3D Plate-Lattices: An Emerging Class of Low-Density Metamaterial Exhibiting Optimal Isotropic Stiffness

Abstract

In lightweight engineering, there is a constant quest for low-density materials featuring high mass-specific stiffness and strength. Additively-manufactured metamaterials are particularly promising candidates as the controlled introduction of porosity allows for tailoring their density while activating strengthening size-effects at the nano- and microstructural level. Here, plate-lattices are conceived by placing plates along the closest-packed planes of crystal structures. Based on theoretical analysis, a general design map is developed for elastically isotropic plate-lattices of cubic symmetry. In addition to validating the design map, detailed computational analysis reveals that there even exist plate-lattice compositions that provide nearly isotropic yield strength together with elastic isotropy. The most striking feature of plate-lattices is that their stiffness and yield strength are within a few percent of the theoretical limits for isotropic porous solids. This implies that the stiffness of isotropic plate-lattices is up to three times higher than that of the stiffest truss-lattices of equal mass. This stiffness advantage is also confirmed by experiments on truss- and plate-lattice specimens fabricated through direct laser writing. Due to their porous internal structure, the potential impact of the new metamaterials reported here goes beyond lightweight engineering, including applications for heat-exchange, thermal insulation, acoustics, and biomedical engineering.

Keywords: additive manufacturing; isotropy; metamaterials; stiffness; yield strength.