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If μ is the shear modulus of the matrix and V is the volume of the unconstrained hole in the matrix and the elastic energy does not depend on the shape of the precipitate, if so, calculate the elastic strain energy? (Assume the poissons ratio to be 1/3 and Misfit-Δ)

If μ is the shear modulus of the matrix and V is the volume of the unconstrained hole in the matrix and the elastic energy does not depend on the shape of the precipitate, if so, calculate the elastic strain energy? (Assume the poissons ratio to be 1/3 and Misfit-Δ) Correct Answer ΔG=4μΔ2*V

In general, the total elastic energy depends on the shape and elastic properties of both matrix and inclusion. However, if the matrix is elastically isotropic and both precipitate and matrix have equal elastic moduli, the total elastic strain energy ΔG is independent of the shape of the precipitate and is given as ΔG=4μΔ2 *V.

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