This paper presents a model for the description of instantaneous collisions and a
computational method for the simulation of multiparticle systems’ evolution. The
description of the behavior of a collection of discrete bodies is based on the
consideration that the global system is deformable even if particles are rigid. Making
use of the principle of virtual work, the equations describing the regular (that is,
smooth) as well as the discontinuous (that is, the collisions) evolutions of the
motion system are obtained. For an instantaneous collision involving several
rigid particles, the existence and the uniqueness of the solution as well as its
satisfaction of a Clausius–Duhem inequality (proving that the evolution is
dissipative) are proved. In this approach, forces are replaced by a succession of
percussions (that is, forces concentrated in time). The approach is therefore named
Atomized stress Contact Dynamics respecting the Clausius–Duhem inequality
(A-CD).
This paper focuses also on nonassociated behaviors, and in particular on Coulomb’s
friction law. The use of this constitutive law represents a further theoretical and
numerical enhancement of the model. The theory is finally illustrated by some
numerical examples, using the associated constitutive laws and Coulomb’s
(nonassociated) friction law.
Keywords
discrete model, instantaneous collisions, principle of
virtual work, Coulomb's friction law, A-CD$^2$ method,
granular media
Division for Soil and Rock Mechanics
and Engineering Geology
Laboratoire Central des Ponts et Chaussées
MSRGI-LCPC
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France