Micromechanical modeling of piezo-magneto-thermo-elastic composite structures: Part I – Theory

Abstract

The comprehensive micromechanical models for the analysis of piezo-magneto-thermo-elastic smart composite structures with orthotropic constituents are developed. The asymptotic homogenization models are derived, the governing equations are determined. Subsequently general relations called unit cell problems are derived. They can be used to determine the effective elastic, piezoelectric, piezomagnetic, thermal expansion, dielectric, magnetic permeability , magnetoelectric, pyroelectric and pyromagnetic coefficients. The latter three sets of coefficients are particularly interesting in the sense that they represent product or cross-properties; they are generated in the macroscopic composite via the interaction of the different phases, but may be absent from some of the constituents themselves. The derived relations pertaining to the unit-cell problems and the resultant effective coefficients are very general and they are valid for any 3D geometry of the unit cell. In Part II of this work the results of the asymptotic homogenization models for practically important smart composite structures are obtained and presented graphically. ► We develop two Asymptotic Homogenization Models pertaining to 3D smart composites. ► One Model uses Maxwell's Equations. ► The second Model uses Quasi-static approximation of Maxwell's equations. ► All effective properties including product properties are determined.