Verify the inequality restrictions on the elastic moduli for orthotropic, transversely isotropic, cubic and isotropic materials given by Table 11.1.

Table 11.1

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Table 11.1 Positive definite restrictions on elastic moduli. Material Restriction inequalities Orthotropic C > 0, C44 > 0, C55>0, C660, C1C22 - 0 C1C2C33-C11C3 - C22C3 - C33C12 + 2C12C23 C310 C > 0, C44>0, C-C >0, C1 - C2 > 0 C1C22C33-C11C3 - C22C3 - C33C12 + 2C12C23 C31 > 0 C10, C440, C-C > 0. Transversely Isotropic Cubic Isotropic C-3C11C2+2012 > 0 or (C1C12) (C11 +2C12) > 0 +2>0, +>0 3 +2> 0, >0 C1+2C2 > 0