  An anisotropic equation of state is proposed for accurate extrapolation of
high-pressure shock Hugoniot states to other thermodynamics states for shocked
single crystals and polycrystalline alloys. The proposed equation of state
represents mathematical and physical generalization of the Mie-Gr\"{u}neisen
equation of state for isotropic material and reduces to this equation in the
limit of isotropy. Using an anisotropic nonlinear continuum framework and
generalized decomposition of a stress tensor [Int. J. Plasticity \textbf{24},
140 (2008)], the shock waves propagation along arbitrary directions in
anisotropic solids of any symmetry can be examined. The non-associated strength
model includes the distortion effect of the yield surface which can be used to
describe the anisotropic strength differential effect. A numerical calculation
showed that the general pulse shape, Hugoniot Elastic Limits (HELs), and
Hugoniot stress levels for aluminum alloy 7010-T6 agree with the experimental
data. The results are presented and discussed, and future studies are outlined.

Materials Science