The prediction of magnetoelectric (ME) coupling in nano-scaled multiferroic composites is significant for nano-devices. In this paper, we propose a nonlinear multi-field coupling model for ME effect in layered multiferroic nanocomposites based on the surface stress model, strain gradient theory and nonlinear magneto-elastic-thermal coupling constitutive relation. With this novel model, the influence of external fields on strain gradient and flexoelectricity is discussed for the first time. Meanwhile, a comprehensive investigation on the influence of size-dependent parameters and multi-field conditions on ME performance is made. The numerical results show that ME coupling is remarkably size-dependent as the thickness of the composites reduces to nanoscale. Especially, the ME coefficient is enhanced by either surface effect or flexoelectricity. The strain gradient in composites at the nano-scale is significant and influenced by the external stimuli at different levels via the change in materials’ properties. More importantly, due to the nonlinear multi-field coupling behavior of ferromagnetic materials, appropriate compressive stress and temperature may improve the value of ME coefficient and reduce the required magnetic field. This paper provides a theoretical basis to analyze and evaluate multi-field coupling characteristics of nanostructure-based ME devices.
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