Impact of node geometry on the effective stiffness of non-slender three-dimensional truss lattice architectures

Three-dimensional (3D), lattice-based micro- and nano-architected materials can possess desirable mechanical properties that are unattainable by homogeneous materials. Manufacturing these so-called structural metamaterials at the nano- and microscales typically results in non-slender architectures (e.g., struts with a high radius-to-length ratio r∕l), for which simple analytical and computational tools are inapplicable since they fail to capture the effects of nodes at strut junctions. We report a detailed analysis that quantifies the effect of nodes on the effective Young's modulus (E∗) of lattice architectures with different unit cell geometries through (i) simple analytical constructions, (ii) reduced-order computational models, and (iii) experiments at the milli- and micrometer scales. The computational models of variable-node lattice architectures match the effective stiffness obtained from experiments and incur computational cost that are three orders-of-magnitude lower than alternative, conventional methods. We highlight a difference in the contribution of nodes to rigid versus non-rigid architectures and propose an extension to the classical stiffness scaling laws of the form E∗∝C1(r∕l)α+C2(r∕l)β, which holds for slender and non-slender beam-based architectures, where constants C1 and C2 change with lattice geometry. We find the optimal scaling exponents for rigid architectures to be α=2 and β=4, and α=4 and β=6 for non-rigid architectures. These analytical, computational, and experimental results quantify the specific contribution of nodes to the effective stiffness of beam-based architectures and highlight the necessity of incorporating their effects into calculations of the structural stiffness. This work provides new, efficient tools that accurately capture the mechanics and physics of strut junctions in 3D beam-based architected materials.