Force and flow at the onset of drag in plowed granular media
Umbanhowar, Paul B.
Goldman, Daniel I.
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We study the transient drag force F[subscript D] on a localized intruder in a granular medium composed of spherical glass particles. A flat plate is translated horizontally from rest through the granular medium to observe how F[subscript D] varies as a function of the medium’s initial volume fraction, φ. The force response of the granular material differs above and below the granular critical state, φ[subscript c], the volume fraction which corresponds to the onset of grain dilatancy. For φ<φ[subscript c] F[subscript D] increases monotonically with displacement and is independent of drag velocity for the range of velocities examined (<10 cm/s). For φ>φ[subscript c], F[subscript D] rapidly rises to a maximum and then decreases over further displacement. The maximum force for φ>φ[subscript c] increases with increasing drag velocity. In quasi-two-dimensional drag experiments, we use granular particle image velocimetry (PIV) to measure time resolved strain fields associated with the horizontal motion of a plate started from rest. PIV experiments show that the maxima in F[subscript D] for φ>φ[subscript c] are associated with maxima in the spatially averaged shear strain field. For φ>φ[subscript c] the shear strain occurs in a narrow region in front of the plate, a shear band. For φ<φ[subscript c] the shear strain is not localized, the shear band fluctuates in space and time, and the average shear increases monotonically with displacement. Laser speckle measurements made at the granular surface ahead of the plate reveal that for φ<φ[subscript c] particles are in motion far from the intruder and shearing region. For φ>φ[subscript c], surface particles move only during the formation of the shear band, coincident with the maxima in F[subscript D], after which the particles remain immobile until the sheared region reaches the measurement region.