Multiple scales of shock waves in dissipative laminate materials

Pedro Franco Navarro, David J. Benson, and Vitali F. Nesterenko
Phys. Rev. E 94, 033002 – Published 15 September 2016

Abstract

The shock waves generated by a plate impact are numerically investigated in Al-W laminates with different mesostructures. The main characteristic time scales (and the corresponding spatial scales) related to the formation of the stationary shock are identified: the duration (width) of the leading front, the time (distance) from the impact required to establish a stationary profile, and the shock front width, identified as a time span (distance) from the initial state to the final quasiequilibrium state. It is demonstrated that the width of the leading front and the maximum strain rates are determined by the dispersive and the nonlinear parameters of the laminate and not by the dissipation, as is the case for uniform solids. The characteristic spatial scale of the leading front is related to the spatial scale observed on solitarylike waves, which are satisfactorily described by the Korteweg–de Vries (KdV) approximation, as well as the speed of the wave and the ratio of maximum to final strain. The dissipation affects the width of the transition distance (shock front width) where multiple loading-unloading cycles bring the laminate into the final quasiequilibrium state. This spatial scale is of the same order of magnitude as the distance to form stationary shock wave. The period of fast decaying oscillations is well described by the KdV approach and scales linearly with the cell size. The rate of the decay of the oscillations in the numerical calculations does not scale with the square of the cell size as expected from the dissipative KdV approach that assumes a constant viscosity. This is due to the different mechanisms of dissipation in high-amplitude compression pulses.

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  • Received 29 April 2016

DOI:https://doi.org/10.1103/PhysRevE.94.033002

©2016 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsInterdisciplinary Physics

Authors & Affiliations

Pedro Franco Navarro1, David J. Benson2, and Vitali F. Nesterenko1,3

  • 1Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, California 92093-0411, USA
  • 2Department of Structural Engineering, University of California, San Diego, La Jolla, California 92093-0085, USA
  • 3Materials Science and Engineering Program, University of California, San Diego, La Jolla, California 92093-0418, USA

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Issue

Vol. 94, Iss. 3 — September 2016

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