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Published November 2009 | Published
Journal Article Open

Stationary shocks in periodic highly nonlinear granular chains


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.

Additional Information

© 2009 The American Physical Society. Received 26 May 2009; published 17 November 2009. C.D. acknowledges the Army Research Office Proposal No. 54272-EG and the NSF CAREER for support of this work. C.D. thanks the University of Metz for hospitality during her visit. We also thank Dr. Mason Porter for providing the program code for the numerical calculations.

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Published - Molinari2009p6631Phys_Rev_E.pdf


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