Effective properties of three-phase electro-magneto-elastic composites

Coupling between the electric field, magnetic field, and strain of composite materials is achieved when electro-elastic (piezoelectric) and magneto-elastic (piezomagnetic) particles are joined by an elastic matrix. Although the matrix is neither piezoelectric nor piezomagnetic, the strain field in the matrix couples the electric field of the piezoelectric phase to the magnetic field of the piezomagnetic phase. This three-phase electro-magneto-elastic composite should have greater ductility and formability than a two-phase composite in which the electric field and the magnetic field are coupled by directly bonding two brittle materials. A finite element analysis (FEA) and micromechanics based averaging of a representative volume element (RVE) are performed in this work to determine the effective dielectric, magnetic, mechanical, and coupled-field properties of an elastic matrix reinforced with piezoelectric and piezomagnetic fibers as functions of the phase volume fractions, the fiber arrangements in the RVE, and the fiber material properties with special emphasis on the poling directions of the piezoelectric and piezomagnetic fibers. The effective magneto-electric moduli of this three-phase composite are found to be less than the effective magneto-electric moduli of a two-phase piezoelectric/piezomagnetic composite, because the elastic matrix is not stiff enough to transfer significant strains between the piezomagnetic and piezoelectric fibers.