A Reformulation of Nonlinear Anisotropic Elasticity for Impact Physics

Report No. ARL-TR-6837
Authors: John D. Clayton
Date/Pages: February 2014; 22 pages
Abstract: A new anisotropic Eulerian theory of nonlinear thermoelasticity developed in the present work has been shown to provide superior accuracy and/or stability over existing Lagrangian thermoelasticity theory for large static compression and shear deformation of ideal cubic crystals and diamond, and for the shock response of three different metallic crystals. For the shock response of single crystals of quartz and sapphire, Eulerian and Lagrangian theories are of comparable accuracy, with fourth-order elastic constants (quartz) and third-order elastic constants (diamond) necessary for a best fit to published experimental shock-compression data. Superior accuracy of this Eulerian theory, which degenerates to a Birch-Murnaghan equation-of-state when deviatoric stresses are negligible, has been demonstrated for representing the shock-compression response of aluminum, copper, and magnesium.
Distribution: Approved for public release
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Last Update / Reviewed: February 1, 2014