A general closed-form solution for the overall response of piezoelectric composites with periodic and random particulate microstructures

In this paper, we make use of a new iterative homogenization technique in finite electroelastostatics (Lopez-Pamies, 2014) to derive a closed-form solution for the overall response of two-phase piezoelectric composites with particulate microstructures. The calculations amount to solving a system of Riccati differential equations for the effective elastic, dielectric, and piezoelectric tensors of the composites, where the volume fraction of the inclusions plays the role of independent variable. The solution is valid for any choice of piezoelectric behaviors for the underlying matrix and inclusions, and any choice of the one- and two-point correlation functions describing the microstructure. In addition to discussing the key theoretical and practical features of the solution, its descriptive and predictive capabilities are illustrated via comparisons with a broad range of experimental data and full-field simulations (available from the literature) for composites with periodic and random distributions of inclusions of various shapes.