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

For isostress, loading is in the 2 direction and the stress seen by each component is the same so that:

s_c = s_f = s_m

All the components remain in the elastic range
obeying Hooke's Law: s = Ee

The total strain in the 2 direction is the volume fraction weighted sum of the strain of the components: e_c = V_fe_f + V_me_m

Substitute into this expression from Hooke's law and divide through by s_i :1/Ec = V_f/E_f + V_m/E_m

so that: E_c = {E_fE_m}/{V_fE_m + (1- V_f)E_f}