Comparative analysis of piezoelectric regular foams from two types of Gibson–Ashby cells with uniform and piecewise homogeneous polarizations

Modern achievements in the development of additive technologies allow the creation of highly porous piezoelectric metamaterials with a specified microstructure. Preliminary computer simulation of their properties depending on the initial geometric and physical data opens up wide possibilities in the design of effective piezoelectric devices with unique characteristics. Gibson–Ashby cells are classic versions of elementary structures of metamaterials and their mechanical properties are well studied. However, piezoelectric metamaterials have been investigated to a much lesser extent. Thus, for cells made of piezoceramics, it is fundamentally important to know the type of inhomogeneous polarization field. We investigated two types of canonical Gibson–Ashby cells: symmetric one with four connecting edges on each face and asymmetric one with two connecting edges on each face. Regular lattices can be composed of these cells, which were also studied. In addition, we compared the structures with uniform and with piecewise uniform polarization of piezoceramics. Effective moduli were found from numerical solutions of homogenization problems using the finite element method. The results obtained allowed us to identify the anisotropy classes of a homogeneous material for all considered variants and to establish the influence of geometry and polarization field on effective moduli. New unusual properties of effective transverse piezoelectric moduli, different from the properties of the corresponding piezoelectric moduli of conventional piezoceramics, were noted.