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Center for Nonlinear Studies |
“[Granular media] are omnipresent: from the rings of Saturn to the snow of our mountains. [They] represent a major object of human activities: as measured in tons, the first material manipulated on earth is water; the second is granular matter.” P.-G. de Gennes “ From Rice to Snow”, 2008 Nishina Foundation Nobelist Lectures, In Lect. Notes Phys. 746, 297-318 (2008). The past forty years or so have witnessed a resurgence and continuous growth of interest in the mechanics of granular materials, whose scientific origins go back at least to the 18th Century. The subject is relevant to a number of geotechnical and technological processes, such as stability of slopes and natural avalanches, mechanics of desert sands, and vibratory conveying and compaction. The challenge of understanding and mathematically modeling these materials and processes has attracted researchers from a wide array of disciplines, ranging from soil mechanics to theoretical physics, who bring complementary but sometimes opposing philosophies and methodologies to the table. This lecture provides a broad overview of the field, including the distinguished flow regimes of elastoplastic solid, viscoplastic fluid and viscous gas. The focus in this talk is mainly on the first two regimes, which involve several fascinating phenomena such as Reynolds dilatancy, seismic liquefaction, mesoscopic force chains, shear bands and Faraday patterns on vibrated layers. Some attempts are made to relate these qualitatively to certain geotechnical and technological processes mentioned above. A brief summary is given of some of the more promising phenomenological continuum models for the elastoplasticity and viscoplasticity of non-cohesive granular media. One conclusion is that multiscale and multipolar continuum models involving additional kinematic degrees of freedom and conjugate hyperstress, may be essential to the rheology of granular media, particularly the elastoplastic behavior. Owing to their typically large particle size, this becomes much more compelling for granular media than for other complex solids and fluids.
Host: Ivan Christov