach, the behaviour of rough surfaces can be assessed with a deterministic description of the surface, and contact stresses include valid adhesive interactions between all non-contacting surface nodes. The model is first compared to similar analyses from smooth surface models, where good agreement with published results is obtained. The model is then applied to randomly rough surfaces and shows both the significant impact of roughness on adhesive behaviour and how individual surface asperities influence the loading–unloading response of adhesive contacts. Lastly, the ability of the model to investigate nano-scale contacts is assessed through comparisons with atomistic simulations previously published elsewhere. It is clearly shown that our continuum mechanics-based model, in which an atomistic configuration is represented by a discretised continuum representation of the surface using a hard-sphere atomic model, is capable of reproducing many of the features identified through detailed atomistic simulations. The suitability of the presented model for studying adhesive contacts from the nano-scale to much larger, soft contacts, where adhesive forces can alter the contact mechanics, is demonstrated. The developed modelling tool and the algorithms implemented by the authors open the possibility to perform fast and accurate calculations using a deterministic description of the roughness for a wide variety of contact conditions.