An experimental investigation has been carried out to capture the magneto-mechanical behavior and material parameters of magnetostrictive material. Further, the experimental study is extended to capture the magnetoelectric (ME) coupling response of trilayered composites by applying both alternating and static magnetic fields. From the experiments, it is observed that the magnetostrictive material has a nonlinear hysteretic behavior. Hence, a three dimensional (3-D) nonlinear constitutive model has been proposed based on a thermodynamic framework and multisurface plasticity. In ME composites, it is also observed that a large ME coupling response can be obtained while operating near resonance frequencies. To capture the resonant ME effects, a theoretical formulation has been proposed based on axial vibrations theory and the proposed constitutive model has been incorporated in the formulation. The simulated resonant ME coupling response based on the proposed formulation is compared with the experimental data and found to be in agreement with each other. Further, a parametric study has been performed to address the variation of the resonant ME response as a function of various parameters such as axial compliance ratio, volume fraction of constituents, temperature, direction of magnetic loading and aspect ratio. This study reveals that the coupling response can be optimized by choosing the suitable parameters based on design requirement. © 2019 Elsevier Masson SAS