Experimental and Simulation Analysis for the Impact of a Two-Link Chain with Granular Matter

The resistance force of the granular matter is modeled as a linear superposition of a static (quadratic depth-dependent) resistance force and a dynamic (quadratic velocity-dependent) frictional force. The impact is defined from the moment the end point of the system comes in contact with the granular matter surface until the vertical linear velocity of the end point is zero. The variables of interest are the final depth at the end of the penetration phase and the stopping time. The results for a two-link kinematic chain with two points of contact were compared to the results obtained by applying the resistance force formulation developed to corresponding CAD simulation models. The results revealed that the final displacement increases with initial velocity, while the stopping time decreases. The sensitivity to the initial velocity was studied and an improvement to the resistance force formulated as a result. A series of expressions are proposed for the resistance force coefficients.

[1]  A. Seguin,et al.  Dense granular flow around a penetrating object: experiment and hydrodynamic model. , 2011, Physical review letters.

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

[3]  D J Durian,et al.  Dynamics of shallow impact cratering. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  A. Barabasi,et al.  Granular drag on a discrete object: shape effects on jamming. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  D. Durian,et al.  Depth-dependent resistance of granular media to vertical penetration. , 2013, Physical review letters.

[6]  Olivier Pouliquen,et al.  Depth-independent drag force induced by stirring in granular media. , 2013, Physical review letters.

[7]  W. Marsden.  I and J , 2012 .

[8]  Daniel I Goldman,et al.  Force and flow at the onset of drag in plowed granular media. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  Dan B. Marghitu,et al.  Analysis of a rigid body obliquely impacting granular matter , 2009 .

[10]  Chen Li,et al.  Multi-functional foot use during running in the zebra-tailed lizard (Callisaurus draconoides) , 2012, Journal of Experimental Biology.

[11]  D. Goldman,et al.  Utilization of granular solidification during terrestrial locomotion of hatchling sea turtles , 2010, Biology Letters.

[12]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[13]  P. Schiffer,et al.  Low-velocity granular drag in reduced gravity. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  John R. de Bruyn,et al.  Penetration of spheres into loose granular media , 2004 .

[15]  D. Marghitu,et al.  Analytical and Experimental Analysis of a Free Link in Contact with a Granular Medium , 2013, TheScientificWorldJournal.

[16]  D. Goldman,et al.  Drag induced lift in granular media. , 2010, Physical review letters.

[17]  Xiaoyan Ye,et al.  The scaling and dynamics of a projectile obliquely impacting a granular medium , 2012, The European Physical Journal E.

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

[19]  Hiroaki Katsuragi,et al.  Power law statistics of force and acoustic emission from a slowly penetrated granular bed , 2014 .

[20]  Y. Forterre,et al.  Lift forces in granular media , 2014 .

[21]  A. Barabasi,et al.  Slow Drag in a Granular Medium , 1999 .

[22]  Haldun Komsuoglu,et al.  The Effect of Limb Kinematics on the Speed of a Legged Robot on Granular Media , 2010, 1303.7276.

[23]  Chen Li,et al.  A Terradynamics of Legged Locomotion on Granular Media , 2013, Science.

[24]  T. Faug,et al.  Mean steady granular force on a wall overflowed by free-surface gravity-driven dense flows. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  L. S. Tsimring,et al.  Modeling of impact cratering in granular media , 2005 .

[26]  T. Faug,et al.  Equation for the force experienced by a wall overflowed by a granular avalanche: experimental verification. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[28]  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.

[29]  C. Chan,et al.  Dynamics of a projectile penetrating in granular systems. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

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