Bending transition in the penetration of a flexible intruder in a two-dimensional dense granular medium.
Nicolas Algarra, Panagiotis G Karagiannopoulos, Arnaud Lazarus, Damien Vandembroucq, Evelyne Kolb
Author Information
Nicolas Algarra: Laboratoire PMMH, UMR 7636 CNRS/ESPCI Paris/PSL Research University/Sorbonne Universités, UPMC Univ Paris 06,/Univ Paris Diderot, 10 rue Vauquelin, 75231 Paris cedex 05, France.
Panagiotis G Karagiannopoulos: Laboratoire PMMH, UMR 7636 CNRS/ESPCI Paris/PSL Research University/Sorbonne Universités, UPMC Univ Paris 06,/Univ Paris Diderot, 10 rue Vauquelin, 75231 Paris cedex 05, France.
Arnaud Lazarus: Sorbonne Universités, UPMC Univ Paris 06, CNRS, UMR 7190, Institut Jean Le Rond d'Alembert, F-75005, Paris, France.
Damien Vandembroucq: Laboratoire PMMH, UMR 7636 CNRS/ESPCI Paris/PSL Research University/Sorbonne Universités, UPMC Univ Paris 06,/Univ Paris Diderot, 10 rue Vauquelin, 75231 Paris cedex 05, France.
Evelyne Kolb: Laboratoire PMMH, UMR 7636 CNRS/ESPCI Paris/PSL Research University/Sorbonne Universités, UPMC Univ Paris 06,/Univ Paris Diderot, 10 rue Vauquelin, 75231 Paris cedex 05, France.
We study the quasistatic penetration of a flexible beam into a two-dimensional dense granular medium lying on a horizontal plate. Rather than a buckling-like behavior we observe a transition between a regime of crack-like penetration in which the fiber only shows small fluctuations around a stable straight geometry and a bending regime in which the fiber fully bends and advances through series of loading and unloading steps. We show that the shape reconfiguration of the fiber is controlled by a single nondimensional parameter L/L_{c}, which is the ratio of the length of the flexible beam L to L_{c}, a bending elastogranular length scale that depends on the rigidity of the fiber and on the departure from the jamming packing fraction of the granular medium. We show, moreover, that the dynamics of the bending transition in the course of the penetration experiment is gradual and is accompanied by a symmetry breaking of the granular packing fraction in the vicinity of the fiber. Together with the progressive bending of the fiber, a cavity grows downstream of the fiber and the accumulation of grains upstream of the fiber leads to the development of a jammed cluster of grains. We discuss our experimental results in the framework of a simple model of bending-induced compaction and we show that the rate of the bending transition only depends on the control parameter L/L_{c}.
