Role of anisotropy in the elastoplastic response of a polygonal packing

Alonso‐Marroquín, Fernando; Luding, Stefan; Herrmann, Hans J.; Vardoulakis, I.

doi:10.1103/physreve.71.051304

Cited by 132 publications

(99 citation statements)

References 46 publications

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“…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%

“…Only few theories, see e.g. [2,7,15,[18][19][20]22] and references therein, involve an anisotropy state variable. The influence of the micromechanics on the noncoaxiality of stress, strain and anisotropy of soils is described e.g.…”

Section: Introductionmentioning

confidence: 99%

“…This involves dilatancy, yield stress, history de-V. Magnanimo, S. Luding Multi Scale Mechanics (MSM), CTW, UTwente, POBox 217, 7500 AE Enschede, Netherlands; v.magnanimo@utwente.nl, s.luding@utwente.nl pendence, as well as ratcheting [1,2] and anisotropy [6,13,[22][23][24] -among many others.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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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“…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%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Magnanimo¹,

Luding²

2011

Granular Matter

Self Cite

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“…Even though the spatial structure and anisotropies of the force network may be important [5,[7][8][9][10][11], a more basic quantity, the probability density of contact forces P͑f͒, has emerged as a key characterization of static granular matter [2,3,[12][13][14][15]. Recently this quantity has also been studied for a wider range of thermal and athermal systems [15,16].…”

Section: Introductionmentioning

confidence: 99%

Ensemble theory for force networks in hyperstatic granular matter

et al. 2004

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An ensemble approach for force networks in static granular packings is developed. The framework is based on the separation of packing and force scales, together with an a priori flat measure in the force phase space under the constraints that the contact forces are repulsive and balance on every particle. In this paper we will give a general formulation of this force network ensemble, and derive the general expression for the force distribution P͑f͒. For small regular packings these probability densities are obtained in closed form, while for larger packings we present a systematic numerical analysis. Since technically the problem can be written as a noninvertible matrix problem (where the matrix is determined by the contact geometry), we study what happens if we perturb the packing matrix or replace it by a random matrix. The resulting P͑f͒'s differ significantly from those of normal packings, which touches upon the deep question of how network statistics is related to the underlying network structure. Overall, the ensemble formulation opens up a different perspective on force networks that is analytically accessible, and which may find applications beyond granular matter.

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“…DEM allows the specification of particle properties and interaction laws and then the numerical solution of Newton's equations of motion [4,5] of all particles. Finding the connection between the micro-mechanical properties and the macroscopic behavior involves the so-called micromacro transition [6][7][8][9][10][11]. Extensive "microscopic" simulations of many homogeneous small samples, i.e., so-called representative volume elements (RVE), have to be used to derive the macroscopic constitutive relations needed to describe the material within the framework of a continuum theory.…”

Section: Introductionmentioning

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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Role of anisotropy in the elastoplastic response of a polygonal packing

Cited by 132 publications

References 46 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

Ensemble theory for force networks in hyperstatic granular matter

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

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