Buckling of a rod penetrating into granular media

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.