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Research Papers

Extended Greenwood–Williamson Models for Rough Spheres

[+] Author and Article Information
T. Zhao

Zienkiewicz Centre for Computational
Engineering,
Swansea University,
Swansea SA1 8EN, UK

Y. T. Feng

Zienkiewicz Centre for Computational
Engineering,
Swansea University,
Swansea SA1 8EN, UK
e-mail: y.feng@swansea.ac.uk

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received May 13, 2018; final manuscript received June 8, 2018; published online July 3, 2018. Assoc. Editor: Yashashree Kulkarni.

J. Appl. Mech 85(10), 101007 (Jul 03, 2018) (9 pages) Paper No: JAM-18-1280; doi: 10.1115/1.4040537 History: Received May 13, 2018; Revised June 08, 2018

The current work aims to develop two extended Greenwood–Williamson (GW) models for spherical particles with surface roughness which can be incorporated into the discrete element modeling (DEM) framework. The defects of the classic GW model when directly adopted in DEM are fully addressed and illustrated by both theoretical and numerical results. The first model, the extended elastic GW (E-GW) model, which evaluates the elastic deformation of the asperities and the bulk substrate separately is developed to consider the positive overlap involved in the contact problem. The capability of incorporating the extended elastic model into the DEM is illustrated by the comparison between the classic and extended models. The second model, the extended elasto–plastic GW (EP-GW) model, is further developed to consider the plastic deformation of the asperities which reduces the pressure increased by the surface roughness. Numerical comparisons between the E-GW and EP-GW models are also conducted to demonstrate the effect of the plastic deformation on the pressure and deformation distributions in the contact region.

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Figures

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Fig. 1

Profile of the contact between a smooth sphere and a rough surface: δ≤0

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Fig. 2

Profile of the contact between a smooth sphere and a rough surface: δ≥0

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Fig. 3

Comparison of nondimensional total contact forces between the GW and E-GW models for different degrees of roughness

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Fig. 4

Comparison of pressure distributions over the contact zone: (a) pressure distribution and (b) pressure difference distribution

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Fig. 5

Comparison of deformation distributions with over the contact zone: (a) deformation distribution and (b) deformation difference distribution

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Fig. 6

Force displacement relationships based on different contact models

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Fig. 7

Comparisons of the pressure distribution between different contact models: (a) K = 0.6 and (b) ψ = 4

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Fig. 8

Comparisons of the force–displacement relationship between different contact models: (a) K = 0.6 and (b) ψ = 4

Tables

Errata

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