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Goldman, Daniel I.

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    Force and flow at the onset of drag in plowed granular media
    (Georgia Institute of Technology, 2014) Gravish, Nick ; Umbanhowar, Paul B. ; Goldman, Daniel I.
    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.
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    Force and flow transition in plowed granular media
    (Georgia Institute of Technology, 2010-09-06) Gravish, Nick ; Umbanhowar, Paul B. ; Goldman, Daniel I.
    We use plate drag to study the response of granular media to localized forcing as a function of volume fractionϕ. A bifurcation in the force and flow occurs at the onset of dilatancy ϕ [subscript c]. Below ϕ [subscript c] rapid fluctuations in the drag force F [subscript D] are observed. Above ϕ [subscript c] fluctuations in F [subscript D] are periodic and increase in magnitude with ϕ. Velocity field measurements indicate that the bifurcation in F [subscript D] results from the formation of stable shear bands above ϕ [subscript c] which are created and destroyed periodically during drag. A friction-based wedge flow model captures the dynamics for ϕ >ϕ [subscript c].
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    Granular impact and the critical packing state
    (Georgia Institute of Technology, 2010-07-15) Umbanhowar, Paul B. ; Goldman, Daniel I.
    Impact dynamics during collisions of spheres with granular media reveal a pronounced and nontrivial dependence on volume fraction ϕ. Postimpact crater morphology identifies the critical packing state ϕcps, where sheared grains neither dilate nor consolidate, and indicates an associated change in spatial response. Current phenomenological models fail to capture the observed impact force for most ϕ; only near ϕcps is force separable into additive terms linear in depth and quadratic in velocity. At fixed depth the quadratic drag coefficient decreases (increases) with depth for ϕ<ϕcps (ϕ>ϕcps). At fixed low velocity, depth dependence of force shows a Janssen-type exponential response with a length scale that decreases with increasing ϕ and is nearly constant for ϕ>ϕcps.
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    Scaling and Dynamics of Sphere and Disk Impact into Granular Media
    (Georgia Institute of Technology, 2008-02-29) Goldman, Daniel I. ; Umbanhowar, Paul B.
    Direct measurements of the acceleration of spheres and disks impacting granular media reveal simple power law scalings along with complex dynamics which bear the signatures of both fluid and solid behavior. The penetration depth scales linearly with impact velocity while the collision duration is constant for sufficiently large impact velocity. Both quantities exhibit power law dependence on sphere diameter and density, and gravitational acceleration. The acceleration during impact is characterized by two jumps: a rapid, velocity-dependent increase upon initial contact and a similarly sharp depth-dependent decrease as the impacting object comes to rest. Examination of the measured forces on the sphere in the vicinity of these features leads to an experimentally based granular force model for collision. We discuss our findings in the context of recently proposed phenomenological models that capture qualitative dynamical features of impact but fail both quantitatively and in their inability to capture significant acceleration fluctuations that occur during penetration and which depend on the impacted material.