Directional Wave Propagation in a Highly Nonlinear Square Packing of Spheres

We studied the dynamic response of a two-dimensional square packing of uncompressed stainless steel spheres excited by impulsive loadings. We developed a new experimental measurement technique, employing miniature tri-axial accelerometers, to determine the stress wave properties in the array resulting from both an in-plane and out-of-plane impact. Results from our numerical simulations, based on a discrete particle model, were in good agreement with the experimental results. We observed that the impulsive excitations were resolved into solitary waves traveling only through initially excited chains. The observed solitary waves were determined to have similar (Hertzian) properties to the extensively studied solitary waves supported by an uncompressed, uniform, one-dimensional chain of spheres. The highly directional response of this system could be used as a basis to design granular crystals with predetermined wave propagation paths capable of mitigating stress wave energy.

[1]  F. Fraternali,et al.  Highly nonlinear pulse splitting and recombination in a two-dimensional granular network. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  C Daraio,et al.  Anomalous wave reflection at the interface of two strongly nonlinear granular media. , 2005, Physical review letters.

[3]  J Hong,et al.  Effects of gravity and nonlinearity on the waves in the granular chain. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Green’s function measurements of force transmission in 2D granular materials , 2002, cond-mat/0211031.

[5]  A. Shukla,et al.  Angular dependence of dynamic load transfer due to explosive loading in granular aggregate chains , 1988 .

[6]  M. M. Smirnov,et al.  PROPAGATION OF NONLINEAR COMPRESSION PULSES IN GRANULAR MEDIA , 2004 .

[7]  Mason A Porter,et al.  Dissipative solitary waves in granular crystals. , 2008, Physical review letters.

[8]  Bruno Gilles,et al.  On the validity of Hertz contact law for granular material acoustics , 1999 .

[9]  A. Hurd,et al.  Crossing of identical solitary waves in a chain of elastic beads. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Sound propagation in impure granular columns. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[11]  C. Caroli,et al.  Pressure dependence of the sound velocity in a two-dimensional lattice of Hertz-Mindlin balls: mean-field description. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  DEM simulations and experiments for projectile impacting two-dimensional particle packings including dissimilar material layers , 2010 .

[13]  A. Shukla,et al.  Numerical analysis of wave propagation through assemblies of elliptical particles , 1997 .

[14]  Arun Shukla,et al.  Contact law effects on wave propagation in particulate materials using distinct element modeling , 1993 .

[15]  V. Nesterenko,et al.  Observation of a new type of solitary waves in a one-dimensional granular medium , 1985 .

[16]  C. Coste,et al.  Low-frequency behavior of beads constrained on a lattice. , 2003, Physical review letters.

[17]  C. Daraio,et al.  Tunability of solitary wave properties in one-dimensional strongly nonlinear phononic crystals. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  Adam Sokolow,et al.  Solitary wave trains in granular chains: experiments, theory and simulations , 2007, 0712.0006.

[19]  V. Loreto,et al.  SHOCK PROPAGATION IN A GRANULAR CHAIN , 1999 .

[20]  Masami Nakagawa,et al.  Impulse dispersion in a tapered granular chain , 2003 .

[21]  V. Gusev,et al.  Elastic waves in noncohesive frictionless granular crystals. , 2010, Ultrasonics.

[22]  M. Nishida,et al.  DEM simulation of wave propagation in two-dimensional ordered array of particles , 2009 .

[23]  A. Chatterjee.  Asymptotic solution for solitary waves in a chain of elastic spheres. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[24]  C. Daraio,et al.  Energy trapping and shock disintegration in a composite granular medium. , 2006, Physical review letters.

[25]  C. Daraio,et al.  Strongly nonlinear waves in a chain of Teflon beads. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  E. Hinch,et al.  The fragmentation of a line of balls by an impact , 1999, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[27]  A. Shukla,et al.  Role of particle shape and contact profile on the dynamic response of particulate materials , 1993 .

[28]  F. Melo,et al.  Wave localization in strongly nonlinear Hertzian chains with mass defect. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  Sen,et al.  Nonlinear Dynamics in Granular Columns. , 1995, Physical review letters.

[30]  J. Goddard.  Nonlinear elasticity and pressure-dependent wave speeds in granular media , 1990, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[31]  Thermalizing an impulse , 2001 .

[32]  Eric Falcon,et al.  Solitary waves in a chain of beads under Hertz contact , 1997 .

[33]  Adam Sokolow,et al.  How hertzian solitary waves interact with boundaries in a 1D granular medium. , 2005, Physical review letters.

[34]  Arun Shukla,et al.  The effect of microstructural fabric on dynamic load transfer in two dimensional assemblies of elliptical particles , 1996 .

[35]  V. Nesterenko,et al.  The decay of soliton at the contact of two “acoustic vacuums” , 1995 .

[36]  J. U. Brackbill,et al.  Dynamic stress bridging in granular material , 1998 .