Simple closed-form expressions for the effective properties of multilaminated flexoelectric composites

A multilayered rectangular flexoelectric structure is considered. This composite has a unit cell of N-constituents which belong to the cubic crystal symmetry. Using the two-scale asymptotic homogenization method, explicit expressions of the local problems are derived. Simple closed-form formulas of the effective stiffness, piezoelectric, dielectric, and flexoelectric tensors are given, based on the solutions of local problems of stratified multilayered composites with perfect contact at the interface. These formulas provide information about the symmetry of the homogenized structure. As a numerical example, a bilaminate composite where the layers are perpendicular to the $$x_3$$ axis is studied, and the constituents are Barium Titanate and Gallium Arsenide. The composite after the homogenization process exhibits flexoelectric properties with tetragonal $$\bar{4}2$$ m crystal symmetry. The effective properties are computed for several constituents of volume fractions.