Micromechanical Aspects of Isotropic Granular Assemblies With Linear Contact Interactions

Abstract

The paper presents a micromechanical analysis of plane granular assemblies of discs with a range of diameters, and interacting according to linear contact force-interparticle compliance relationships. Contacts are assumed to be fixed and indestructible. Macroscopically, the system is described in terms of a two-dimensional analogue of generalized Hooke’s law. Explicit expressions for elastic constants in terms of microstructure are derived for dense isotropic assemblies. It is shown that Poisson’s ratio for dense systems depends on the ratio of tangential to normal contact stiffnesses. The derived expression for Poisson’s ratio is verified by numerically simulating plane assemblies comprising 1000 particles. The effect of density on Poisson’s ratio is investigated using numerical simulations. The theory of dense plane systems is extended to dense three-dimensional systems comprising spheres. Finally, it is shown that Poisson’s result ν=1/4 is recovered for spherical particles with central interactions.

Memory of the unjamming transition during cyclic tiltings of a granular pile

“…On the contrary, the strain and the fabric evolutions of the pile, related to structural disorder, are very sensitive to the amplitude of the cycles. These observations will hardly be explained by a simple constitutive law relating only stress and strain of the granular pile : such a relation should be not so trivial, but should take into account the anisotropy of the pile micro-structure [46,47,48,49,50,55]. The observation of piles with the same stress state but characterized by different granular fabrics, would suggest that stress induced by gravity are transmitted in the pile whatever the geometry of the total contact network, and whatever the structural disorder level.…”

“…In this picture, the hysteresis with a jump in the weak contact network would suggest that the size of correlations is larger than the typical lengthscale of the structural disorder in this phase, contrary to the predominant role of disorder in the micro-structure of the packing. Altogether, such complex behavioursspatial correlations and memory effects-call for more elaborated constitutive laws as in [46,47,48,49,50,55].…”

“…We now investigate the effect of the deformations on the evolution of the micro-structure, i.e., the geometry of the contact network, that are candidates at relevant internal variables [8,9,46,47,48,49,50]. The coordinancy Z, i.e., the mean number of contacts per grain, slide-averaged over 1 • -intervals is plotted in Figure 10 as a function of the pile slope during the cyclic solicitations.…”

A comparison of micro-mechanical modeling of asphalt materials using finite elements and doublet mechanics

“…A large volume of work has used fabric tensor theories to characterize the material microstructure and relate particular fabric tensors to the materialÕs constitutive stress-strain response; e.g. Nemat-Nasser and Mehrabadi (1983), Konshi and Naruse (1988) and Bathurst and Rothenburg (1988). Another area of analytical modeling has used distributed body theory whereby porous/ multiphase micro-structure is accounted for using an additional independent volume distribution function.…”

Orientation-based Continuum Damage Models for Rocks

“…In many homogenization studies on granular assemblies the 2532 X. Liu et al Pure appl. geophys., contribution of the antisymmetric part is neglected (CHRISTOFFERSON et al, 1981;WALTON, 1987;BATHURST and ROTHENBURG, 1988). Accordingly, the relative displacement vector between elements a and b is rewritten as u ðaÞ À u ðbÞ % EðxÞ Á ðX ðaÞ À X ðbÞ Þ; EðxÞ ¼ 1 2 uðxÞ r X þ r X uðxÞ ð Þ ;…”