Elastically-isotropic truss lattice materials of reduced plastic anisotropy

The elastically-anisotropic octet truss lattice exhibits high specific stiffness due to its stretching-dominated mechanical behavior. Here, elastically-isotropic truss lattices are designed in a way that the constituent beams respond in a stretching-dominated manner instead of bending. Topology constraints ensuring an isotropic elastic response at the macroscopic level are derived from a detailed theoretical analysis of generic periodic truss structures. Specific elastically-isotropic structures are designed by combining elementary cubic truss lattices including the Simple Cubic (SC), Body-Centered Cubic (BCC) and Face-Centered Cubic (FCC) lattices. It is shown through periodic homogenization that these isotropic truss lattice compositions exhibit less initial yield anisotropy than the octet truss lattice. For example, the ratio of maximum to minimum yield stress of an SC-BCC-FCC truss lattice composition is 1.4 as compared to 2 for the octet truss lattice. Computational unit cell analysis is carried out to confirm the analytical Young's modulus and yield stress estimates. Selected isotropic structures of 20% relative density are built from a photopolymer using stereolithography. The Young's modulus and Poison's ratio measurements on specimens with different lattice orientations confirm the validity of the design constraints. In addition, the trends regarding the plastic anisotropy are confirmed by the experimental results.