The focus of the present paper is to construct a general purpose micromechanics model to predict the effective fully coupled time-dependent and non-linear multiphysics responses of smart composites. The present model is established on the basis of the variational asymptotic method and implemented using the finite element method. In light of the time-dependent and non-linear characteristics of composites, an incremental procedure in conjunction with an instantaneous tangential electromagnetomechanical matrix of composites was established. The accuracy of the proposed model was verified through the comparison with ABAQUS results. Finally, a numerical example was employed to demonstrate the capability of the proposed model.