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Based on the shear-transformation-zone (STZ) theory, we propose a constitutive model for describing homogeneous elastoplastic deformation of amorphous solids where the interaction of shear transformations and free volume dynamics is incorporated. This theoretical model can reproduce the stress overshoot behavior that shows the dependence of strain rate, temperature, STZ population and dilatancy of systems. It reveals that the stress overshoots its steady state value due to the delayed activation of shear transformations that results from the insufficient free volume in the system. However, the subsequent strain softening (stress drop) is attributed to the shear-induced dilatation that is a result of the positive interplay between shear transformations and free volume creation, the latter playing the dominant role. Our analysis also demonstrates that the STZs, as basic carriers of amorphous plasticity, govern the yielding of the system, whereas the free volume dynamics significantly affects the post-yielding behaviors.