Plane stress analysis of magnetoelectric composite and reinforced plates: Micromechanical modeling and application to laminated structures

Abstract

A new comprehensive micromechanical model for the analysis of thin smart composite and reinforced piezo-magneto-thermo-elastic plates is developed in the present paper. The model is developed on the basis of asymptotic homogenization utilizing dynamic force and thermal balance and the time-varying form of Maxwell's equations. Once the governing equations are determined, a set of twenty unit cell problems is extracted from which the effective coefficients of the homogenized structure can be obtained in a closed-form design-oriented format. Unlike previous models, it is discovered in this work that the effective coefficients are not constants, but rather functions of time. Consequently, the dependent field variables (mechanical stress, electric and magnetic fields, heat flux, and others) are also functions of time and the homogenized structure exhibits memory-like behavior. Of particular interest in this work is the development of general expressions pertaining to the so-called product properties which are manifested in the macroscopic composite plate via the interaction of the different phases but may be absent from some individual constituents of the composite. Examples of product properties are the magnetoelectric, pyroelectric and pyromagnetic coefficients. The developed model however also extracts an interesting new set of product properties relating current density to mechanical deformation, magnetic field and temperature change. It is shown in this paper that other previously derived models can be viewed as particular special cases of the model developed here when electrical conductivity is ignored and all pertinent quantities are time-averaged by integrating them over the entire time spectrum. Collectively, the results presented here represent a significant refinement of previously established results. The work is illustrated by means of a thin laminated piezo-magneto-thermo-elastic composite plates with orthotropic constituents.