Analysis of microstructural strain tensors for granular assemblies

Bagi, Katalin

doi:10.1016/j.ijsolstr.2005.07.016

Cited by 126 publications

(99 citation statements)

References 11 publications

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“…Bagi [13] also observed this effect in 2D simulations of a uniaxial compression test, showing data which Figure 3. Local best-fit strain versus distance from the bottom boundary non-dimensionalized by the mean particle diameter: stress increment 0-1 MPa.…”

Section: Strain Resultsmentioning

confidence: 73%

“…A measure of the internal strain can then be obtained by calculating some deformation gradient. A summary of different proposed methods for strain calculation based on individual particle displacements is given by O'Sullivan et al [12] and Bagi [13]. A few key methods will be mentioned here.…”

Section: Strain Calculationmentioning

confidence: 99%

“…A few key methods will be mentioned here. Bagi [13] and other similar methods (e.g. [14]) require a partition of space in different cells based on the particle centroids.…”

Section: Strain Calculationmentioning

confidence: 99%

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Flat boundaries and their effect on sand testing

Marketos

Bolton

2009

Num Anal Meth Geomechanics

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SUMMARYA study of the effect of the use of flat boundaries on the stressing of a sample of an idealized granular material with no applied shear is presented. Discrete element method (DEM) data of 1D compression were analysed and the local strain field inside the sample was investigated as the sample was stressed. A best-fit strain was seen to best describe the material behaviour free from boundary effects. The individual particle displacements were probed, providing insight into the behaviour of particles adjacent to the boundaries. In addition, the porosity and force distribution inside the sample were observed, allowing for estimates of the width of a boundary region to be made. This region, non-representative of far-field material behaviour, will affect the behaviour of a granular sample in DEM or laboratory tests, with local porosity differences leading to a change in the transport properties of the sample, and force distribution changes leading to a bias in the location of grain cracking or crushing events for sufficiently high stress levels. Nevertheless, the largest effect of the boundary region was a severe underestimation of the stiffness of a granular material.

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Section: Strain Resultsmentioning

confidence: 73%

Section: Strain Calculationmentioning

confidence: 99%

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Flat boundaries and their effect on sand testing

Marketos

Bolton

2009

Num Anal Meth Geomechanics

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“…In this study, the local results are found by looking at particle quantities with respect to their neighboring particles; specifically, the strain in the vicinity of each particle, which is computed using Cundall's best-fit strain [5], which represents the average deformation of a set of points undergoing displacement:…”

Section: Local Behaviormentioning

confidence: 99%

All you need is shape: Predicting shear banding in sand with LS-DEM

Kawamoto

Andò

Viggiani

et al. 2018

Journal of the Mechanics and Physics of Solids

277

111

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This paper presents discrete element method (DEM) simulations with experimental comparisons at multiple length scales-underscoring the crucial role of particle shape. The simulations build on technological advances in the DEM furnished by level sets (LS-DEM), which enable the mathematical representation of the surface of arbitrarily-shaped particles such as sands. We show that this ability to model shape enables unprecedented capture of the mechanics of granular materials across scales ranging from macroscopic behavior to local behavior to particle behavior. Specifically, the model is able to predict the onset and evolution of shear banding in sands, replicating the most advanced high-fidelity experiments in triaxial compression equipped with sequential X-ray tomography imaging. We present comparisons of the model and experiment at an unprecedented level of quantitative agreement-building a one-to-one model where every particle in the more than 53,000-particle array has its own avatar or numerical twin. Furthermore, the boundary conditions of the experiment are faithfully captured by modeling the membrane effect, as well as the platen displacement and tilting. The results show a computational tool that can give insight into the physics and mechanics of granular materials undergoing shear deformation and failure, with computational times comparable to those of the experiment. One quantitative measure that is extracted from the LS-DEM simulations that is currently not available experimentally is the evolution of three dimensional force chains inside and outside of the shear band. We show that the rotations on the force chains are correlated to the rotations in stress principal directions.

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“…There are several methods for transforming between discrete, grainscale parameters and macroscopic, continuum stress and strain (e.g. [31,32]). We consider the pack to be a representative volume of a larger medium, and compute the average stress and strain within this volume as described below.…”

Section: Evaluating Macroscopic Parametersmentioning

confidence: 99%

Mechanical properties of granular materials: A variational approach to grain‐scale simulations

Holtzman

Silin

Patzek

2008

Num Anal Meth Geomechanics

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SUMMARYThe mechanical properties of cohesionless granular materials are evaluated from grain-scale simulations. A three-dimensional pack of spherical grains is loaded by incremental displacements of its boundaries. The deformation is described as a sequence of equilibrium configurations. Each configuration is characterized by a minimum of the total potential energy. This minimum is computed using a modification of the conjugate gradient algorithm.Our simulations capture the nonlinear, path-dependent behavior of granular materials observed in experiments. Micromechanical analysis provides valuable insight into phenomena such as hysteresis, strain hardening and stress-induced anisotropy. Estimates of the effective bulk modulus, obtained with no adjustment of material parameters, are in agreement with published experimental data. The model is applied to evaluate the effects of hydrate dissociation in marine sediments. Weakening of the sediment is quantified as a reduction in the effective elastic moduli.

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Analysis of microstructural strain tensors for granular assemblies

Cited by 126 publications

References 11 publications

Flat boundaries and their effect on sand testing

Flat boundaries and their effect on sand testing

All you need is shape: Predicting shear banding in sand with LS-DEM

Mechanical properties of granular materials: A variational approach to grain‐scale simulations

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