Communications in Applied Mathematics and Computational Science

Theoretical approach to and numerical simulation of instantaneous collisions in granular media using the A-CD$^2$ method

Stefano Dal Pont and Eric Dimnet

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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-CD2). 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.

Article information

Commun. Appl. Math. Comput. Sci., Volume 3, Number 1 (2008), 1-24.

Received: 13 February 2007
Revised: 24 September 2007
Accepted: 26 September 2007
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 78M50: Optimization

discrete model instantaneous collisions principle of virtual work Coulomb's friction law A-CD$^2$ method granular media


Dal Pont, Stefano; Dimnet, Eric. Theoretical approach to and numerical simulation of instantaneous collisions in granular media using the A-CD$^2$ method. Commun. Appl. Math. Comput. Sci. 3 (2008), no. 1, 1--24. doi:10.2140/camcos.2008.3.1.

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