Composites of magnetostrictive and piezoelectric materials have been prospective candidates in the field of sensing and energy harvesting due to their multifunctional capabilities. These magnetoelectric (ME) composites develop a voltage in response to external magnetic fields and vice versa. The developed voltage depends strongly on the stresses in the magnetostrictive phase and the resonant frequency of the structure. While symmetric laminated structures offer simplicity in terms of analysis, they possess very high resonant frequencies, which is accompanied by high power requirements and eddy current losses. Unsymmetric ME composites have been receiving significant attention in this regard due to their low resonant frequencies under bending resonant modes, while also offering ease of fabrication. Further, the constitutive behavior of the magnetostrictive material is nonlinear with respect to the stress and the magnetic field. Characterization of this material nonlinearity and its influence on the ME response of the composite is thus imperative to facilitate device applications.
This work deals with the prediction of the static and resonant ME voltage characteristics in unsymmetric composite beams subjected to thermo-magneto-mechanical loading. The magnetostrictive constitutive relations assumed are implicit in nature and hence an iterative algorithm based on a one-dimensional Timoshenko beam element is used to model the response of the ME structure. The model predictions are further validated by experimental characterization of the magnetostrictive and ME characteristics in response to simultaneous mechanical, magnetic and thermal stimuli. The results indicate deterioration of the ME coupling under compressive stresses in the magnetostrictive phase and higher temperatures. Further, the magnetic field dependent Young’s modulus and hence tunable resonant frequency characteristics are investigated. Extension of the model to a fully coupled two-dimensional plane stress condition has also been attempted. This however proves cumbersome using classical displacement-based finite element (FE) procedures due to the implicit nature of the constitutive relations. Hence, a special FE framework is established wherein, unlike classical FE methods, the constitutive relation is satisfied in a weak integral sense while ensuring exactness of the equilibrium. A fully coupled plane stress magnetostrictive element is developed using the proposed framework incorporating the aforementioned implicit constitutive relations thus facilitating the analysis of magnetostatic Multiphysics boundary value problems (BVPs). The predictions from the proposed element are validated against analytical solutions and the efficacy of the framework is established.