[en] A finite element methods based homogenization approach is presented to simulate the nonlinear behavior of magnetoactive composites under a macroscopic deformation and an external magnetic field. The coupled magnetoelastic constitutive law and governing equations are developed in micro-scale for large deformations. Micro-scale formulation is employed on a characteristic volume element, taking into account periodic boundary conditions. A periodic homogenization method is utilized to compute macroscopic properties of the magnetoelastic composite at different mechanical and magnetic loading paths. A new and cost effective numerical scheme is used to develop the magnetoelastic tangent moduli tensors. A sensitivity analysis is proposed to compute the overall tangent moduli tensors of the composite through the finite difference method. The presented approach is useful in the characterization of magnetoactive and electroactive composites and FE"2 methods. Results are presented for typical equilibrium states. (paper)