Granular Impact Model as an Energy-Depth Relation

Abstract

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.

References in corpus (5)

• Unified force law for granular impact cratering
• Scaling and dynamics of sphere and disk impact into granular media
• Particle Scale Dynamics in Granular Impact
• Granular impact and the critical packing state
• Cratering Experiments on the Self Armoring of Coarse-Grained Granular Targets

Cited by in corpus (19)

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• Collisional Model for Granular Impact Dynamics
• Granular Dynamics during Impact
• Collisional Model of Energy Dissipation in 3D Granular Impact
• System-spanning dynamically jammed region in response to impact of cornstarch and water suspensions
• Constitutive relation for the system-spanning dynamically jammed region in response to impact of cornstarch and water suspensions
• Granular Response to Impact: Topology of the Force Networks
• Steady Flow Dynamics during Granular Impact
• Intrusion into granular media beyond the quasi-static regime
• Power law scaling of early-stage forces during granular impact
• `Sinking' in a bed of grains activated by shearing
• Impact drag force exerting on a projectile penetrating into a hierarchical granular bed
• Stagnant Zone Formation in a 2D Bed of Circular and Elongated Grains under Penetration
• Sink versus tilt penetration into shaken dry granular matter: The role of the foundation
• Granular Impact: A Grain-scale Approach
• Force on a sphere suspended in flowing granulate