  An anisotropic equation of state (EOS) is proposed for the accurate
extrapolation of high-pressure shock Hugoniot (anisotropic and isotropic)
states to other thermodynamic (anisotropic and isotropic) states for a shocked
carbon-fibre epoxy composite (CFC) of any symmetry. The proposed EOS, using a
generalised decomposition of a stress tensor [Int. J. Plasticity \textbf{24},
140 (2008)], represents a mathematical and physical generalisation of the
Mie-Gr\"{u}neisen EOS for isotropic material and reduces to this equation in
the limit of isotropy. Although a linear relation between the generalised
anisotropic bulk shock velocity $U^{A}_{s}$ and particle velocity $u_{p}$ was
adequate in the through-thickness orientation, damage softening process
produces discontinuities both in value and slope in the $U^{A}_{s}$-$u_{p}$
relation. Therefore, the two-wave structure (non-linear anisotropic and
isotropic elastic waves) that accompanies damage softening process was proposed
for describing CFC behaviour under shock loading. The linear relationship
$U^{A}_{s}$-$u_{p}$ over the range of measurements corresponding to non-linear
anisotropic elastic wave shows a value of $c^{A}_{0}$ (the intercept of the
$U^{A}_{s}$-$u_{p}$ curve) that is in the range between first and second
generalised anisotropic bulk speed of sound [Eur. Phys. J. B \textbf{64}, 159
(2008)]. An analytical calculation showed that Hugoniot Stress Levels (HELs) in
different directions for a CFC composite subject to the two-wave structure
(non-linear anisotropic elastic and isotropic elastic waves) agree with
experimental measurements at low and at high shock intensities. The results are
presented, discussed and future studies are outlined.
