The non-smooth view for contact dynamicsby Michel Frémondextended to the  modeling of crowd movements

Philippe Pécol; Pierre Argoul; Stefano Dal Pont; Silvano Erlicher

doi:10.3934/dcdss.2013.6.547

Article Contents

2013, Volume 6, Issue 2: 547-565. Doi: 10.3934/dcdss.2013.6.547

This issue Previous Article On a class of sixth order viscous Cahn-Hilliard type equations Next Article Pseudo-potentials and bipotential: A constructive procedure for non-associated plasticity and unilateral contact

The non-smooth view for contact dynamics by Michel Frémond extended to the modeling of crowd movements

1.
Laboratoire Navier (ENPC/IFSTTAR/CNRS), École des Ponts ParisTech, Université Paris-Est, 6 & 8 av Blaise Pascal, 77455 Marne-la-Vallée
2.
IFSTTAR, Université Paris-Est, 58 boulevard Lefebvre, 75732 Paris
3.
EGIS Industries, 4 rue Dolores Ibarruri, 91188 Montreuil

Received: June 30, 2011

Revised: January 31, 2012

Published: March 2013

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Abstract

The non-smooth view of Michel Frémond has already been proven successful in managing collisions between rigid particles and in this paper, it will be adapted so as to represent pedestrians and their strategy of displacement. The developed discrete approach applies a rigorous thermodynamic framework in which the local interactions between particles are managed by the use of pseudopotentials of dissipation. It handles local interactions such as pedestrian-pedestrian and pedestrian-obstacle in order to reproduce the global and real dynamics of pedestrian traffic. Social forces are introduced and implemented in order to simulate the behavior of pedestrians and subgroups of pedestrians. The numerical implementation allows us to perform simulations in various situations so that the safety and comfort of public spaces can be enhanced.

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Mathematics Subject Classification: 70F.

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