Compliance of Elastic Bodies in Contact

Mindlin, R. D.

doi:10.1007/978-1-4613-8865-4_24

Cited by 658 publications

(939 citation statements)

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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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Section: Assumptionsmentioning

confidence: 99%

A theoretical analysis of sliding of rough surfaces

Walsh¹

2003

J. Geophys. Res.

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“…(52), the tangential shift increases with increasing k. When the state of full-slip is reached, a 30% larger displacement is obtained for k0.9 in comparison to the homogeneous case. Finally, it should be noted that we have assumed the usual approximations which are already contained in the classic solution of Cattaneo [17] and Mindlin [18] and have been discussed in detail by Ciavarella [11]. With reference to the corresponding paper we therefore waive an explicit listing.…”

Section: Figmentioning

confidence: 99%

Method of Dimensionality Reduction in Contact Mechanics and Friction: A User's Handbook. Ii. Power-Law Graded Materials

Heß

Popov

2016

FU Mech Eng

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“…It aims at determining the seismic attributes at time zero and their variations with time because of pressure, saturation and temperature changes. Elastic properties are predicted referring to Hertz-Mindlin relations (Mindlin, 1949) to account for pressure and to the generalized Gassmann equations (Ciz and Shapiro, 2007) for fluid substitution.…”

Section: Forward Modelingmentioning

confidence: 99%

Simultaneous Inversion of Production Data and Seismic Attributes: Application to a Synthetic SAGD Produced Field Case

Tillier

Ravalec

Veiga

2012

Oil Gas Sci. Technol. – Rev. IFP Energies nouvelles

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Résumé -Inversion simultanée des données de production et des attributs sismiques : application à un champ synthétique produit par injection de vapeur -L'utilisation conjointe des données de production et des attributs de sismique répétée facilite la compréhension des mouvements de fluide dans les formations géologiques et aide à la construction de modèles numériques fiables représentant ces formations. Ceci a récemment motivé le développement de techniques d'inversion ou de calage dédiées à l'identification de modèles cohérents avec l'ensemble des données disponibles. La méthodologie décrite dans ce papier permet de déterminer les cartes de propriétés pétrophysiques comme les faciès, les porosités ou les perméabilités à partir des données de production et des attributs de sismique répétée. Elle est appliquée avec succès à un champ synthétique d'huile lourde produite par injection de vapeur. Ce cas d'étude, inspiré d'un cas réel, illustre comment définir une méthodologie d'inversion qui respecte l'ensemble des données disponibles. L'étude est centrée sur trois points particuliers de la méthodologie qui sont les clés du succès. Premièrement, le choix de la paramétrisation est essentiel. La paramétrisation doit permettre des variations locales avec peu de paramètres. Deuxièmement, cette étude met en évidence la nécessité d'une formulation alternative pour mesurer l'erreur entre les attributs sismiques de référence et les attributs sismiques simulés. Finalement, nous étudions deux approches pour l'intégration des attributs sismiques de référence. Ils peuvent être intégrés en temps ou bien en profondeur. Nous montrons que, dans le cas étudié, ce dernier point n'influence pas la qualité du résultat obtenu car l'erreur de conversion temps-profondeur est faible. (after a time-to-depth conversion). In the case studied, it is shown that the two approaches are equivalent since time-to depth-conversion error is quite small.

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Compliance of Elastic Bodies in Contact

Cited by 658 publications

References 2 publications

A theoretical analysis of sliding of rough surfaces

A theoretical analysis of sliding of rough surfaces

Method of Dimensionality Reduction in Contact Mechanics and Friction: A User's Handbook. Ii. Power-Law Graded Materials

Simultaneous Inversion of Production Data and Seismic Attributes: Application to a Synthetic SAGD Produced Field Case

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