Macroscopic Continuous Approach versus Discrete Approach, Fluctuations, criticality and SOC. A state of the question based on articles in Powders & Grains 2001

As a complementary tool to laboratory experiments, discrete numerical simulation, applied to granular materials, provides valuable information on the grain and contact scale microstructure, thereby enabling one to better understand the microscopic origin of macroscopic mechanical behaviours. We first introduce different simulation methods, which we regard as techniques for numerical experimentation, in connection with micromechanical models for intergranular contacts. We lay ...

In general, the mechanics of granular matter is described using continuum mechanics approach; this requires to introduce the concepts of stress and strain, which are averaged quantities, so that this needs also to introduce the notion of representative elementary volume (REV) above which averaged quantities have some physical meaning. As local quantities fluctuate spatially in granular matter; a local measure of stress and strain shall exhibit fluctuations too, whose typical ...

A unified continuum-mechanical theory has been until now lacking for granular media, some believe it could not exist. Derived employing the hydrodynamic approach, GSH is such a theory, though as yet a qualitative one. The behavior being accounted for includes static stress distribution, elastic wave, elasto-plastic motion, the critical state and rapid dense flow. The equations and application to a few typical experiments are presented here.

This communication establishes first, that basis of discontinuous granular materials mechanics, are the explicit result of a new approach of the physics of energy dissipation by friction, and second, that these mechanics of discontinua, transposed to the equivalent continuous media, as used in geomechanics, is directly responsible for a large set of practical properties of these materials, part of the fundamentals of Soil Mechanics. These physics of energy dissipation are dev...

The stress response of a granular assembly subject to different changes of boundary conditions is studied experimentally in order to define the stress propagation characteristics. These results demonstrate that no simple and single relationship between local stresses exists, which would be imposed by the local structure of the granular assembly only in general. On the contrary, it is demonstrated that these results are controlled by the boundary conditions themselves and that...

Recent experimental results on the static or quasistatic response of granular materials have been interpreted to suggest the inapplicability of the traditional engineering approaches, which are based on elasto-plastic models (which are elliptic in nature). Propagating (hyperbolic) or diffusive (parabolic) models have been proposed to replace the `old' models. Since several recent experiments were performed on small systems, one should not really be surprised that (continuum) ...

The paper addresses the underlying source of two forms of induced anisotropy in granular materials: contact orientation anisotropy and contact force anisotropy. A rational, mathematical structure is reviewed for the manner in which fabric anisotropy emerges and evolves during loading. Fabric is expressed as an orientation density, and transport phenomena such as convection, contact generation, and diffusion control the rate of fabric evolution during loading. The paper propos...

Discrete-element simulations are used to monitor several micro-scale characteristics within a granular material, demonstrating their convergence during loading toward the critical state, their stationarity at the critical state, and the evolution of their disorder toward the critical state. Convergence, stationarity and disorder are studied in the context of the Shannon entropy and two forms of Kullback-Leibler relative entropy. Probability distributions of 20 aspects of micr...

Systematic numerical simulations of model dense granular materials in monotonous, quasistatic deformation reveal the existence of two different r\'egimes. In the first one, the macroscopic strains stem from the deformation of contacts. The motion can be calculated by purely static means, without inertia, stress controlled or strain rate controlled simulations yield identical smooth rheological curves for a same sample. In the second r\'egime, strains are essentially due to in...

We review the influence of micromechanical parameters on the macroscopic mechanical behaviour of granular materials, as numerically simulated in discrete element approaches, both in quasistatic conditions an din dense flow. We insist in particular on the role of suitably defined dimensionless numbers apt to provide a classification of rheological regimes of quite general validity.