By Cambou B., Jean M. (eds.)
Approximately all solids are compised of grains. even though such a lot reports deal with fabrics as a continious good. The ebook applies research used on unfastened granular fabrics to dense grainular fabrics. This title’s major concentration is dedicated to static or dynamic loadings utilized to dense fabrics, even though fast flows and greatly dispersed media also are pointed out in short. 3 crucial components are lined: neighborhood variable research: touch forces, displacements and rotations, orientation of contacting debris and upholstery tensors are all examples of neighborhood variables. Their statistical distributions, comparable to spatial distribution and attainable localization, are analyzed, considering experimental effects or numerical simulations. swap of scales approaches: sometimes called “homogenization techniques”, those approaches give the opportunity to build continuum legislation for use in a continuum mechanics procedure or appearing smaller scale analyses. Numerical modeling: numerous tools designed to calculate approximate options of dynamical equations including unilateral touch and frictional legislation are offered, together with molecular dynamics, the detailed aspect approach and non-smooth touch dynamics. Numerical examples are given and the standard of numerical approximations is mentioned.
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Extra resources for Micromechanics of Granular Materials
Conclusion In this chapter, several generic features of the granular texture, force transmission and kinematics were analyzed by means of discrete element simulations and experiments. Some of the concepts and notions developed in this framework are currently used for the description and modeling of granular media. For example, the fabric tensors are important for the characterization of the texture. In the same way, the weak and strong contact networks are helpful for a ﬁne description of stress transmission in granular materials.
22) allows us to evaluate the evolution of the texture from the incremental macroscopic deformation. It is consistent with our observations about the evolution of contact orientations. e. ΔN (θ) = 0) along the zero extension lines Δεn (θ) = 0. 5. Space partition: tessellation A useful geometrical representation of granular texture consists of dividing the space occupied by the particles into contiguous cells. This procedure is called ‘tessellation’ and it can be considered as a ﬁrst step towards a continuum description of the material.
22. Let Pn be a point inside the particle (Gn ). This point may be chosen arbitrarily but it is usually the geometrical or inertial center of the particle. The Delaunay triangulation is obtained by simply connecting the points belonging to neighboring cells. In this network, the material points Pn are the nodes and the elements are triangles in 2D and tetrahedra in 3D surrounding the intergranular voids. This duality can be used to deﬁne macroscopic quantities [BAG 96]. The cells (Cn ) allow for the deﬁnition of neighbors and contacts.