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An anisotropic equation of state (EOS) is proposed for the accurateextrapolation of high-pressure shock Hugoniot (anisotropic and isotropic)states to other thermodynamic (anisotropic and isotropic) states for a shockedcarbon-fibre epoxy composite (CFC) of any symmetry. The proposed EOS, using ageneralised decomposition of a stress tensor [Int. J. Plasticity \textbf{24},140 (2008)], represents a mathematical and physical generalisation of theMie-Gr\"{u}neisen EOS for isotropic material and reduces to this equation inthe limit of isotropy. Although a linear relation between the generalisedanisotropic bulk shock velocity $U^{A}_{s}$ and particle velocity $u_{p}$ wasadequate in the through-thickness orientation, damage softening processproduces discontinuities both in value and slope in the $U^{A}_{s}$-$u_{p}$relation. Therefore, the two-wave structure (non-linear anisotropic andisotropic elastic waves) that accompanies damage softening process was proposedfor describing CFC behaviour under shock loading. The linear relationship$U^{A}_{s}$-$u_{p}$ over the range of measurements corresponding to non-linearanisotropic 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 secondgeneralised anisotropic bulk speed of sound [Eur. Phys. J. B \textbf{64}, 159(2008)]. An analytical calculation showed that Hugoniot Stress Levels (HELs) indifferent directions for a CFC composite subject to the two-wave structure(non-linear anisotropic elastic and isotropic elastic waves) agree withexperimental measurements at low and at high shock intensities. The results arepresented, discussed and future studies are outlined.

An Equation of State of a Carbon-Fibre Epoxy Composite under Shock Loading