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Center for Nonlinear Studies |
The flow of granular materials is of widespread practical and fundamental interest. One challenge to understanding and controlling behavior is that the response is nonlinear, with a forcing threshold below which the medium is static. Furthermore, just above threshold the response may be unsteady even though the forcing is smooth. Two familiar examples are avalanches on a heap and clogging in a silo. Another example occurs in laboratory-scale granular impact cratering, which will be the main focus of this talk. Low-speed impact of solid objects into granular media have been used both to mimic geophysical events and to probe the unusual nature of the granular state of matter. Observations have been interpreted in terms of conflicting stopping forces, reminiscent of high-speed ballistics impact in the 19th and 20th centuries when a plethora of empirical rules were proposed. To make progress, we developed a means to measure projectile dynamics with 100 nm and 20 us precision. For a 1-inch diameter steel sphere dropped from a wide range of heights into non-cohesive glass beads, we reproduce prior observations either as reasonable approximations or as limiting behaviors. Furthermore, we demonstrate that the interaction between projectile and medium can be decomposed into the sum of velocity-dependent inertial drag plus depth-dependent friction. The latter is also explored by partially fluidizing the medium with an upflow of air. Thus we achieve a unified description of low-speed impact phenomena and show that the complex response of granular materials to impact, while fundamentally different from that of liquids and solids, can be simply understood.
Host: Cristiano Nisoli