3D Hierarchical lattice ferroelectric metamaterials

Abstract

Hierarchical cellular materials are ubiquitous in nature and lead to many extraordinary mechanical properties, such as ultralight, ultrastiff, and high toughness properties. Inspired by the biological materials, the purpose of this paper is to analyze three families, including cubic, octahedron, and hybrid, of 3D hierarchical lattice ferroelectric metamaterials and determine the relationship between architecture and effective thermo-electro-mechanical properties by proposing a multiscale asymptotic homogenization technique. The effect of hierarchical order, lattice topology and relative density on piezoelectric and pyroelectric figures of merit, measure for assessing the performance of ferroelectric metamaterials as sensors and energy harvesters, is explored. The 1st-order ferroelectric metamaterials remarkably improve the figures of merit compared to the fully-solid ferroelectrics; increasing hierarchical order can magnify these improvements. Hybrid hierarchical ferroelectric metamaterials show further improvement in ferroelectric properties, not achievable by fractal-like metamaterials. For example, compared to the 1st-order body centered cube (BCC) with a piezoelectric energy harvesting figure of merit (FOM33) of more than 50 times higher than the bulk ferroelectric materials, FOM33 of 2nd-order hybrid hierarchical octet truss/BCC can be 50.7% higher, this improvement is 43.8% and 43.2% for 2nd-order hierarchical fractal-like BCC and octet truss, respectively. Finally, scaling relationships for predicting the multiphysical behavior of ferroelectric metamaterials, covering the whole range of relative densities, are proposed. This study introduces bioinspired hierarchical ferroelectric metamaterials as a new class of lightweight multifunctional advanced materials with integrated mechanical, piezoelectric and pyroelectric properties for developing the next generation of hydrophones, pressure and temperature sensors, and energy harvesters.