Nonlinear anisotropic description for shocked single crystals: Thermoelastic response and pure mode wave propagation

Abstract

An anisotropic continuum framework for describing the nonlinear thermoelastic response of shocked single crystals has been developed. Using this framework, the propagation of large amplitude stress waves along arbitrary directions in crystals of any symmetry can be examined. We developed an incremental approach, where the reference state for the dynamical variables and the material properties is updated throughout the calculation. Results from our incremental approach are in excellent agreement with the results from a finite strain formulation. Using a finite-difference wave propagation code, we performed numerical simulations of large amplitude elastic wave propagation in single crystals. Results of impact loading simulations for quartz and sapphire single crystals are presented. The framework developed was also useful for examining the propagation of pure mode nonlinear waves for various crystal symmetries. Our calculations showed that pure longitudinal waves resulted from impact loading along any rotational symmetry axis for all crystal symmetry classes. Differences between pure mode wave propagation for linear and nonlinear elastic deformation are discussed.