Using the approach described in Example 2.6, derive the expressions for all the averaged stiffnesses for the planar isotropic lamina in terms of invariants. Use these results to find the corresponding averaged engineering constants (modulus of elasticity, shear modulus, and Poisson's ratio) in terms of invariants.

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EXAMPLE 2.6 A tensile test specimen is cut out along the x direction of the pressure vessel described in Example 2.5. What effective modulus of elasticity would you expect to get during a test of this specimen?