Friday, October 26, 2012

1210.6692 (Abram H. Clark et al.)

Granular Impact Model as an Energy-Depth Relation    [PDF]

Abram H. Clark, Robert P. Behringer
The modeling framework of several recent studies of granular impact is a force law consisting of three terms: gravity, a depth-dependent static term, and a collisional term. We recast this usual force differential equation for $F(t)$ into an equation for the kinetic energy vs. depth, $K(z)$. We show that this reformulation is beneficial, both theoretically and experimentally. With the original force-law form, obtaining closed-form solutions may be difficult, and experimental comparisons require acceleration data, which is difficult to obtain at high speeds. By contrast, with the kinetic energy formulation, standard differential equation methods yield solutions for $K(z)$. We apply the kinetic energy approach to experimental data for the trajectory and velocity of an intruder that is impacting on a quasi-two-dimensional array of photoelastic disks. We also directly relate the two phenomenological terms in the force law to detailed properties of the granular medium and intruder.
View original: http://arxiv.org/abs/1210.6692

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