Variable kinematics equivalent single layer theories for magneto-electro-elastic multilayered plates

In recent years, the employment of smart materials able to provide multi-functional capabilities, besides the traditional structural functions, has been gaining attention in several technological fields (automotive, aerospace, biomedical, robotics, etc.). This possibility of coupling different physical fields can be and it has been exploited in transducer applications, structural health monitoring, vibration control, energy harvesting and other applications. In this framework, magneto-electro-elastic (MEE) materials are attracting increasing consideration from academic and industrial audiences: MEE materials have the ability to couple mechanical, electrical and magnetic fields and this makes them particularly suitable for smart applications. Generally, besides few exceptions, single-phase materials exhibit either piezoelectric or piezomagnetic behavior, but no direct magneto-electric coupling is observed. The full magneto-electro-elastic coupling is actually obtained by employing composites with piezoelectric and piezomagnetic phases, that then provide the magneto-electric effect through the elastic field. MEE composites are obtained in the form of multi-phase materials, i.e. piezoelectric and piezomagnetic particles and/or fibers, or in the form of laminated structures, with piezoelectric and piezomagnetic layers stacked to achieve the desired coupling effects. Multilayered configurations appear to be more effective than bulk composites. Thus, reliable and efficient modeling tools are required for the analysis and design of smart magneto-electro-elastic laminated plates. Actually, numerical solutions are needed and considering that fully-coupled 3D finite element solutions for multilayered plates and shells present very high computational costs, 2D efficient laminated plates theories and the corresponding finite element solutions have been developed with the aim of reducing the analysis effort while preserving a suitable level of accuracy. In the framework of 2D plate theories, finite elements solutions based on layer-wise modeling have been proposed. The layerwise approach enables high accuracy; however its computational cost grows as the number of layers increases. Additionally, layer-wise modeling of laminated plates requires the development of ad hoc procedures and elements which make somehow difficult to integrate them into finite element commercial codes. On the other hand, equivalent single-layer plate theories do not present these drawbacks as their solution complexity is independent from the number of layers although they are generally less accurate than the layer-wise ones, especially for thick plates and first order through-the-thickness expansion. Recently, an equivalent single-layer approach for multilayered MEE plates and its finite element solution have been proposed by the authors, who developed an effective purely mechanical plate model as result of the condensation of the electro-magnetic state to the mechanical variables. It is worth noting that such a modeling strategy could take advantage of the solution tools available for the mechanics of classical multi-layered plates and could lead to the straightforward integration of MEE plate elements into available codes. In the present work the proposed model is systematically extended to refined equivalent single layer plates theories approaching the problem through a suitable application of the Carrera Unified Formulation. Finite element solutions for magneto-electro-elastic multilayered plates obtained by theories with different expansion order are presented and compared to ascertain the effect of the employed theory on the plate response accuracy.