A Mathematical Theory of Dilatancy

Reiner, Markus

doi:10.2307/2371950

Cited by 405 publications

(110 citation statements)

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“…We have modified the constitutive relation originally derived by Reiner (1945), to describe dilatancy in wet sand, by suggesting that the shear viscosity would also depend on the shear rate and the volume fraction. As a result of this modification, the fluid referred to as the Reiner-Rivlin equation, now has the possibility of being shear-thickening (dilatant) not only due to shear rate, but also due to the dependence of the viscosity on the volume fraction.…”

Section: Discussionmentioning

confidence: 99%

“…For a review of this aspect of the modeling activities we refer the reader to the recent article by Elaskar and Godoy (1998). Reiner (1945Reiner ( , 1948 proposed and derived a constitutive relation for wet sand whereby the concept of dilatancy is given a mathematical structure. This was accomplished through the relation between two tensors and the resulting second order effects in viscous and elastic media.…”

Section: Constitutive Equationsmentioning

confidence: 99%

“…In this paper we modify the constitutive relation derived by Reiner (1945), to describe dilatancy in wet sand, by suggesting that the shear viscosity would depend on the shear rate and the volume fraction. We then look at the flow of a saturated densely packed bed of particles (with liquid in the pores) between two horizontal flat plates.…”

Section: Introductionmentioning

confidence: 99%

“…The work of Reynolds was followed by the experimental studies of Jenkin (1931), Rowe (1962), Andrade and Fox (1949), and Bolton (1986) to name a few (see Massoudi and Mehrabadi, 2001 for details). In fact, Reiner (1945Reiner ( , 1948Reiner ( , 1958 was one of the first who derived a non-Newtonian fluid model to predict dilatancy in wet sand. Even though this model does not take into account how the voidage (volume fraction) affects the stress, Reiner was able to show that application of a non-zero shear stress produces a change in volume.…”

Section: Introductionmentioning

confidence: 99%

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A generalization of Reiner's mathematical model for wet sand

Massoudi

2011

Mechanics Research Communications

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a b s t r a c tIn this paper we modify the constitutive relation derived by Reiner (1945), to describe dilatancy in wet sand, by suggesting that the shear viscosity would depend on the shear rate and the volume fraction. We then look at the flow of a saturated densely packed bed of particles (with liquid in the pores) between two horizontal flat plates. We obtain exact solutions for a very special case.Published by Elsevier Ltd.

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Section: Discussionmentioning

confidence: 99%

Section: Constitutive Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A generalization of Reiner's mathematical model for wet sand

Massoudi

2011

Mechanics Research Communications

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“…Therefore, linearly elastic materials undergoing infinitesimal strain do not exhibit dilatancy. Stuart and Dieterich (1974) considered a model of nonlinear elasticity complete to second order in stress (Reiner, 1945) ,…”

Section: Introductionmentioning

confidence: 99%

Applications of Geodesy to Geodynamics an International Symposium

Mueller

1977

Bull. Geodesique

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Numerical simulations of impact crater formation with dilatancy

2014

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Impact‐induced fracturing creates porosity that is responsible for many aspects of the geophysical signature of an impact crater. This paper describes a simple model of dilatancy—the creation of porosity in a shearing geological material—and its implementation in the iSALE shock physics code. The model is used to investigate impact‐induced dilatancy during simple and complex crater formation on Earth. Simulations of simple crater formation produce porosity distributions consistent with observations. Dilatancy model parameters appropriate for low‐quality rock masses give the best agreement with observation; more strongly dilatant behavior would require substantial postimpact porosity reduction. The tendency for rock to dilate less when shearing under high pressure is an important property of the model. Pressure suppresses impact‐induced dilatancy: in the shock wave, at depth beneath the crater floor, and in the convergent subcrater flow that forms the central uplift. Consequently, subsurface porosity distribution is a strong function of crater size, which is reflected in the inferred gravity anomaly. The Bouguer gravity anomaly for simulated craters smaller than 25 km is a broad low with a magnitude proportional to the crater radius; larger craters exhibit a central gravity high within a suppressed gravity low. Lower crustal pressures on the Moon relative to Earth imply that impact‐induced dilatancy is more effective on the Moon than Earth for the same size impact in an initially nonporous target. This difference may be mitigated by the presence of porosity in the lunar crust.

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A Mathematical Theory of Dilatancy

Cited by 405 publications

References 0 publications

A generalization of Reiner's mathematical model for wet sand

A generalization of Reiner's mathematical model for wet sand

Applications of Geodesy to Geodynamics an International Symposium

Numerical simulations of impact crater formation with dilatancy

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