The mechanical analysis of thermo-magneto-electric laminated composites in nanoscale with the consideration of surface and flexoelectric effects

A theoretical thermo-magneto-electric (TME) bilayer model is established based on the Hamilton principle, in which both surface effect and flexoelectricity are all taken into account. The governing equations are proposed with the aid of the nonlinear constitutive relations of giant magnetostrictive materials. These equations are general, which can be applied to analyze the coupled extensional, shear and bending deformations at both macroscale and nanoscale. As a specific example, the coupled extensional and bending motion of a slender beam suffering from external magnetic field and thermal variation is investigated, in which the Miller-Shenoy coefficient, magneto-electric (ME) effect, strain gradient and displacement are discussed in detail. After the necessary verification, a critical thickness of the TME model is proposed, below which the surface effect exhibits a remarkable influence on the mechanical behaviors and can not be ignored. It is revealed that the surface effect, flexoelectric effect and temperature increment are beneficial for the enhancement of the induced electric field. This study can provide theoretical basis for the design of nanoscale laminates, especially for the performance evaluation of ME composites under complex environment.