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Stationary shocks in periodic highly nonlinear granular chains

Alain Molinari1 and Chiara Daraio2,*

  • 1Laboratoire de Physique et Mécanique des Matériaux, Université Paul Verlaine-Metz, Ile du Saulcy, Metz 57045, France
  • 2Graduate Aerospace Laboratories (GALCIT) and Applied Physics, California Institute of Technology, Pasadena, California 91125, USA

  • *Author to whom correspondence should be addressed; daraio@caltech.edu
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Phys. Rev. E 80, 056602 – Published 17 November, 2009

DOI: https://doi.org/10.1103/PhysRevE.80.056602

Abstract

We study the existence of stationary shock waves in uniform and periodic heterogeneous highly nonlinear granular chains governed by a power-law contact interaction, comparing discrete and continuum approaches, as well as experiments. We report the presence of quasisteady shock fronts without the need for dissipative effects. When viscous effects are neglected, the structure of the leading front appears to be solely the result of dispersive effects related to the lattice wave dispersion and, for heterogeneous bead chains, to the impedance mismatch between material domains. We report analytically and numerically the shock-width scaling with the variation in the particles periodicity (cell size) and compare the obtained results with experiments. We check the state (−) behind the shock front via quasistatic compression analysis and report a very good agreement between theory and numerical data.

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Phys. Rev. E 80, 056602– Published 17 November, 2009
  • Received 26 May 2009

© 2009 American Physical Society

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