On the relationships between cellular structure, deformation modes and electromechanical properties of piezoelectric cellular solids

Piezoelectrically active cellular solids are reminiscent of passive structural cellular solids, and therefore, depending on their inner cellular architecture, their cellular ligaments can deform locally by either bending or axial stretching. Three main cellular solid structures (i.e. hexagonal, tetragonal and triangular) that exemplify bending and stretching dominated piezoelectrically active cellular solids are considered. Three-dimensional finite element models were developed to understand the relationships between cellular structure, deformation modes and their effective electromechanical properties. The principal elastic, dielectric and piezoelectric properties of piezoelectric 3-1 cellular solids are insensitive to inner structure or topology in the longitudinally poled systems and highly sensitive to structure in the transversely poled systems. The in-plane electromechanical properties are highly sensitive to cellular architecture and connectivity as well. The effective out-of-plane elastic properties for all the three cellular structures depend linearly on relative density (i.e. stretching dominated), while the dependence of the in-plane effective elastic properties is linear for triangular and tetragonal cellular structures (i.e. stretching dominated) and generally non-linear for hexagonal honeycombs (i.e. bending dominated). Amongst the longitudinally poled systems, the triangular structures exhibit the highest in-plane stiffness properties. Amongst the transversely poled systems, the tetragonal structure exhibits the best overall combination of piezoelectric figures of merit.