Experimental Mechanics

, Volume 53, Issue 3, pp 327–337

Directional Wave Propagation in a Highly Nonlinear Square Packing of Spheres


DOI: 10.1007/s11340-011-9544-6

Cite this article as:
Leonard, A., Fraternali, F. & Daraio, C. Exp Mech (2013) 53: 327. doi:10.1007/s11340-011-9544-6


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.


Two-dimensional square packingGranular crystalsHighly nonlinear dynamicsDirectional wave propagationImpulsive excitation

Copyright information

© Society for Experimental Mechanics 2011

Authors and Affiliations

  1. 1.Department of Engineering and Applied ScienceCalifornia Institute of TechnologyPasadenaUSA
  2. 2.Department of Civil EngineeringUniversity of SalernoFiscianoItaly