L’approche énergétique en mécanique des milieux granulaires

E. Frossard. Expert, Bureau d’ingénieurs-conseils Coyne et Bellier, frossardetienne@aol.com


Abstract: 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 developped on the original concept of energy rate tensor of internal actions.

The communication displays first:

- an original tensorial pattern underlying the well known laws of friction, at the elementary scale of moving contact;

- the macrostructural solution for the discontinuous granular mass, under general threedimensional movements, as a result of a tensorial structure associated with the distribution of moving contacts.

It is shown that the jump from the individual behaviour (elementary contact) to the collective behaviour (granular mass) makes appear into the general dissipation equation, a population effect, related to the intensity of a kind of interaction between moving contacts, the “internal feedback”(réalimentation interne), and related to the grade of disorder in the distribution of moving contacts, interaction and disorder determining the intensity of energy dissipation.

Among the solutions, appear those of minimal dissipation, associated with ordered patterns in the distribution of moving contacts orientations: in plane strain these ordered patterns result precisely into the RANKINE slip-lines, well known in geomechanics.

Concerning the equivalent continuous media, the communication draws a parallel with a dissipation equation for the continuum, established an published long ago by the author, on the basis of physical interpretation of a wide set of experimental results on these materials. This equation leads analytically to:

- the ROWE “stress-dilatancy” relations;

- the COULOMB failure criterion, at critical state;

- the densification by cyclical strains, in certain conditions, and other features of the “characteristic domain”.

The structure of this dissipation equation for the equivalent continuum, is shown to be formally identical to the general dissipation equation for the discontinuous granular mass, including the presence of a particular energy rate tensor of internal actions, build on stress and strain rate tensors.This identification leads to express the macroscopic quantities, stress and strain rates,in function of microscopic variables, contact forces, sliding velocities, and geometry of packing.

It is shown also that experimental results suggest strongly the presence of a minimum energy principle: according to limit conditions allowance, the movements into the material tend towards one of the minimal dissipation solutions.The physical meaning of this principle, is then related to a key result of the thermodynamicians of irreversible processes (Prigogine): the theorem of minimum entropy production.


poudres & grains NS 2, 1-56 (décembre 2001)