On the Contact of Elastic Solids

Journal Article•

On the Contact of Elastic Solids

01 Jan 1882-Crelle's Journal-Vol. 92, pp 156-171

About: This article is published in Crelle's Journal.The article was published on 1882-01-01 and is currently open access. It has received 3249 citations till now.

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Journal Article•DOI•

Force measurements with the atomic force microscope: Technique, interpretation and applications

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Hans-Jürgen Butt¹, Brunero Cappella², Michael Kappl¹•Institutions (2)

Max Planck Society¹, Bundesanstalt für Materialforschung und -prüfung²

01 Oct 2005-Surface Science Reports

TL;DR: The atomic force microscope (AFM) is not only used to image the topography of solid surfaces at high resolution but also to measure force-versus-distance curves as discussed by the authors, which provide valuable information on local material properties such as elasticity, hardness, Hamaker constant, adhesion and surface charge densities.

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3,281 citations

Journal Article•DOI•

A survey of models, analysis tools and compensation methods for the control of machines with friction

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Brian Armstrong-Hélouvry¹, Pierre E. Dupont², Carlos Canudas de Wit³•Institutions (3)

University of Wisconsin–Milwaukee¹, Boston University², École nationale supérieure d'ingénieurs électriciens de Grenoble³

01 Jul 1994-Automatica

TL;DR: This survey is the first to bring to the attention of the controls community the important contributions from the tribology, lubrication and physics literatures, and provides a set of models and tools for friction compensation which will be of value to both research and application engineers.

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2,658 citations

Cites background or result from "On the Contact of Elastic Solids"

...22, also from Hess and Soom (1990). The data presented were acquired driving their pin-on-disk contact at three different frequencies. Figure 22(b) shows the friction curves predicted by their model with frictional memory modeled as a pure lag and should be compared with the experimental data illustrated in Fig. 22(a). Indicative of the progress of triboiogy, the friction model of Hess and Soom (1990) which accounts for contact geometry and loading, material properties, velocity, lubricant viscosity and Stribeck friction, is to a large degree based on contact and lubricant parameters, only three parameters are fit a p o s t e r i o r i to the data....
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...The data of Bell and Burdekin (1966, 1969) and Hess and Soom (1990) indicate such a curve. When boundary lubrication is more effective, the friction is relatively constant up to the velocity at which partial fluid lubrication begins to play a role. Vinogradov et al. (1967) and Khitrik and Shmakov (1987) present data supporting a flat (f-v) curve through the region of boundary lubrication, as suggested by curve (b) of Fig....
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...22, also from Hess and Soom (1990). The data presented were acquired driving their pin-on-disk contact at three different frequencies....
[...]
...22, also from Hess and Soom (1990). The data presented were acquired driving their pin-on-disk contact at three different frequencies. Figure 22(b) shows the friction curves predicted by their model with frictional memory modeled as a pure lag and should be compared with the experimental data illustrated in Fig. 22(a). Indicative of the progress of triboiogy, the friction model of Hess and Soom (1990) which accounts for contact geometry and loading, material properties, velocity, lubricant viscosity and Stribeck friction, is to a large degree based on contact and lubricant parameters, only three parameters are fit a p o s t e r i o r i to the data. Evidence for frictional memory is available from a range of experimental sources: Sampson et al. (1943), Rabinowicz (1958, 1965), Bell and Burdekin (1966, 1969), Walrath (1984), Rice and Ruina (1983), Hess and Soom (1990). Tribology is not yet able to offer a theoretically motivated model of the frictional memory, though Xiaolan and Haiqing (1987) numerically investigate transient elasto-hydrodynamic lubrication using an analysis that starts with Reynold's equation and Hertzian contact analysis; with this they find a time lag of 3 ms between velocity and friction changes in simulated sliding contact....
[...]
...22, also from Hess and Soom (1990). The data presented were acquired driving their pin-on-disk contact at three different frequencies. Figure 22(b) shows the friction curves predicted by their model with frictional memory modeled as a pure lag and should be compared with the experimental data illustrated in Fig. 22(a). Indicative of the progress of triboiogy, the friction model of Hess and Soom (1990) which accounts for contact geometry and loading, material properties, velocity, lubricant viscosity and Stribeck friction, is to a large degree based on contact and lubricant parameters, only three parameters are fit a p o s t e r i o r i to the data. Evidence for frictional memory is available from a range of experimental sources: Sampson et al. (1943), Rabinowicz (1958, 1965), Bell and Burdekin (1966, 1969), Walrath (1984), Rice and Ruina (1983), Hess and Soom (1990)....
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Journal Article•DOI•

Adhesion of spheres : the JKR-DMT transition using a dugdale model

[...]

