Granular solid hydrodynamics

Jiang, Yimin; Liu, Mario

doi:10.1007/s10035-009-0137-3

Cited by 147 publications

(172 citation statements)

References 88 publications

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“…Under shear deformation, the shear stress builds up until it reaches a yield-limit, as described by classical and more recent models, e.g. [11,13,23,24]. Also the anisotropy of the contact network varies, as related to the opening and closing of contacts, restructuring, and the creation and destruction of force-chains, as confirmed by DEM simulations [15,25].…”

Section: Introductionmentioning

confidence: 57%

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A local constitutive model with anisotropy for ratcheting under 2D axial-symmetric isobaric deformation

Magnanimo¹,

Luding²

2011

Granular Matter

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A local constitutive model for anisotropic granular materials is introduced and applied to isobaric (homogeneous) axial-symmetric deformation. The simplified model (in the coordinate system of the bi-axial box) involves only scalar values for hydrostatic and shear stresses, for the volumetric and shear strains as well as for the new ingredient, the anisotropy modulus.The non-linear constitutive evolution equations that relate stress and anisotropy to strain are inspired by observations from Discrete Element Method (DEM) simulations. For the sake of simplicity, parameters like the bulk and shear modulus are set to constants, while the shear stress ratio and the anisotropy evolve with different rates to their critical state limit values when shear deformations become large.When applied to isobaric deformation in the bi-axial geometry, the model shows ratcheting under cyclic loading. Fast and slow evolution of anisotropy with strain (relative to the evolution of anisotropy in stress) lead to dilatancy and contractancy, respectively. Furthermore, anisotropy acts such that it works "against" the strain/stress, e.g., a compressive strain builds up anisotropy that creates additional stress acting against further compression.

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Section: Introductionmentioning

confidence: 57%

“…Such an approach is similar to hypoplasticity [13] or GSH [11] and differs from elasto-plastic models. In the former both elastic and plastic strains always coexist [2].…”

Section: Non-linear Stress Evolutionmentioning

confidence: 99%

A local constitutive model with anisotropy for ratcheting under 2D axial-symmetric isobaric deformation

Magnanimo¹,

Luding²

2011

Granular Matter

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“…To achieve this goal, several constitutive models have been proposed in the literature, as those based on either dimensional analyses [30,31,32] or granular solid hydrodynamics [33]. In contrast, the theoretical constitutive model hereafter presented, as in Johnson and Jackson [34,35], Savage [36], Louge [37], Lee and Huang [38], Berzi et al [39] and Vescovi et al [40], assumes a parallel scheme according to which the stress tensor is evaluated as the sum of two contributions: one "ratedependent" and another "rate-independent".…”

Section: Introductionmentioning

confidence: 99%

A visco‐elasto‐plastic model for granular materials under simple shear conditions

Redaelli

Prisco

Vescovi

2015

Num Anal Meth Geomechanics

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SUMMARYThe numerical simulation of rapid landslides is quite complex mainly because constitutive models capable of simulating the mechanical behaviour of granular materials in the pre-and post-collapse regimes are still missing. The goal of this paper is to introduce a constitutive model capable of capturing the response of dry granular flows from quasi-static to dynamic conditions, in particular when the material experiences a sort of from solid to fluid phase transition. An ideal assembly of identical spheres under simple shear conditions is condsidered. In the constitutive model, void ratio and granular temperature have been chosen as state variables, and both shear and normal stresses are computed as the sum of two contributions: the quasi static and the collisional one. The former one is determined by using a perfect elasto-plastic model including the critical state concept, while the latter one is derived from the kinetic theory of granular gases. The evolution of the granular temperature, fundamentally governing the material phase transition, is obtained by imposing the kinetic fluctuating energy balance. The constitutive relationship has been integrated, under both constant pressure and constant volume conditions, and the influence of shear strain rate, initial void ratio and normal pressure on the mechanical response has been investigated.

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“…It can also help in empirical evaluation of the internal energy changes in appropriate continuum theories (e.g like Granular Solid Hydrodynamics [59], with recent advances in [60]), or for calibration in numerical simulations, e.g. [61,62].…”

Section: Resultsmentioning

confidence: 99%

State equation of mineral sands

Ivšić

2011

Granular Matter

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The pressure-volume analogy between compressible fluids and macroscopic sand bodies (Ivsic et al. in Phys A, 277:47-61, 2000) is further extended using quantitative determination of corresponding empirical constants based on adapted van der Waals state equation. The isothermal constants obtained by interpretation of triaxial sand tests at so called "critical state of sand" are clearly related to the universal ideal gas properties and molar properties of mineral sands. The corresponding constants for sand and gases or other volatile liquids have the same order of magnitude. The apparent bulk repulsion/attraction effects in sand bodies are also discussed.

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Granular solid hydrodynamics

Cited by 147 publications

References 88 publications

A local constitutive model with anisotropy for ratcheting under 2D axial-symmetric isobaric deformation

A local constitutive model with anisotropy for ratcheting under 2D axial-symmetric isobaric deformation

A visco‐elasto‐plastic model for granular materials under simple shear conditions

State equation of mineral sands

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