Equivalence of Strain Energy Approach:

We can derive the effective bulk modulus using the concept of equivalence of strain energy. The strain energy of the equivalent homogeneous single cylinder is given as

(7.238)

The stresses and strains are known from Equation (7.219), Equation (7.222) and Equation (7.223). When these are substituted in above equation, for a unit length, it gives

(7.239)

Now this strain energy is compared with that obtained for concentric cylinders as given in Equation (7.212). The stresses and strains in fibre and matrix for this expression can be obtained as the constants  and  are known.