Variational asymptotic homogenization of heterogeneous electromagnetoelastic materials. The variational asymptotic method is used to develop a micromechanics model for predicting the effective properties and local fields of heterogeneous electromagnetoelastic materials. Starting from the total electromagnetic enthalpy of the heterogeneous continuum, we formulate the micromechanics model as a constrained minimization problem taking advantage of the fact that the size of the microstructure is small compared to the macroscopic size of the material. To handle real microstructures in engineering applications, we implement this new model using the finite element method. A few examples are used to demonstrate the application and accuracy of this theory and the companion computer program, VAMUCH. The present results are compared with those available in the literature.