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We address the issue of the composition and strain dependence of the piezoelectric effect in semiconductor materials, which is manifested by the appearance of an electric field in response to shear crystal deformation. We propose a model based on expressing the direct and dipole contributions to the polarization in terms of microscopic quantities that can be calculated by density functional theory. We show that when applied to the study of In_xGa_1-xAs alloys, the model is able to explain and accurately predict the often- observed discrepancies between the experimentally deduced values of e14 and those linearly interpolated between the values of InAs and GaAs. The values of the piezoelectric coefficient predicted by our approach compare very well with values deduced from photocurrent measurements of quantum well samples grown on (111) GaAs substrates by molecular beam epitaxy.