$E=\frac{9BG}{3B+G}$

$v=\frac{\left(3B-2G\right)}{\left(6B+2G\right)}$

$B=\frac{C_{11}+2C_{12}}{3}$

$G=\frac{3c_{44}+c_{11}-c_{12}}{5}$

$C_{66}=\frac{C_{11}-C_{12}}{2}$

$M=C_{11}+C_{12}+2C_{33}-4C_{13}$

$B_{Hill}=\frac{1}{2}\left(B_{Reuss}+B_{Voigt}\right)$

$B_R=\frac{\left(C_{11}+C_{12}\right)C_{33}-2C_{13}^2}{C_{11}+C_{12}-4C_{13}+2C_{33}}$

$B_V=\frac{2C_{11}+2C_{12}+4C_{13}+C_{33}}{9}$

$G_{Hill}=\frac{1}{2}\left(G_{Reuss}+G_{Voigt}\right)$

$G_R=\frac{5\left(C_{11}-C_{12}\right)C_{44}}{4C_{44}+3\left(C_{11}-C_{12}\right)}$

$G_v=\frac{C_{11}+C_{12}-4C_{13}+2C_{33}+12C_{44}+12C_{66}}{30}$