Micromechanical modeling of thin composite and reinforced magnetoelectric plates – Effective electrical, magnetic, thermal and product properties

Abstract

Maxwell's equations and the equations of dynamic force and thermal balance are used to develop an asymptotic homogenization model for the analysis and design of magnetoelectric composite and reinforced plates. The developed model generates a set of unit cell problems the solution of which enables the determination of the effective coefficients of the homogenized structure. Of particular importance among the effective coefficients are the product properties which are manifested in the macroscopic structure but are not usually exhibited by the individual constituents. Examples of effective properties are the magnetoelectric, pyroelectric and pyromagnetic coefficients. The model is illustrated by means of several examples such as diagonally restrained magnetoelectric plates, plates reinforced with a triangular arrangement of ribs, wafer reinforced magnetoelectric plates and three-layered sandwich plates. From the nature of the structures considered, it is shown that it is more practical if a basic unit cell consisting of only a single arbitrarily oriented rib and a base plate is analyzed first. Then, the effective properties of magnetoelectric structures with more families of ribs can be obtained by superposition. It is shown in this paper that the effective coefficients as well as the field variables are functions of time and are not constants as predicted by other models. In fact, it is shown that other models are special cases of the model derived here when electrical conductivity is ignored and the aforementioned temporal functions are time-averaged by integrating them over the entire time spectrum. Thus, overall, this paper represents an important addition to the existing literature in terms of the complex geometries that can be designed and analyzed and at the same time constitutes an important refinement over previously established work. In fact, the present work permits the design and analysis of a fully-coupled magnetoelectric plate or sandwich plate with any desired arrangement of the actuators/reinforcements.