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

Xu Guo, Benben Ma+1 more|arXiv (Cornell University)|Dec 18, 2017

Adhesion, Friction, and Surface Interactions19 references4 citations

TL;DR

This paper proposes a magnification-based multi-asperity (MBMA) model that unifies the Greenwood-Williamson (G-W) asperity model and Persson's pressure diffusion theory for rough surface contact. By integrating morphological multiresolution analysis into a hierarchical asperity representation, the model accurately predicts contact area and pressure distribution across the entire compression range, bridging the gap between G-W’s small-scale accuracy and Persson’s full-contact performance.

ABSTRACT

Contact analysis without adhesion is still a challenging problem, mainly owing to the multiscale and self-fractal characteristics of rough surfaces. Up to now, theories for analyzing contact behavior of rough surfaces in literature can be generally categorized into two groups: the asperity-based Hertz contact models initiated by Greenwood and Williamson (G-W model), which is shown more accurate under small indentation distance, and the magnification-based pressure diffusion theory initiated by Persson, which is shown to work well under full contact conditions. The aim of this paper is to propose a theoretical model that can effectively formulate the contact status of rough surfaces during the entire compression process. This is achieved by integrating the idea of magnification, or evolving resolution into an asperity representation of rough surfaces, and a magnification-based multi-asperity model is thus established. 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. Benefiting from the explicit results given by Greenwood and Williamson, the proposed method is relatively easy for numerical implementation. Compared to other G-W type models, the proposed method has especially 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. For its validation, the proposed model is well compared with existing numerical, theoretical and experimental results. In particular, the proposed model has shown its excellency through comparison with representative theoretical, numerical and experimental data compiled in the contact challenge test by Mueser et al.

Motivation & Objective

• Address the challenge of modeling rough surface contact across multiple scales due to self-affine fractal morphology.
• Overcome the limitations of existing models: G-W for small indentation and Persson for full contact conditions.
• Develop a unified theoretical framework that seamlessly connects asperity-based and magnification-based approaches.
• Enable accurate and numerically efficient computation of contact area and pressure distribution during full compression.
• Validate the model against experimental, numerical, and theoretical benchmarks, including the Mueser contact challenge dataset.

Proposed method

• Introduce a magnification-based approach that applies evolving resolution to represent rough surfaces at multiple scales.
• Decompose the global contact problem into a hierarchy of simpler sub-problems on morphologically distinct contact islands.
• Apply the Greenwood-Williamson (G-W) Hertzian asperity model to each sub-problem at its respective resolution level.
• Use the concept of pressure diffusion from Persson’s theory to model the interaction between asperities across scales.
• Integrate results from all resolution levels to compute the total real contact area and pressure distribution.
• Leverage analytical solutions from the G-W model at each scale to ensure computational efficiency and accuracy.

Experimental results

Research questions

• RQ1 How can a unified theoretical model be constructed that captures both the initial asperity-level contact and the full-area transition in rough surfaces?
• RQ2 To what extent can the magnification-based approach improve the accuracy of contact area prediction compared to standard G-W models?
• RQ3 Can the proposed model bridge the theoretical gap between the Greenwood-Williamson and Persson theories?
• RQ4 How does the MBMA model perform against experimental and numerical data across the full range of compression?
• RQ5 What is the role of multiscale resolution in improving the physical consistency and numerical tractability of rough contact modeling?

Key findings

• The MBMA model successfully unifies the Greenwood-Williamson and Persson theories by integrating multiscale resolution into an asperity-based framework.
• The model demonstrates superior accuracy in predicting real contact area, especially in the transition regime between partial and full contact.
• Compared to standard G-W models, the MBMA model shows significant improvement in contact area computation across all compression levels.
• The model achieves strong agreement with experimental data from the Mueser contact challenge, confirming its predictive power.
• The proposed method enables efficient numerical implementation due to the use of analytical G-W solutions at each resolution level.
• The model reveals a smooth transition between the regimes described by G-W and Persson theories, validating their theoretical connection.