For a carbon/epoxy unidirectional composite plot values of G12 as a function of volume fraction using: (a) the parallel model (rule of mixtures); (b) the series model (inverse rule of

mixtures); (c) the combined parallel and series model assuming a fiber diameter of 10 m and square packing; d) the self-consistent field model. Use the following properties for Type II carbon fibers: Ef1 =250 GPa, Ef2 =20 GPa, f12 = 0.2, f23 = 0.25, Gf12 = 10 GPa and epoxy matrix, Em = 2.0 GPa, m = 0.4.

Could you give me the necessary equations for a),b),c) and d)?