Effective properties of multilayered functionally graded multiferroic composites

A micromechanics approach is employed to derive the effective properties (including the thermal properties) of a multilayered functionally graded multiferroic composite with 2–2 connectivity among the phases. Concise matrix expressions of the effective properties of the layered composite are presented. The derived formulas are then applied to find the explicit expressions of the effective properties for three practical cases: (a) a multiferroic composite composed of an orthotropic piezoelectric phase and an orthotropic magnetostrictive phase; (b) a multiferroic composite composed of an orthotropic piezoelectric phase, an orthotropic magnetostrictive phase and an orthotropic elastic substrate; (c) a multiferroic composite composed of a functionally graded orthotropic piezoelectric phase and a functionally graded orthotropic magnetostrictive phase. Our results clearly show that: (i) the magnetoelectric coupling effect for case (b) dramatically drops as the volume of the elastic substrate increases; and (ii) the magnetoelectric coupling effect for case (c) can be significantly enhanced or reduced depending on the material gradient manner for the functionally graded piezoelectric and magnetostrictive phases.