A discrete-mechanical approach to granular materials

Satake, Masatada

doi:10.1016/0020-7225(92)90162-a

Cited by 85 publications

(43 citation statements)

References 2 publications

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“…The geometric structure of a 2D granular assembly can be described by a particle graph which entirely subdivides the assembly into polygonal sub-domains (Satake, 1992). In this paper, subdomains are similar to the void-cells considered in the framework of Kuhn (1997Kuhn ( , 1999 which are surrounded by the branches connecting two centers of particles participating in the load-bearing.…”

Section: Choice Of An Appropriate Meso-scalementioning

confidence: 99%

“…The difference between these approaches lies in the partition of a granular assembly. Kuhn (1997Kuhn ( , 1999Kuhn ( , 2003 used the partition proposed by Satake (1992) that subdivides a 2D granular assembly into polygonal sub-domains called void-cells whose edges connect the centers of particles in contact. In this framework, Kuhn modified the partition so that it includes only the particles which are part of the load-bearing framework.…”

Section: Introductionmentioning

confidence: 99%

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

Nguyen

Magoariec

Cambou

et al. 2009

International Journal of Solids and Structures

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a b s t r a c tIn this paper, we introduce a new scale called the meso-scale in order to define an appropriate local scale for multi-scale kinematic analysis in granular materials. The proposed meso-scale corresponds to subdomains obtained by subdividing a 2D granular assembly taking into account load-bearing contacts. For each sub-domain, a strain tensor is defined and a description of its structure is proposed. Our analysis, carried out on a biaxial compression test, reveals that strain is significantly related to the structure at the meso-scale: (1) strain in the major (respectively, minor) principal compression direction is largest within the sub-domains which are elongated in the minor (respectively, major) principal compression direction, and (2) contractancy takes place within the sub-domains which are elongated in the minor principal compression direction whereas dilatancy takes place within the sub-domains which are elongated in the major principal compression direction. Furthermore, we emphasize a relation between strain at the meso-scale and the induced anisotropy of granular materials during deviatoric loading.

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Section: Choice Of An Appropriate Meso-scalementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Nguyen

Magoariec

Cambou

et al. 2009

International Journal of Solids and Structures

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“…This situation is encountered in 2D granular materials, in which the polygon's vertices could be attached to the centres of grains, forming an interior void cell (Figure 1(a) and Reference [1]). The polygonal void cell is transported with the grains while the entire granular assembly is being deformed.…”

Section: Polygonal Regionsmentioning

confidence: 96%

“…The problem is illustrated in Figure 1(a), where a two-dimensional region has been partitioned into smaller polygonal sub-regions that encompass the void spaces inside of grain clusters. In this standard particle graph representation, the nodes (vertices) are associated with individual grains, and the sides (edges) are the branch vectors that connect particle centres [1]. We seek to compute the average strain within each polygon that results from the movements and rotations of its particles, and preferably in a computationally efficient manner.…”

Section: Introductionmentioning

confidence: 99%

A boundary integral for gradient averaging in two dimensions: application to polygonal regions in granular materials

Kuhn

2003

Numerical Meth Engineering

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SUMMARYA boundary integral is derived for averaging the gradients of a function within a two-dimensional (2D) region. The double integral uses the boundary derivative of the function to compute the average gradients, and it accounts for possible discontinuities in the function along the boundary. The integral reduces to a simple matrix expression for a polygonal region. When applied to a 2D granular material, the matrix expression can be used to compute the averaged local strains within polygonal void regions (particle clusters). In this situation, a realistic calculation of strain must account for the discontinuous movements among rigid particles along the polygon sides, as might occur if the particles are rotating as well as translating. The matrix expression provides a simple and efficient means of correcting the average strain to account for the discontinuous movements. For a cluster of circular disks, the correction is a consequence of the rolling and sliding among particles. The significance of the correction is illustrated with an example simulation of a large dense assembly of circular disks. Although the paper applies the boundary integral to the kinematics of granular regions, the integral will likely find other applications in 2D situations that involve discontinuous fields.

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“…Following previous works, Kanatani (1980); Satake (1992); Bagi (1996), we assign to a granular assembly a (Satake) graph, which we associate with a Delaunay triangulation. The graph consists of a network of vertices or nodes, representing particle centroids, connected by edges or "bonds", representing nearest-neighbor pairs.…”

Section: Delaunay Triangulation Deformation and Stressmentioning

confidence: 99%

Entropy and Material Instability in the Quasi-Static Mechanics of Granular Media

Goddard

Bifurcations, Instabilities, Degradation in Geomechanics

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SummaryStarting from a maximum-entropy model of granular statics, this brief note explores a possible material instability in the form of a "stress localization" anticipated in previous work (Goddard, 2002). After a brief review of the maximum-entropy model, it is shown that a special case allows for nonconvex pressure-volume response of a kind that could lead to heterogeneous stress states in an isotropically compressed granular packing.

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A discrete-mechanical approach to granular materials

Cited by 85 publications

References 2 publications

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

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

A boundary integral for gradient averaging in two dimensions: application to polygonal regions in granular materials

Entropy and Material Instability in the Quasi-Static Mechanics of Granular Media

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