Review Articles

Frontiers in the Constitutive Modeling of Anisotropic Shock Waves

[+] Author and Article Information
Alexander A. Lukyanov

 Abingdon Technology Centre, Schlumberger,Abingdon, OX14 1UJ, UK

Steven B. Segletes

 U.S. Army Research Laboratory, Aberdeen Proving Ground, MD 21005-5066

Appl. Mech. Rev 64(4), 040802 (Aug 20, 2012) (13 pages) doi:10.1115/1.4006253 History: Received November 18, 2011; Revised February 27, 2012; Published April 27, 2012; Online August 20, 2012

Studies of anisotropic materials and the discovery of various novel and unexpected phenomena under shock loading has contributed significantly to our understanding of the behavior of condensed matter. The variety of experimental studies for isotropic materials displays systematic patterns, giving basic insights into the underlying physics of anisotropic shock wave modeling. There are many similarities and significant differences in the phenomena observed for isotropic and anisotropic materials under shock-wave loading. Despite this, the anisotropic constitutive equations must represent mathematical and physical generalization of the conventional constitutive equations for isotropic material and reduce to the conventional constitutive equations in the limit of isotropy. This article presents the current state of the art in the constitutive modeling of this fascinating field.

Copyright © 2011 by American Society of Mechanical Engineers
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Figure 1

Cold-compression and shock-Hugoniot curves for aluminum (a) to 2.4 megabars and (b) to 11 megabars. Note that cold-compression data are filled symbols and Hugoniot data are open symbols.

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Figure 2

The Kevlar/Epoxy IFPT simulated and experimental back surface velocities for 572m/s, 788m/s, and 1015m/s. The experimental data Kevlar/Epoxy materials recovered after flyer plate testing were taken from Hayhurst [47]. The experimental data was reproduced with permission from the International Journal of Impact Engineering, pp. 26, 309–320. Copyright 2001 Elsevier Science Ltd.

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Figure 3

Representative experimental gauge traces from the through thickness orientation at the 0mm position and at the back surface, respectively (see Millett [56]). The specimen was 3.8mm thick. The impact conditions were a 5mm dural flyer at V=504m/s. The dotted curve is the numerical data obtained using proposed model; the solid curve is the experimental data.

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Figure 4

Representative experimental gauge traces from the fiber 0° orientation (see Millett [56]). The specimen was 10mm thick. The impact conditions were a 5mm copper flyer at V=936m/s. According to Hereil [55], the precursor was due to a high velocity wave transmitted along the fibers orientated in the shock axis, while the main shock was transmitted through the “matrix.”

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Figure 5

Back-surface gauge stress traces from plate-impact experiments versus numerical simulation of stress (PMMA) waves for plate impact test (impact velocity 450 m/s), target AA7010 T6 for longitudinal and transverse directions, respectively




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