Generalized Granular Resistive Force Theory for Rate-Dependent Intrusions

The resistive forces during intrusion into granular media can be described accurately by reduced-order models like Resistive Force Theory, but rate effects may emerge as intrusion speed increase. We demonstrate with both rapid plate drag data and freely locomoting rigid wheel experiments how such rate-dependent dynamics diverge from the quasistatic limit. Additional forces from a continuum momentum balance are sufficient for describing the forces in rapid plate drag, but do not capture the effects of rapid rotational shear in the wheeled locomotion experiments. A frictional flow continuum model captures these phenomena without needing to account for micro-inertial effects such as frictional dependence on grain inertia. Based on the observed physics of the flow model simulation, we propose a modified RFT for arbitrary intruders that reconciles both cases using a geometry-dependent modification and an additional macro-inertial resistance, extending RFT beyond describing quasistatic intruding bodies.