Reexamining the mechanical property space of three-dimensional lattice architectures

Lightweight materials that are simultaneously strong and stiff are desirable for a range of applications from transportation to energy storage to defense. Micro- and nanolattices represent some of the lightest fabricated materials to date, but studies of their mechanical properties have produced inconsistent results that are not well captured by existing lattice models. We performed systematic nanomechanical experiments on four distinct geometries of solid polymer and hollow ceramic (Al_2O_3) nanolattices. All samples tested had a nearly identical scaling of strength (σy) and Young's modulus (E) with relative density (ρ¯), ranging from σy∝ρ¯1.45 to ρ¯1.92 and E∝ρ¯1.41 to ρ¯1.83, revealing that changing topology alone does not necessarily have a significant impact on nanolattice mechanical properties. Finite element analysis was performed on solid and hollow lattices with structural parameters beyond those realized experimentally, enabling the identification of transition regimes where solid-beam lattices diverge from existing analytical theories and revealing the complex parameter space of hollow-beam lattices. We propose a simplified analytical model for solid-beam lattices that provides insight into the mechanisms behind their observed stiffness, and we investigate different hollow-beam lattice parameters that give rise to their aberrant properties. These experimental, computational and theoretical results uncover how architecture can be used to access unique lattice mechanical property spaces while demonstrating the practical limits of existing beam-based models in characterizing their behavior.