Vertical drag force acting on intruders of different shapes in granular media

The penetration of large objects into granular media is encountered commonly both in nature (e.g. impacts of meteors and projectiles) and engineering applications (e.g. insertion of tractor blades into sand). The motion of the impacting intruder in granular media is resisted by a granular drag force. In this work, we assess the effect of intruder shape on the granular drag force using discrete element modelling (DEM). The following intruder shapes were modelled: spherical, conical, cylindrical and cubical. We observed that the drag force can be described well by a power-law relationship with intrusion depth, independent of the intruder shape. However, the exponent of the power-law expression increases with increasing “flatness” of the intruder’s impacting surface due to an increasing fraction of the granular media affected by the impact of the intruder.

[1]  Work distributions for Ising chains in a time-dependent magnetic field. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  R. Behringer,et al.  Particle scale dynamics in granular impact. , 2012, Physical review letters.

[3]  Djaoued Beladjine,et al.  Impact of a projectile on a granular medium described by a collision model. , 2007, Physical review letters.

[4]  P. Cundall,et al.  A discrete numerical model for granular assemblies , 1979 .

[5]  E. B. Mayfield,et al.  Dynamics of a Projectile Penetrating Sand , 1957 .

[6]  P. Umbanhowar,et al.  Scaling and dynamics of sphere and disk impact into granular media. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  P. Umbanhowar,et al.  Granular impact and the critical packing state. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  M. Dentz,et al.  Effective transport in random shear flows. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  Zhilong Peng,et al.  Projectile impact and penetration in loose granular bed , 2005 .

[10]  D J Durian,et al.  Low-speed impact craters in loose granular media. , 2003, Physical review letters.

[11]  Depth dependence of vertical plunging force in granular medium. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  D. Durian,et al.  Unified force law for granular impact cratering , 2007, cond-mat/0703072.

[13]  M. J. Forrestal,et al.  Penetration into soil targets , 1992 .

[14]  G. Hill,et al.  Scaling vertical drag forces in granular media , 2005 .