Topics in the Analysis of Shear-Wave Propagation in Oblique-Plate Impact Tests

Report No. ARL-SR-157
Authors: Mike Scheidler
Date/Pages: September 2007; 26 pages
Abstract: This report addresses several topics in the theoretical analysis of shock waves, acceleration waves, and centered simple waves, with emphasis on the propagation of shear waves generated in oblique-plate impact tests. The first report, Formulas for the Pressure and Bulk Modulus in Uniaxial Strain, demonstrates that for a general, nonlinear, isotropic elastic solid, the shear stress in the uniaxially strained region ahead of the shear wave may be inferred from the measured shear-wave speed and the density. This result, which improves on approximate analyses in the literature, is applied to the study of fused silica in the shocked state. The second report, Response of Nonlinear Elastic Solids to Oblique-Plate Impact, treats the case where the shear wave is a centered simple wave (or ramp wave). Approximate relations are derived for the stress, strain, particle velocity, wave speed, and rise time, and applications to material characterization are discussed. The third report, Universal Relations for Pressure-Shear Waves in Nonlinear Elastic Solids, treats centered simple shear waves and shear shocks. Here, we obtain approximate relations between stress, strain, particle velocity, and wave speeds that do not explicitly involve the constitutive functions or elastic constants of the material. The fourth report, Approximate Universal Relations Between Shock and Acceleration Wave Speeds for Oblique Plate Impact of Inelastic Solids, extends some of the results of the previous report to a large class of inelastic solids, although a completely different method of proof is required for the inelastic case. The results of the latter three reports apply not only to isotropic solids but also to certain anisotropic solids, provided that the symmetry axes are appropriately aligned with the test geometry.
Distribution: Approved for public release
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Last Update / Reviewed: September 1, 2007