A Local Constitutive Model with Anisotropy for Various Homogeneous 2D Biaxial Deformation Modes

Luding, Stefan; Perdahcıoğlu, Emin Semih

doi:10.1002/cite.201000180

Cited by 21 publications

(82 citation statements)

References 35 publications

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“…The evolution of the shear stress towards the steady state was the subject of study in 2D [30,31] and 3D [12], but will not be addressed here. A model that connects, in particular, the evolution of stress and structure is in development and will be published elsewhere [32,33].…”

Section: Discussion Of the Present Approachmentioning

confidence: 99%

The critical-state yield stress (termination locus) of adhesive powders from a single numerical experiment

Luding¹,

Alonso‐Marroquín

2011

Granular Matter

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Dry granular materials in a split-bottom ring shear cell geometry show wide shear bands under slow, quasistatic, large deformation. This system is studied in the presence of contact adhesion, using the discrete element method (DEM). Several continuum fields like the density, the deformation gradient and the stress tensor are computed locally and are analyzed with the goal to formulate objective constitutive relations for the flow behavior of cohesive powders. From a single simulation only, by applying time-and (local) space-averaging, and focusing on the regions of the system that experienced considerable deformations, the critical-state yield stress (termination locus) can be obtained. It is close to linear, for non-cohesive granular materials, and nonlinear with peculiar pressure dependence, for adhesive powdersdue to the nonlinear dependence of the contact adhesion on the confining forces. The contact model is simplified and possibly will need refinements and additional effects in order to resemble realistic powders. However, the promising method of how to obtain a critical-state yield stress from a single numerical test of one material is generally applicable and waits for calibration and validation.

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Section: Discussion Of the Present Approachmentioning

confidence: 99%

The critical-state yield stress (termination locus) of adhesive powders from a single numerical experiment

Luding¹,

Alonso‐Marroquín

2011

Granular Matter

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“…[17] is adopted: positive (+) for dilatation/extension and negative (-) for compression/contraction. Therefore, compressive stresses like σ 0 are negative.…”

Section: Model Systemmentioning

confidence: 99%

“…where C 1111 , C 2222 and λ = C 1122 are elements of the (rank four) stiffness/acoustic tensor of the system, which in a general constitutive relation of anisotropic elasticity, relates stress and strain increments [17]:…”

Section: Model Systemmentioning

confidence: 99%

“…(8) is reversible (elastic), while the second contains the stress response due to possibly irreversible changes of structure. Using B, G, and A, one can directly relate isotropic and deviatoric stress and strain [17]:…”

Section: Model Systemmentioning

confidence: 99%

“…In the following, a recently proposed constitutive model [17] is briefly presented and then applied to isobaric axial-symmetric deformation. The (classical) bulk and shear moduli are constants here, in order to be able to focus on the effect of anisotropy and the anisotropy material parameters exclusively.…”

Section: Introductionmentioning

confidence: 99%

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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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The discrete element method with deformable particles

Rojek

Zubelewicz

Madan

et al. 2018

Numerical Meth Engineering

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Summary This work presents a new original formulation of the discrete element method (DEM) with deformable cylindrical particles. Uniform stress and strain fields are assumed to be induced in the particles under the action of contact forces. Particle deformation obtained by strain integration is taken into account in the evaluation of interparticle contact forces. The deformability of a particle yields a nonlocal contact model, it leads to the formation of new contacts, it changes the distribution of contact forces in the particle assembly, and it affects the macroscopic response of the particulate material. A numerical algorithm for the deformable DEM (DDEM) has been developed and implemented in the DEM program DEMPack. The new formulation implies only small modifications of the standard DEM algorithm. The DDEM algorithm has been verified on simple examples of an unconfined uniaxial compression of a rectangular specimen discretized with regularly spaced equal bonded particles and a square specimen represented with an irregular configuration of nonuniform‐sized bonded particles. The numerical results have been verified by a comparison with equivalent finite element method results and available analytical solutions. The micro‐macro relationships for elastic parameters have been obtained. The results have proved to have enhanced the modeling capabilities of the DDEM with respect to the standard DEM.

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A Local Constitutive Model with Anisotropy for Various Homogeneous 2D Biaxial Deformation Modes

Cited by 21 publications

References 35 publications

The critical-state yield stress (termination locus) of adhesive powders from a single numerical experiment

The critical-state yield stress (termination locus) of adhesive powders from a single numerical experiment

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

The discrete element method with deformable particles

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