A Reformulation of Nonlinear Anisotropic Elasticity for Impact Physics

Abstract

Approved for public release; distribution unlimited. ii REPORT DOCUMENTATION PAGEForm Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing the burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. REPORT DATE (DD-MM-YYYY) February 20142. REPORT TYPE ARL-TR-6837 SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR'S ACRONYM(S) SPONSOR/MONITOR'S REPORT NUMBER(S) DISTRIBUTION/AVAILABILITY STATEMENTApproved for public release; distribution unlimited. SUPPLEMENTARY NOTES ABSTRACTA 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 fourthorder 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.