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The Isostrain Situation: Parallel Loading

From: Hull, "An Iintroduction to Composite Materials," Cambridge (1981)

 For Isostrain, loading is in the 1 direction and the strain in the composite and each of its components is the same so that: ec = ef = em

All the components remain in the elastic range obeying Hooke's Law: 
s = Ee , and the force is distributed among the components in proportion to their Volume Fraction: scVc = sfVf + smVm

Substitute for s in this last expression in terms of E and e, and divide through by e to give the expression for the Isostrain (Parallel) Young's modulus: 

Ecp = EfVf + EmVm