Numerical evaluation of three non‐coaxial kinematic models using the distinct element method for elliptical granular materials

Jiang, Mingjing; Liu, J. D.; Arroyo, Marcos

doi:10.1002/nag.2540

Cited by 9 publications

(6 citation statements)

References 54 publications

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“…[20][21][22][23][24][25]. The DEM has also been applied to correlate the macro-and micromechanical performances of geomaterials [15,26,27]. Thornton [26] relates the normal and tangential contact forces to the stress tensor, respectively.…”

Section: Introductionmentioning

confidence: 99%

Discrete Element Method Analyses of Bond Degradation Evolutions for Cemented Soils

He,

Li,

Rui

2024

Fractal Fract

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The degradation of soil bonding, which can be described by the evolution of bond degradation variables, is essential in the constitutive modeling of cemented soils. A degradation variable with a value of 0/1.0 indicates that the applied stress is completely sustained by bonded particles/unbounded grains. The discrete element method (DEM) was used for cemented soils to analyze the bond degradation evolution and to evaluate the degradation variables at the contact scale. Numerical cemented soil samples with different bonding strengths were first prepared using an advanced contact model (CM). Constant stress ratio compression, one-dimensional compression, conventional triaxial tests (CTTs), and true triaxial tests (TTTs) were then implemented for the numerical samples. After that, the numerical results were adopted to investigate the evolution of the bond degradation variables BN and B0. In the triaxial tests, B0 evolves to be near to or larger than BN due to shearing, which indicates that shearing increases the bearing rate of bond contacts. Finally, an approximate stress-path-independent bond degradation variable Bσ was developed. The evolution of Bσ with the equivalent plastic strain can be effectively described by an exponential function and a hyperbolic function.

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Section: Introductionmentioning

confidence: 99%

Discrete Element Method Analyses of Bond Degradation Evolutions for Cemented Soils

He,

Li,

Rui

2024

Fractal Fract

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“…It has been concluded that the theory may be a viable law to describe the deformation of granular materials. The discrete element method has been employed in [21] to show that the model [22] for plastically incompressible materials provides a reasonable continuum mechanics description of the behavior of some granular materials. The present paper adopts the double shearing and rotation model proposed in [22].…”

Section: Introductionmentioning

confidence: 99%

General Planar Ideal Flow Solutions with No Symmetry Axis

Alexandrov,

Mokryakov

2023

Materials

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Bulk ideal flows constitute a wide class of solutions in plasticity theory. Ideal flow solutions concern inverse problems. In particular, the solution determines part of the boundary of a region where it is valid. Bulk planar ideal flows exist in the case of (i) isotropic rigid/plastic material obeying an arbitrary pressure-independent yield criterion and its associated flow rule and (ii) the double sliding and rotation model based on the Mohr–Coulomb yield criterion. In the latter case, the intrinsic spin must vanish. Both models are perfectly plastic, and the complete equation systems are hyperbolic. All available specific solutions for both models describe flows with a symmetry axis. The present paper aims at general solutions for flows with no symmetry axis. The general structure of the solutions consists of two rigid regions connected by a plastic region. The characteristic lines between the plastic and rigid regions must be straight, which partly dictates the general structure of the characteristic nets. The solutions employ Riemann’s method in regions where the characteristics of both families are curvilinear. Special solutions that do not have such regions are considered separately. In any case, the solutions are practically analytical. A numerical technique is only necessary to evaluate ordinary integrals. The solutions found determine the tool shapes that produce ideal flows. In addition, the distribution of pressure over the tool’s surface is calculated, which is important for predicting the wear of tools.

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“…It is a non-coaxial theory, since it does not assume the principal axes of the stress tensor and the rate-of-strain tensor coincide. Applications of the double-shearing theory to problems in granular flow have been documented throughout the literature [16][17][18][19][20][21][22][23][24]. The theory itself is closely related to other well-studied non-coaxial kinematic models for granular flow [25][26][27][28][29], which themselves have been studied in detail over the past decades [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

“…Applications of the double-shearing theory to problems in granular flow have been documented throughout the literature [16][17][18][19][20][21][22][23][24]. The theory itself is closely related to other well-studied non-coaxial kinematic models for granular flow [25][26][27][28][29], which themselves have been studied in detail over the past decades [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Axially symmetric continuum mechanical model for the oscillon

Hill

Spencer

McCue

2022

Mathematics and Mechanics of Solids

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The oscillon is a highly localized dynamical phenomenon occurring in a thin horizontal layer of granular material, which rests on a rigid plate oscillating in the vertical direction. The geometry is axially symmetric and physically resembles a splash of liquid due to a falling drop, except that it continually perpetuates itself and does not generate a spreading wave, as is the case for a liquid splash. The oscillon moves from “peak” to “crater” and “crater” to “peak” such that the time from “peak” to “peak” or “crater” to “crater” is twice the period of the oscillating plate. The physics of granular phenomena is not properly understood, and there is no continuum mechanical theory of granular materials which is widely accepted as accurately describing their behaviour. Here for a free-flowing (cohesion-less) granular material, under axially symmetric conditions, we present a partial continuum mechanical analysis assuming the Coulomb–Mohr yield function and non-dilatant double-shearing theory. We examine small perturbations superimposed upon a purely vertical vibration, and make the assumption that throughout the motion, the lower surface of the layer remains in contact with the rigid metal plate. We show how the temporal dependence, which decouples from the spatial structure, is governed by Mathieu’s equation for the physically relevant case of the rigid plate oscillating sinusoidally, and therefore stability is determined by certain key parameters. We explore a variety of possible forms for spatial dependence. The present axially symmetric analysis complements that presented by the authors for plane strain conditions, and we find, quite remarkably, that apart from constants, both flows are governed by similar fourth-order systems of ordinary differential equations. This means that for both plane strain and axially symmetry, analogous pattern forming conditions can operate.

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Numerical evaluation of three non‐coaxial kinematic models using the distinct element method for elliptical granular materials

Cited by 9 publications

References 54 publications

Discrete Element Method Analyses of Bond Degradation Evolutions for Cemented Soils

Discrete Element Method Analyses of Bond Degradation Evolutions for Cemented Soils

General Planar Ideal Flow Solutions with No Symmetry Axis

Axially symmetric continuum mechanical model for the oscillon

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