Stress- and rate-controlled granular rheology

Jiang, Yimin; Liu, Mario

doi:10.1063/1.4811867

Cited by 7 publications

(5 citation statements)

References 32 publications

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“…As both the pressure and the shear stress may be written as e 1 + e 2γ 2 , where e 1 is the elastic, and e 2 the seismic, or viscous, contributions, we have a quadratic dependence of the Bagnold flow for e 2γ 2 ≫ e 1 , and hypoplastic rate-independence for e 2γ 2 ≪ e 1 . This rate regime has already been considered in [47].…”

Section: Discussionmentioning

confidence: 96%

“…So both may be written as e 1 + e 2 v 2 s , implying a quadratic dependence on the rate for e 2 v 2 s ≫ e 1 , and rate-independence for e 2 v 2 s ≪ e 1 . Rapid dense flow is considered in [47]. This ends the brief presentation of gsh.…”

Section: Discussionmentioning

confidence: 98%

“…The next two sections are respectively devoted to granular behavior in the quasi-elastic and hypoplastic regime, as defined above. (Application of gsh to fast dense flow of Regime 3 is in [47].) The manuscript ends with a conclusion and a list of symbols.…”

Section: Introductionmentioning

confidence: 99%

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Granular Solid Hydrodynamics (GSH): a broad-ranged macroscopic theory of granular media

Jiang

Liu

2014

Acta Mech

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A unified continuum-mechanical theory has been until now lacking for granular media, some believe it could not exist. Derived employing the hydrodynamic approach, gsh is such a theory, though as yet a qualitative one. The behavior being accounted for includes static stress distribution, elastic wave, elasto-plastic motion, the critical state and rapid dense flow. The equations and application to a few typical experiments are presented here.

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Section: Discussionmentioning

confidence: 96%

Section: Discussionmentioning

confidence: 98%

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Granular Solid Hydrodynamics (GSH): a broad-ranged macroscopic theory of granular media

Jiang

Liu

2014

Acta Mech

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“…The GSH used here reduces to various different, more classical theories, in the respective limits-when set appropriately, as was shown in: Refs. [156] for hypoplasticity, [160] for the (I)-rheology, and [47] for fluidity, etc. The question is now if it is possible to catch the complex phenomenology at yielding, jamming, un-jamming, elasticity and loss of elasticity with a simple model that only knows about four state-variables: , , u s , and T g .…”

Section: Granular Solid Hydrodynamics (Gsh)mentioning

confidence: 99%

Un-jamming due to energetic instability: statics to dynamics

2021

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Jamming/un-jamming, the transition between solid- and fluid-like behavior in granular matter, is an ubiquitous phenomenon in need of a sound understanding. As argued here, in addition to the usual un-jamming by vanishing pressure due to a decrease of density, there is also yield (plastic rearrangements and un-jamming that occur) if, e.g., for given pressure, the shear stress becomes too large. Similar to the van der Waals transition between vapor and water, or the critical current in superconductors, we believe that one mechanism causing yield is by the loss of the energy’s convexity (causing irreversible re-arrangements of the micro-structure, either locally or globally). We focus on this mechanism in the context of granular solid hydrodynamics (GSH), generalized for very soft materials, i.e., large elastic deformations, employing it in an over-simplified (bottom-up) fashion by setting as many parameters as possible to constant. Also, we complemented/completed GSH by using various insights/observations from particle simulations and calibrating some of the theoretical parameters—both continuum and particle points of view are reviewed in the context of the research developments during the last few years. Any other energy-based elastic-plastic theory that is properly calibrated (top-down), by experimental or numerical data, would describe granular solids. But only if it would cover granular gas, fluid, and solid states simultaneously (as GSH does) could it follow the system transitions and evolution through all states into un-jammed, possibly dynamic/collisional states—and back to elastically stable ones. We show how the un-jamming dynamics starts off, unfolds, develops, and ends. We follow the system through various deformation modes: transitions, yielding, un-jamming and jamming, both analytically and numerically and bring together the material point continuum model with particle simulations, quantitatively. Graphic abstract

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“…Examples are flows on an inclined plane or in a rotating drum, with a delay between jamming (angle of repose ϕ re ) and liquefaction (angle of stability ϕ st ), see Sec 3.4.3. Part of the results of this section is in [99].…”

Section: The µ−Rheology Versus Gshmentioning

confidence: 99%

Applying GSH to a wide range of experiments in granular media

Jiang

Liu

2015

Eur. Phys. J. E

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Abstract. Granular solid hydrodynamics (gsh) is a continuum-mechanical theory for granular media, the range of which is shown in this paper. Simple, frequently analytic solutions are related to classic observations at different shear rates, including: (i) static stress distribution, clogging; (ii) elasto-plastic motion: loading and unloading, approach to the critical state, angle of stability and repose; (iii) rapid dense flow: the µ-rheology, Bagnold scaling and the stress minimum; (iv) elastic waves, compaction, wide and narrow shear band. Less conventional experiments have also been considered: shear jamming, creep flow, visco-elastic behavior and nonlocal fluidization. With all these phenomena ordered, related, explained and accounted for, though frequently qualitatively, we believe that gsh may be taken as a unifying framework, providing the appropriate macroscopic vocabulary and mindset that help one coming to terms with the breadth of granular physics.

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Stress- and rate-controlled granular rheology

Cited by 7 publications

References 32 publications

Granular Solid Hydrodynamics (GSH): a broad-ranged macroscopic theory of granular media

Granular Solid Hydrodynamics (GSH): a broad-ranged macroscopic theory of granular media

Un-jamming due to energetic instability: statics to dynamics

Applying GSH to a wide range of experiments in granular media

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