Numerical simulations are performed to study wave propagation in an infinite domain of square packed spheres with intruders at interstitial locations. Randomness is uniformly distributed in the densities of the spheres and the packing contains no precompression. The simulations reveal the two regimes of force amplitude decay: exponential and power law, similar to those previously reported in 1D random granular chains. The source of transition between the regimes is identified as a function of the amplitude of the leading pulse and the backscatter. An analysis of the contours of force amplitude demonstrates the anisotropy of wave propagation with respect to the distance traveled by the wave and the level of randomness. An investigation of the evolution of ensemble kinetic energy shows a gradual increase with increasing randomness, and the results are compared with the corresponding 1D random chains. The study of angular decay provides a way to identify suitable sphere properties to design optimized granular structures.

Original languageEnglish (US)
Pages (from-to)42-48
Number of pages7
JournalPhysica D: Nonlinear Phenomena
StatePublished - 2014


  • Granular materials
  • Hertzian contact
  • Randomness
  • Wave propagation

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics


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