Intrusion into granular media beyond the quasi-static regime

Efficacy of simple continuum models for diverse granular intrusions

“…With Y = µ × P and supposing P grows linearly along the edge of the no-shear-zone wedge, the mean strength along the edge grows ∝ L. Substitution of Y ∝ L in the limit analysis formula then gives the observed quadratic dependence of the drag force on L. We do not further investigate these forces but identify that the existence of small regions of under-compacted granular media near free surfaces is expected to suppress the growth of such forces in many cases (see figure 8D). Our simulations indicate that the drag forces' dependence of F on L enter linear regimes at depths z ∼ O(10 −1 )L. These forces are unique from the 'added mass' effects 52 and other macro-inertial effects 46,47 in granular impacts that are common in high-speed intrusion (and vary ∝ v 2 ) since our intrusion velocities are small.…”

“…The expected trends from the dimensional analysis are apparent. Besides our own simulation results, the linear dependence of drag force on intruder area, once deep enough, is a well studied relation [46][47][48] . We reiterate that our simulations are all in the quasistatic regime.…”

“…(1) At low depths z L, the variable z/L is negligible and can be ignored. And (2), at larger depths, the drag forces F D are known to show a linear dependence on depth (after an initial jump in the vertical drag near free surfaces [46][47][48][49] ). In both of these regimes, we can set the dependence of F D on w to be linear assuming the plane-strain nature of the intrusions.…”