1,625 research outputs found
Power law scaling of early-stage forces during granular impact
We experimentally and computationally study the early-stage forces during
intruder impacts with granular beds in the regime where the impact velocity
approaches the granular force propagation speed. Experiments use 2D assemblies
of photoelastic disks of varying stiffness, and complimentary discrete-element
simulations are performed in 2D and 3D. The peak force during the initial
stages of impact and the time at which it occurs depend only on the impact
speed, the intruder diameter, the mass density of the grains, and the elastic
modulus of the grains according to power-law scaling forms that are not
consistent with Poncelet models, granular shock theory, or added-mass models.
The insensitivity of our results to many system details suggest that they may
also apply to impacts into similar materials like foams and emulsions.Comment: 5 pages, 4 figure
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
Granular Response to Impact: Topology of the Force Networks
Impact of an intruder on granular matter leads to formation of mesoscopic
force networks seen particularly clearly in the recent experiments carried out
with photoelastic particles, e.g., Clark et al., Phys. Rev. Lett., 114 144502
(2015). These force networks are characterized by complex structure and evolve
on fast time scales. While it is known that total photoelastic activity in the
granular system is correlated with the acceleration of the intruder, it is not
known how the structure of the force network evolves during impact, and if
there is a dominant features in the networks that can be used to describe
intruder's dynamics. Here, we use topological tools, in particular persistent
homology, to describe these features. Persistent homology allows quantification
of both structure and time evolution of the resulting force networks. We find
that there is a clear correlation of the intruder's dynamics and some of the
topological measures implemented. This finding allows us to discuss which
properties of the force networks are most important when attempting to describe
intruder's dynamics. Regarding temporal evolution of the networks, we are able
to define the upper bound on the relevant time scale on which the networks
evolve
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