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

2016

Acta Geotech.

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Accounting for elasto-plastic motion in granular media, hypoplasticity is a state-of-the-art constitutive model derived from data accumulated over many decades. In contrast, GSH, a hydrodynamic theory, is derived from general principles of physics, with comparatively few inputs from experiments, yet sporting an applicability ranging from static stress distribution via elasto-plastic motion to fast dense flow, including non-uniform ones such as a shear band. Comparing both theories, we find great similarities for uniform, slow, elasto-plastic motion. We also find that proportional paths and the Goldscheider rule used to construct barodesy, another, more recent constitutive model, are natural results of GSH's equations. This is useful as it gives these constitutive relations a solid foundation in physics, and in reverse, GSH a robust connection to reality. The same symbiotic relation exists between GSH and KCR, or Kamrin's non-local constitutive relation, a model that was successfully employed to account for a wide shear band in split bottom cells.

Section: Transition To Quasi-elasticitymentioning

confidence: 74%

Similarities between GSH, hypoplasticity and KCR

2016

Acta Geotech.

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“…Note that ε s does not actually diverge, because as T g → 0, the system enters the quasi-elastic regime, where its relaxation becomes exponential, see [17]. So even if the creep ε s is large close to π c , it comes to a halt eventually, and the system is mechanically stable.…”

Section: D1 Diverging Shear Strainmentioning

confidence: 98%

Why granular media are thermal, and quite normal, after all

2017

Eur. Phys. J. E

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Two approaches exist to account for granular behavior. The thermal one considers the total entropy, which includes microscopic degrees of freedom such as phonons; the athermal one (as with the Edward en-tropy) takes grains as elementary. Granular solid hydrodynamics (GSH) belongs to the first, DEM, granular kinetic theory and athermal statistical mechanics (ASM) to the second. A careful discussion of their conceptual differences is given here. Three noteworthy insights or results are: (1) While DEM and granular kinetic theory are well justified to take grains as elementary, any athermal entropic consideration is bound to run into trouble. (2) Many general principles are taken as invalid in granular media. Yet within the thermal approach, energy conservation and fluctuation-dissipation theorem remain valid, granular temperatures equilibrate, and phase space is well explored in a grain at rest. Hence these are abnormalities of the athermal approximation, not of granular media as such. (3) GSH is a wide-ranged continuum mechanical description of granular dynamics.

“…Because force equilibrium, ∇ j π i j = ρg i , is the condition for S = max with respect to variations of u i j [7][8][9], any stable stacking of grains (the ones being counted in the Edward entropy), is an equilibrium configuration.…”

Section: Athermal Gas and Thermal Solidmentioning

confidence: 99%

Why granular media are thermal after all

2017

EPJ Web Conf.

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Abstract. Two approaches exist to account for granular behavior. The thermal one considers the total entropy, which includes microscopic degrees of freedom such as phonons; the athermal one (as with the Edward entropy) takes grains as elementary. Granular solid hydrodynamics (GSH) belongs to the first, DEM, granular kinetic theory and athermal statistical mechanics (ASM) to the second. A careful discussion of their conceptual differences is given here. Three noteworthy insights or results are: (1) While DEM and granular kinetic theory are well justified to take grains as elementary, any athermal entropic consideration is bound to run into trouble.(2) Many general principles are taken as invalid in granular media. Yet within the thermal approach, energy conservation and fluctuation-dissipation theorem remain valid, granular temperatures equilibrate, and phase space is well explored in a grain at rest. Hence these are abnormalities of the athermal approximation, not of granular media as such. (3) GSH is a wide-ranged continuum mechanical description of granular dynamics.