# zbMATH — the first resource for mathematics

Theoretical approach to and numerical simulation of instantaneous collisions in granular media using the A-CD$$^{2}$$ method. (English) Zbl 1163.74014
Summary: This paper presents a model for the description of instantaneous collisions and a computational method for the simulation of multiparticle system 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 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-CD2). This paper focuses also on nonassociated behaviors, and in particular on Coulomb 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 (nonassociated) friction law.
##### MSC:
 74E20 Granularity 74A15 Thermodynamics in solid mechanics 74M10 Friction in solid mechanics
Full Text: