Plane stress analysis of magnetoelectric composite and reinforced plates: Applications to wafer‐ and rib‐reinforced plates and three‐layered honeycomb shells

Abstract

The equations of dynamic force and thermal balance as well as the time‐varying form of Maxwell's equations are used to develop a comprehensive asymptotic homogenization model for the design and analysis of composite and reinforced magnetoelectric plates. The model generates twenty unit cell problems that can be used to determine the effective elastic, piezoelectric, piezomagnetic, electrical conductivity and other properties of the structure under consideration. Of particular interest among these effective coefficients are the so‐called product properties which are manifested in the macroscopic composite plate via the strain transfer and general interactions between the different phases but may be absent from the behavior of the individual constituents of the composite. Examples of product properties are the magnetoelectric, pyroelectric and pyromagnetic coefficients. This paper applies the model developed to three general magnetoelectric structures; wafer‐reinforced plates, rib‐reinforced plates, and three‐layered honeycomb shells. For the sake of generality, all structures considered are assumed to be made of generally orthotropic constituents. Unlike previous models it is discovered in this work that the effective coefficients of such structures are not constants, but are, instead, functions of time. As a direct consequence, the dependent field variables (stress, strain, electric and magnetic field, heat flux, current density, and all others) are also functions of time; this results in a homogenized structure which exhibits memory‐like behavior. In fact, 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.