Analysis of structure and strain at the meso-scale in 2D granular materials

Nguyen, Ngoc‐Son; Magoariec, Hélène; Cambou, Bernard; Danescu, Alexandre

doi:10.1016/j.ijsolstr.2009.04.019

Cited by 39 publications

(47 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…On the other hand, deformation characteristics have not been studied in much detail. Most studies are restricted to the two-dimensional case (Kruyt and Rothenburg, 2003;Kruyt and Rothenburg, 2004;Kruyt and Antony, 2007;Tordesillas et al, 2010;Nguyen et al, 2009).…”

Section: Introductionmentioning

confidence: 99%

Micro-mechanical analysis of deformation characteristics of three-dimensional granular materials

Durán

Kruyt

Luding

2010

International Journal of Solids and Structures

View full text Add to dashboard Cite

a b s t r a c tThe deformation characteristics of idealized granular materials have been studied from the micromechanical viewpoint, using Bagi's three-dimensional micro-mechanical formulation for the strain tensor [Bagi, K., 1996. Mechanics of Materials 22, 165-177]. This formulation is based on the Delaunay tessellation of space into tetrahedra. The set of edges of the tetrahedra can be divided into physical contacts and virtual contacts between particles. Bagi's formulation expresses the continuum, macro-scale strain as an average over all edges, of their relative displacements (between two successive states) and the complementary-area vectors. This latter vector is a geometrical quantity determined from the set of edges, i.e. from the structure of the particle packing.Results from Discrete Element Method simulations of isotropic and triaxial loading of a three-dimensional polydisperse packing of spheres have been used to investigate statistics of the branch vectors and complementary-area vectors of edges (subdivided into physical and virtual contacts) and of the relative displacements of edges. The investigated statistics are probability density functions and averages over groups of edges with the same orientation. It is shown that these averages can be represented by second-order Fourier series in edge orientation.Edge orientations are distributed isotropically, contrary to contact orientations. The average lengths of the branch vectors and the normal component of the complementary-area vectors are distributed isotropically (with respect to the edge orientation) and their average values are related to each other and to the volume fraction of the assembly. The other two components of the complementary-area vector are zero on average.The total deformation of the assembly, as given by the average of the relative displacements of the edges of the Delaunay tessellation follows the uniform-strain prediction. However, neither the deformation of the physical contact network nor of the virtual contact network has this property. The average relative displacement of physical edges in the normal direction (determined by the branch vector) is smaller than that according to the uniform-strain assumption, while that of virtual contacts is larger. This is caused by the high interparticle stiffness that hinders compression. The reverse observation holds for the tangential component of the relative displacement vector. The contribution of the deformation of the empty space between physical contacts to the continuum, macro-scale strain tensor is therefore very important for the understanding and the prediction of the macro-scale deformation of granular materials.

show abstract

Section: Introductionmentioning

confidence: 99%

Micro-mechanical analysis of deformation characteristics of three-dimensional granular materials

Durán

Kruyt

Luding

2010

International Journal of Solids and Structures

View full text Add to dashboard Cite

show abstract

“…Discrete element method allows for direct quantification of the inherent fabric anisotropy of granular materials. Various forms of contact normal‐based and void vector‐based fabric quantities have been proposed and applied in studying the anisotropic behavior of granular materials (e.g., ). The contact normal fabric tensor F c that characterizes the spatial distribution features of inter‐particle contact normal directions is defined in this paper after Satake to be

F_{c} = \frac{1}{2 N_{c}} \sum_{k = 1}^{2 N_{c}} n_{c}^{k} \otimes n_{c}^{k}

where N c is the number of contacting points in the granular assembly,

n_{c}^{k}

is the unit vector representing the normal direction of the k th inter‐particle contact, and ‘⊗’ denotes the tensor product.…”

Section: Simulation Setupmentioning

confidence: 99%

Strength anisotropy of granular material consisting of perfectly round particles

Wang

Tong

et al. 2017

Num Anal Meth Geomechanics

View full text Add to dashboard Cite

The strength anisotropy of granular materials deposited under gravity has mostly been attributed to elongated particles' tendency to align long axes along the bedding plane direction. However, recent experiments on near‐spherical glass beads, for which preferred particle alignment is inapplicable, have exhibited surprisingly strong strength anisotropy. This study tests the hypothesis that certain amount of fabric anisotropy caused by the anisotropic stress during deposition under gravity can be locked in a circular‐particle deposit. Such locked‐in fabric anisotropy can withstand isotropic consolidation and leads to significant strength anisotropy. 2D discrete element method simulations of direct shear tests on circular‐particle deposits are conducted in this study, allowing for the monitoring of both stress and fabric. Simulations on both monodispersed and polydispersed circular‐particle samples generated under downward gravitational acceleration exhibit clear anisotropy in shear strength, thereby proving the hypothesis. When using contact normal‐based and void‐based fabric tensors to quantify fabric anisotropy in the material, we find that the intensity of anisotropy is discernible but low prior to shearing and is dependent on the consolidation process and the dispersity of the sample. The fact that samples with very low anisotropy intensity measurements still exhibit fairly strong strength anisotropy suggests that current typical contact normal‐based and void‐based second‐order fabric tensor formulations may not be very effective in reflecting the anisotropic peak shear strength of granular materials. Copyright © 2017 John Wiley & Sons, Ltd.

show abstract

“…This method has been used by many other researches [29][30][31]] to generate densely packed particle assemblies and readers can refer to [25] for more details. The numerical specimen studied in this section consists of 16,451 particles and the histogram of the particle sizes, as shown in Fig.4, confirms a uniform distribution.…”

Section: Generation Of Dem Specimenmentioning

confidence: 99%

A DEM model for visualising damage evolution and predicting failure envelope of composite laminae under biaxial loads

Ismail

Yang

2016

Composites Part B: Engineering

View full text Add to dashboard Cite

A two dimensional particle model based on the discrete element method (DEM) is developed for micromechanical modelling of fibre reinforced polymer (FRP) composite laminae under biaxial transverse loads. Random fibre distribution within a representative volume element (RVE) is considered for the micromechanical DEM simulations. In addition to predicting the stress-strain curves of the RVEs subjected to transverse compression and transverse shear stresses against the experimental testing results and other numerical modelling results, the DEM model is also able to capture the initiation and propagation of all micro damage events. Fibre distribution is found to more significantly influence the ultimate failure of composite laminae under transverse shear, while it has much less effect on the failure under transverse compression. The failure envelope of composite laminae under biaxial transverse compression and transverse shear is predicted and compared with Hashin and Puck failure criteria, showing a reasonable agreement. The predicted failure envelope is correlated with the damage evolution and the quantitative analysis of failure events, which improves the understanding of the failure mechanisms.

show abstract

Analysis of structure and strain at the meso-scale in 2D granular materials

Cited by 39 publications

References 19 publications

Micro-mechanical analysis of deformation characteristics of three-dimensional granular materials

Micro-mechanical analysis of deformation characteristics of three-dimensional granular materials

Strength anisotropy of granular material consisting of perfectly round particles

A DEM model for visualising damage evolution and predicting failure envelope of composite laminae under biaxial loads

Contact Info

Product

Resources

About