Analysis of three-dimensional micro-mechanical strain formulations for granular materials: Evaluation of accuracy

Abstract

a b s t r a c tAn important objective of recent research on micro-mechanics of granular materials is to develop macroscopic constitutive relations in terms of micro-mechanical quantities at inter-particle contacts. Although the micro-mechanical formulation of the stress tensor is well established, the corresponding formulation for the strain tensor has proven to be much more evasive, still being the subject of much discussion. In this paper, we study various micro-mechanical strain formulations for three-dimensional granular assemblies, following the work of Bagi in two dimensions . All of these formulations are either based on an equivalent continuum approach, or follow the best-fit approach. Their accuracy is evaluated by comparing their results, using data from Discrete Element Method simulations on periodic assemblies, to the macroscopic deformation. It is found that Bagi's formulation (Bagi, 1996), which is based on the Delaunay tessellation of space, is the most accurate. Furthermore, the best-fit formulation based on particle displacements only did unexpectedly well, in contrast to previously reported results for two-dimensional assemblies.

Constitutive relations for the isotropic deformation of frictionless packings of polydisperse spheres

“…The evolution of, not only, pressure but also of deviatoric stresses is related to the anisotropy of the structure, see the 2D observations in Refs. [28,29] and the more recent results in 3D, [30,31], which also confirm that the scaling relation of the fabric -as observed here without friction -holds also in the presence of friction [23,32].…”

Numerical analysis of compression mechanics of highly polydisperse granular mixtures with different PSD-s

“…Particle size distribution can be described by a continuous or a discrete distribution [13][14][15][16][17]. Normal and lognormal PSDs are often assumed in descriptions of the random variation that occurs in the data from many scientific disciplines [18][19][20] and in descriptions of granular materials, which are important in many industrial and natural processes (e.g., seeds, grains, sands, gravel, powders).…”

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

“…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.…”