Granular impact model as an energy-depth relation
Department of Physics, Duke University - Box 90305, Durham, NC 27708, USA
Received: 16 October 2012
Accepted: 24 February 2013
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 vs. depth, K(z), yields a linear differential equation, and thus general closed-form solutions for the velocity vs. 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.
PACS: 45.70.Mg – Granular flow: mixing, segregation and stratification / 02.30.Hq – Ordinary differential equations / 47.57.Gc – Granular flow
© EPLA, 2013