Granular community goes to the desert

Abstract

The physics of granular media is an ancient science. It is present in practically all fields of applied physical sciences. At a fundamental level, models of hard spheres or disks have been used from the early times of classical Greece to nowadays investigations to characterize the microscopic states of organisation of matter. Conversely, in the last two decades, a large community of physicists has made use of what had been acquired in the microscopic physics world to try to enrich our understanding of the science of “real grains”. In the eighties, as we were testing percolation ideas by mixing conducting and insulating otherwise identical grains in various concentrations [1], we realized then that the way the packings were built had a strong influence on the result of the experiments. Replacing a single conducting grain by an insulating one tells one in particular how many good electrical contacts this grain had, and this varies with filling conditions and packing pressure. The question led us to be acquainted with the British school which since Bernal [2] had studied arrangements of packings in connection with the structure of the liquid state. But probably the most spectacular finding for us was that of a photoelastic experiment by P. Dantu [3] on compressed arrays of parallel aligned photoelastic cylinders which clearly showed that the stresses propagated along continuous chains of cylinders leaving a lot of them practically free of stress due to arching (similar work had been done independently by Josselin de Jong in Holland). This result was not well recognized at this time partly because of a prevalent dogma in mechanics based on homogenization procedures which use phenomenological local constitutive laws to evaluate global properties of heterogeneous - generally periodic structures. Clearly this can not apply in the granular case of a granular assembly; because of the very large distribution of local forces a global geometrical description is needed [4]. Percolation ideas have been applied to the problem taking into account the asymmetry between presence or absence of inter-grain forces when the grains are either pressed together or pulled apart, like a network of fuses or of diodes and unlike a mechanical spring lattice. Such models can account for the fact that the value of the exponent x of the force F deformation D law, F = D x , is much larger than that of an individual contact (given by Hertz law f = d 3/2 ) due to the increase of active mechanical contacts where forces increase. More