From indetermination to inconsistency: how to avoid it

Abstract : For illustrating the limits of the NSCD approach we focus our attention on dense granular systems that are strongly confined. In order to respect the “elegant rusticity” of the Moreau’s approach we restrict the analysis to a collection of rigid bodies without considering global or local deformations of the grains. Some simple examples highlight the issue of inconsistencies, i.e. some configurations for which no solution exists, as well as indeterminacies, i.e. configurations that lead to non-uniqueness of solutions. We recover here the Painlevé paradox underlined at the beginning of the twentieth century. The non existence of solutions is the more important challenge we have to face. We can first identify the situations leading to this non existence among them the granular systems submitted to moving walls. If such a case may not be avoided another response consists in changing the Coulomb friction law. The NSCD approach is well adapted to inelastic shocks that predominate in granular media. However J.J. Moreau introduced the concept of formal velocity to account for an elastic restitution. This concept is richer than a restitution coefficient (Newton or Poisson type) involving a binary shock; this permits to deal with multicontact situations without introducing either deformable grains or elastic-plastic contact laws. However this does not allow to reproduce shock propagation as it occurs for instance in the famous Newton’s cradle. Is it then possible to propose an algorithmic solution in the NSCD framework?
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Communication dans un congrès
Fourth Symposium of the European Network for Nonsmooth Dynamics , Sep 2015, Montpellier, France
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https://hal.archives-ouvertes.fr/hal-01281748
Contributeur : François Gibier <>
Soumis le : mercredi 2 mars 2016 - 16:49:57
Dernière modification le : vendredi 9 juin 2017 - 10:40:35

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  • HAL Id : hal-01281748, version 1

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Pierre Alart. From indetermination to inconsistency: how to avoid it. Fourth Symposium of the European Network for Nonsmooth Dynamics , Sep 2015, Montpellier, France. 〈hal-01281748〉

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