Buckling of a rod penetrating into granular media

Abstract

We investigate experimentally the possible buckling of a thin rod when penetrating downwards into a granular packing. When its bottom end reaches a specific depth, the rod may start buckling provided that the embrace is not enough to stop that phenomenon. The critical rod depth z_{c} at buckling is observed to scale with the rod length L either as 1/L or 1/L^{2}. These two scalings are shown to arise from the two resistant force terms that come into play during the rod penetration: a pressure force at the bottom of the rod that increases linearly with depth and a frictional force on the rod side that increases quadratically with depth. At the buckling point, the destabilizing force corresponds to the expected value given from conventional Euler's critical load for a rod bottom end considered as fixed in the granular clutch. Finally, we draw a buckling-nonbuckling phase diagram in a parameter space given by the rod aspect ratio and a rod-to-grain stress ratio.

Successive reintrusions in a granular medium

“…These values lay in the same range as previous estimations for flat-ended rods penetrating into glass beads [6]. Due to the finite size effect of the container, possible wall effect generated by friction may be expected [28][29][30].…”

“…In this study, we consider as a reference case the intrusion of the rod at a constant and low velocity without cycles. A previous study has shown that this force results from two contributions: the hydrostatic-like pressure applying on the tip of the rod and the frictional force exerting along its length [6]. They provided the following expression for the vertical force F 0 experienced during a continuous intrusion:…”

“…For a rod, they measured C 9.5 and λ 1.6 in penetration, C −0.66 and λ 1.3 in extraction. In the case of penetration alone, another model has been proposed considering that the drag force comes from the contribution of two terms: one coming from the hydrostatic-like pressure at the tip of the rod F ∝ z and another resulting from the friction applying on the lateral surface F ∝ z 2 [6]. Recently, the penetration of objects at shallow depths has shown the presence of a particular regime where the drag force is closely related to the Archimedean force with a pre-factor that strongly increases with the effective friction coefficient of the granular medium [7,8].…”

Elastocapillary deformation of thin elastic ribbons in 2D foam columns

“…14 Such systems form periodically ordered liquid film architectures into which an elastic ribbon can be introduced. Although the question of complex deformation of an intruder in an architected medium has been widely studied in the case of granular media 15,16 with applications in the context of root growth, 17 a limited number of studies on model systems exist in the case of liquid foams, such as the analysis of simple arrangements of soap films interacting with rigid solids, 18 and simulations of flexible fibres in foam under shear. 19 We consider a model system composed of an ordered assembly of monodisperse soap bubbles and an elastomer ribbon (Fig.…”

Elastocapillary deformation of thin elastic ribbons in 2D foam columns

“…Such systems form periodically ordered liquid film architectures into which an elastic ribbon can be introduced. Although the question of complex deformation of an intruder in an architected medium has been widely studied in the case of granular media [15,16] with applications in the context of root growth [17], a limited number of studies on model systems exist in the case of liquid foams, such as the analysis of simple arrangements of soap films interacting with rigid solids [18], and simulations of flexible fibres in foam under shear [19]. We consider a model system composed of an ordered assembly of monodisperse soap bubbles and an elastomer ribbon (Fig.…”