Tensorial form definitions of discrete-mechanical quantities for granular assemblies

Satake, Masatada

doi:10.1016/j.ijsolstr.2004.05.046

Cited by 52 publications

(49 citation statements)

References 11 publications

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“…A volume V is associated with the representative volume, and this volume encompasses both interior and peripheral particles and voids, although several approaches could be used in assigning peripheral void space to this volume. We refer to two unambiguous approaches to volume partitioning: the material cell partition of Bagi (1996) for particles of arbitrary shape, and the Dirichlet partition of Satake (2004) for circular or spherical particles.…”

Section: Equilibrium Equations Of Particlesmentioning

confidence: 99%

On virtual work and stress in granular media

Chang

Kuhn

2005

International Journal of Solids and Structures

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Section: Equilibrium Equations Of Particlesmentioning

confidence: 99%

On virtual work and stress in granular media

Chang

Kuhn

2005

International Journal of Solids and Structures

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“…Most of these techniques rely on an equivalent discrete-continuum approach. Delaunay triangulation [44,45] or Dirichlet tessellation [46] has made it possible to compute a local strain in discrete arrangements. The construction of a domain around the elements is nevertheless necessary which increases the computational time.…”

Section: The Discrete Elementmentioning

confidence: 99%

Experimental Investigation and Discrete Element Modelling of Composite Hollow Spheres Subjected to Dynamic Fracture

Coré

Kopp

Viot

et al. 2017

International Journal of Polymer Science

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This paper deals with the characterization and the numerical modelling of the collapse of composite hollow spherical structures developed to absorb energy during high velocity impacts. The structure is composed of hollow spheres ( = 2-30 mm) made of epoxy resin and mineral powder. First of all, quasi-static and dynamic (V = 5 mm⋅min −1 to V = 2 m⋅s −1 ) compression tests are conducted at room temperature on a single sphere to study energy dissipation mechanisms. Fracture of the material appears to be predominant. A numerical model based on the discrete element method is investigated to simulate the single sphere crushing. The stress-strain-time relationship of the material based on the Ree-Eyring law is numerically implemented. The DEM modelling takes naturally into account the dynamic fracture and the crack path computed is close to the one observed experimentally in uniaxial compression. Eventually, high velocity impacts (V > 100 m⋅s −1 ) of a hollow sphere on a rigid surface are conducted with an air cannon. The numerical results are in good agreement with the experimental data and demonstrate the ability of the present model to correctly describe the mechanical behavior of brittle materials at high strain rate.

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“…This is why Satake (2004) could advantageously apply the 3D extension of the generalized Dirichlet cell complex for the geometrical modeling of granular systems.…”

Section: The Generalized Dirichlet Cell Complexmentioning

confidence: 99%

“…(The power plane of two spheres is the set of those points having equal tangent lengths to the two spheres.) This cell complex is named 'Dirichlet tessellation' in my paper Bagi (1995), and in Satake (2004) citing my work.…”

Section: Introductory Remarksmentioning

confidence: 99%

Discussion of the paper “Tensorial form definitions of discrete mechanical quantities for granular assemblies” [M. Satake, Int. J. Solids and Structures 2004, 41(21), pp. 5775–5791]

Bagi

2006

International Journal of Solids and Structures

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The aim of this Discussion is to clarify a terminological issue in a previous IJSS paper. Introductory remarksSatake (2004) proposes a definition for stress and strain for an assembly of unequal spheres with the help of contact cells, a system of polyhedra carrying the stresses as well as the deformations of the assembly according to the approach of the paper. The assemblies considered by Satake ( Fig. 1) consist of spherical particles that may have contacts with each other. The spheres may intersect, but because of the mechanical background of the problem, these intersections are small compared to the sphere radii.The definition of contact cells is based on a cell complex determined by the power planes of the spheres. (The power plane of two spheres is the set of those points having equal tangent lengths to the two spheres.) This cell complex is named 'Dirichlet tessellation' in my paper Bagi (1995), and in Satake (2004) citing my work.Satake and myself were informed recently that the cell complex we called 'Dirichlet tessellation' for a collection of unequal spheres is known under other names in the mathematical literature. In order to clarify this terminological confusion, an overview will be given here on the history and on the different existing names of this and similar other tessellations. (The figures are in 2D, but most of them are illustrations of 3D systems as indicated in the text.) 0020-7683/$ -see front matter Ó

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Tensorial form definitions of discrete-mechanical quantities for granular assemblies

Cited by 52 publications

References 11 publications

On virtual work and stress in granular media

On virtual work and stress in granular media

Experimental Investigation and Discrete Element Modelling of Composite Hollow Spheres Subjected to Dynamic Fracture

Discussion of the paper “Tensorial form definitions of discrete mechanical quantities for granular assemblies” [M. Satake, Int. J. Solids and Structures 2004, 41(21), pp. 5775–5791]

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