Towards a constitutive law for the unsteady contact stress in granular media |
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Authors: | Roland Borghi Stéphane Bonelli |
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Institution: | 1.Ecole Centrale de Marseille,Marseille,France;2.Laboratoire de Mécanique et d’Acoustique (UPR-CNRS 7051),Marseille,France;3.Cemagref,Aix-en-Provence,France |
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Abstract: | In order to build a unified modelling for granular media by means of Eulerian averaged equations, it is necessary to study
two contributions in the effective Cauchy stress tensor: the first one concerns solid and fluid matter, including contact
and collisions between grains; the second one focuses on the random movements of grains and fluid, similar to Reynolds stress
for turbulent flows. It is shown that the point of view of piecewise continuous media already used for two phase flows allows
one to derive a constitutive equation for the first contribution, under the form of a partial differential equation. Similarly
as for the Reynolds stress in turbulent flows, this equation cannot be written only in terms of averaged quantities without
adequate approximations. The structure of the closed equation is discussed with respect to irreversible thermodynamics, and
in connection with some already existing models. It is emphasised that numerical simulations by the discrete elements method
can be used in order to validate these approximations, through numerical experiments statistically considered. Finally an
extension of this approach to the second contribution of the effective Cauchy stress tensor is briefly discussed, showing
how the modelling of both contributions have to be coupled.
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Keywords: | Granular matter Turbulence Extended thermodynamics Constitutive theories |
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