216 research outputs found
Granular Impact Model as an Energy-Depth Relation
Velocity-squared drag forces are common in describing an object moving
through a granular material. The resulting force law is a nonlinear
differential equation, and closed-form solutions of the dynamics are typically
obtained by making simplifying assumptions. Here, we consider a generalized
version of such a force law which has been used in many studies of granular
impact. We show that recasting the force law into an equation for the kinetic
energy versus depth, K(z), yields a linear differential equation, and thus
general closed-form solutions for the velocity versus depth. This approach also
has several advantages in fitting such models to experimental data, which we
demonstrate by applying it to data from 2D impact experiments. We also present
new experimental results for this model, including shape and depth dependence
of the velocity-squared drag force
Topology of Force Networks in Granular Media under Impact
We investigate the evolution of the force network in experimental systems of
two-dimensional granular materials under impact. We use the first Betti number,
, and persistence diagrams, as measures of the topological properties
of the force network. We show that the structure of the network has a complex,
hysteretic dependence on both the intruder acceleration and the total force
response of the granular material. can also distinguish between the
nonlinear formation and relaxation of the force network. In addition, using the
persistence diagram of the force network, we show that the size of the loops in
the force network has a Poisson-like distribution, the characteristic size of
which changes over the course of the impact
Reynolds Pressure and Relaxation in a Sheared Granular System
We describe experiments that probe the evolution of shear jammed states,
occurring for packing fractions , for frictional
granular disks, where above there are no stress-free static states. We
use a novel shear apparatus that avoids the formation of inhomogeneities known
as shear bands. This fixed system exhibits coupling between the shear
strain, , and the pressure, , which we characterize by the `Reynolds
pressure', and a `Reynolds coefficient', . depends only on , and diverges as , where , and . Under
cyclic shear, this system evolves logarithmically slowly towards limit cycle
dynamics, which we characterize in terms of pressure relaxation at cycle :
. depends only on the shear cycle
amplitude, suggesting an activated process where plays a
temperature-like role.Comment: 4 pages, 4 figure
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