The oblique compression of two elastic spheres

Walton, K.

doi:10.1016/0022-5096(78)90005-4

Cited by 53 publications

(26 citation statements)

References 3 publications

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“…While the former are subject of ongoing dispute, the latter are implemented in a commonly accepted way, based on the first realistic model for static friction, as introduced by Cundall and Strack [6,12,39,64,73]: a virtual tangential spring is attached to each contact and evolves while the contact partners are moving and rotating, relative to each other, due to the contact force and the many other forces from other particles. Even though much more advanced models were discussed in the literature, related to the early works of Mindlin et al [53,54], Derjaguin et al [15], and Johnson et al [26], the basic idea remains the same, being complemented by additional effects like, e.g., hysteresis, non-linearity, and others [27,72,83,84,93,94]. Advanced contact models are then applied to various situations in powder flow [6,29,36,73,80,82,95,97].…”

Section: Frictional Contact Modelsmentioning

confidence: 99%

“…This will lead to a larger contact area with increased stiffness and increased adhesion due to the van der Waals forces. Like in the case of friction, plenty of models are available, some of them based on visco-elasticity [7,32,47,76] others on elastoplasticity [25,27,83,84,93,94]. For spheres, typically contact models in the spirit of Hertz [4,22,35,60,66,70,79] seem appropriate-but only when the forces are small enough so that the yield stress is reached nowhere close to the contact area.…”

Section: Normal Contact Modelingmentioning

confidence: 99%

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Cohesive, frictional powders: contact models for tension

Luding¹

2008

Granular Matter

490

429

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The contacts between cohesive, frictional particles with sizes in the range 0.1-10 µm are the subject of this study. Discrete element model (DEM) simulations rely on realistic contact force models-however, too much details make both implementation and interpretation prohibitively difficult. A rather simple, objective contact model is presented, involving the physical properties of elastic-plastic repulsion, dissipation, adhesion, friction as well as rollingand torsion-resistance. This contact model allows to model bulk properties like friction, cohesion and yield-surfaces. Very loose packings and even fractal agglomerates have been reported in earlier work. The same model also allows for pressure-sintering and tensile strength tests as presented in this study.

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Section: Frictional Contact Modelsmentioning

confidence: 99%

Section: Normal Contact Modelingmentioning

confidence: 99%

Cohesive, frictional powders: contact models for tension

Luding¹

2008

Granular Matter

490

429

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“…However, in experiments of interest here, one rough surface slides against another rough surface, rather than a smooth surface, and deformation on the scale of an asperity my be complicated because of the very anisotropic mineral grains in rock. Further, the slip at contacts has been shown [see Walton, 1978;Elata and Berryman, 1996] to be much more complicated than the simple process described by Mindlin [1949].…”

Section: Assumptionsmentioning

confidence: 99%

A theoretical analysis of sliding of rough surfaces

Walsh¹

2003

J. Geophys. Res.

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[1] I used a model proposed by Greenwood and Williamson [1966], who analyzed closure between a rough surface and a smooth surface under normal stress, to analyze the growth of slip under increasing shear stress, normal stress remaining constant. The two bodies are elastic half-spaces, one rough and one smooth, and Coulomb friction resists slip at sliding contacts. The elastic and dissipative components of the constitutive relation in shear depend upon statistical parameters which describe the topography of the rough surface. I made a parametric study of the effect of topography on the constitutive relations in shear by comparing a model in which the progress of slip at a contact is continuous with one in which the contact goes discontinuously from ''stuck'' to sliding. The effect of topography was also studied by assuming that the probability density distribution of the heights of asperities is Gaussian or, alternatively, a negative exponential. These variations in topography produced only minor differences in the constitutive behavior. This insensitivity of the constitutive behavior to differences in the statistical description of the topography arises in part because, only relatively, a small range of asperity heights is active in typical experiments. Work done against friction introduces a dissipative component into the constitutive behavior which I evaluated analytically; I show that the components have a simple graphical construction on plots of shear stress versus displacement developed from experimental observations. Sliding in the reverse sense which occurs when the applied shear stress is relaxed is analyzed, resulting in expressions which describe the shape of hysteresis loops formed when shear stress is cycled. Introducing measurements made on surfaces of specimens of granite and quartzite into the theoretical relations, I found reasonable agreement with experimental data.INDEX TERMS: 7260 Seismology: Theory and modeling; KEYWORDS: friction, rough surfaces, sliding Citation: Walsh, J. B., A theoretical analysis of sliding of rough surfaces,

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“…This law covers most of the tangential compliance models proposed in the literature [7,26,44,45], and is therefore quite general. Recall that x i is B's endpoint of the overlap segment.…”

Section: Tangential Compliance Modelsmentioning

confidence: 92%

On the mechanics of natural compliance in frictional contacts and its effect on grasp stiffness and stability

Shapiro

Rimon

Burdick

2004

IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004

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This paper considers the effect of natural material compliance on the stiffness and stability of frictional multi-contact grasps and fixtures. The contact preload profile is a key parameter in the nonlinear compliance laws governing such contacts. The paper introduces the Hertz-Walton contact compliance model which is valid for linear contact loading profiles. The model is specified in a lumped parameter form suitable for on-line grasping applications, and is entirely determined by the contact friction and by the material and geometric properties of the contacting bodies. The model predicts an asymmetric stiffening of the tangential reaction force as the normal load at the contact increases. As a result, the composite stiffness matrix of multi-contact grasps governed by natural compliance effects is asymmetric, indicating that these contact arrangements are not governed by any potential energy function. Based on the compliant grasp dynamics, the paper derives rules indicating which contact point locations and what preload profiles guarantee grasp and fixture stability. The paper also describes preliminary experiments supporting the contact model predictions.

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The oblique compression of two elastic spheres

Cited by 53 publications

References 3 publications

Cohesive, frictional powders: contact models for tension

Cohesive, frictional powders: contact models for tension

A theoretical analysis of sliding of rough surfaces

On the mechanics of natural compliance in frictional contacts and its effect on grasp stiffness and stability

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