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A perturbative approach to determining the strain-induced effective interactions in binary alloys with large atomic size mismatch is presented. Using the chemical energy as the reference state, the strain-induced energy of the alloy is cast into a many-body (Kanzaki) force expansion that depends on both the configurational and displacive degrees of freedom. It is shown that the k-space energy expansion is valid for all wavelengths. The theory is then applied to the Cu₃Au alloy where, due to the large difference between atomic sizes, considerable relaxations are observed from first-principles calculations. We found that the inhomogeneous contribution (k ≠ 0) dominates the strain energy in Cu₃Au, whereas the homogeneous part (k = 0), notwithstanding its configurational dependence, contributes only a few per cent.