Daniel Maugis¹•Institutions (1)

Centre national de la recherche scientifique¹

01 Apr 1992

TL;DR: In this article, the energy release rate G is computed by the J-integral and the equilibrium is given by G = w. To avoid self consistent numerical calculations based on a specific interaction model (Lennard-Jones potential for example) we have used a Dugdale model, which allows analytical solutions.

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Abstract: In the Johnson-Kendall-Roberts (JKR) approximation, adhesion forces outside the area of contact are neglected and elastic stresses at the edge of the contact are infinite, as in linear elastic fracture mechanics. On the other hand, in the Derjaguin-Muller-Toporov (DMT) approximation, the adhesion forces are taken into account, but the profile is assumed to be Hertzian, as if adhesion forces Could not deform the surfaces. To avoid self consistent numerical calculations based on a specific interaction model (Lennard-Jones potential for example) we have used a Dugdale model, which allows analytical solutions. The adhesion forces are assumed to have a constant value σO, the theoretical stress, over a length d at the crack tip. This internal loading acting in the air gap (the external crack) leads to a stress intensity factor Km, which is cancelled with the stress intensity factor KI due to the external loading. This cancellation suppresses the stress singularities, ensures the continuity of stresses, and fixes the radius c and the crack opening displacement δt. The energy release rate G is computed by the J-integral and the equilibrium is given by G = w. The equilibrium curves a(P), a(δ), and P(σ), the adherence forces at fixed load or fixed grips, the profiles, and the stress distributions can therefore be drawn as a function of a single parameter λ. When λ increases from zero to infinity there is a continuous transition from the DMT approximation to the JKR approximation. Furthermore the value of G for the DMT approximation is derived. It is shown that it is not physically consistent to have tensile stresses in the area of contact and no adhesion forces outside or no tensile stresses in the area of contact and adhesion forces outside. In the JKR approximation the distribution of adhesion forces is reduced to a singular stress at r = a+. The total attraction force outside the contact being zero, the integral of stresses in the contact is equal to the applied load P and negative applied loads are supported by the elastic restoring forces. In the DMT approximation the adhesion stresses tend toward zero to have a continuity with the stress at r = a−, but their integral is finite and the total attraction force outside the contact is 2πwR. In the area of contact the distribution of stresses is Hertzian, and their integral is P + 27πwR. Negative applied loads are sustained by adhesion forces outside the contact.

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1,808 citations

Journal Article•DOI•

Discrete particle simulation of particulate systems: Theoretical developments

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Haiping Zhu¹, Zongyan Zhou¹, Runyu Yang¹, Aibing Yu¹•Institutions (1)

University of New South Wales¹

01 Jul 2007-Chemical Engineering Science

TL;DR: This paper reviews the work in this area with special reference to the discrete element method and associated theoretical developments, and covers three important aspects: models for the calculation of the particle–particle and particle–fluid interaction forces, coupling of discrete elements method with computational fluid dynamics to describe particle-fluid flow, and the theories for linking discrete to continuum modelling.

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1,563 citations

Monograph•DOI•

The Rock Physics Handbook

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Gary Mavko¹, Tapan Mukerji¹, Jack Dvorkin²•Institutions (2)

Stanford University¹, King Fahd University of Petroleum and Minerals²

09 Jan 2020

TL;DR: The third edition of the reference book as discussed by the authors has been thoroughly updated while retaining its comprehensive coverage of the fundamental theory, concepts, and laboratory results, and highlights applications in unconventional reservoirs, including water, hydrocarbons, gases, minerals, rocks, ice, magma and methane hydrates.

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Abstract: Responding to the latest developments in rock physics research, this popular reference book has been thoroughly updated while retaining its comprehensive coverage of the fundamental theory, concepts, and laboratory results. It brings together the vast literature from the field to address the relationships between geophysical observations and the underlying physical properties of Earth materials - including water, hydrocarbons, gases, minerals, rocks, ice, magma and methane hydrates. This third edition includes expanded coverage of topics such as effective medium models, viscoelasticity, attenuation, anisotropy, electrical-elastic cross relations, and highlights applications in unconventional reservoirs. Appendices have been enhanced with new materials and properties, while worked examples (supplemented by online datasets and MATLAB® codes) enable readers to implement the workflows and models in practice. This significantly revised edition will continue to be the go-to reference for students and researchers interested in rock physics, near-surface geophysics, seismology, and professionals in the oil and gas industries.

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1,387 citations

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On the Contact of Elastic Solids

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