Bioinspired Nested-Isotropic Lattices with Tunable Anisotropy for Additive Manufacturing

This study presents innovative nested-isotropic lattices for additive manufacturing, drawing inspiration from bio-architectures found in cortical bone osteons, golden spirals, and fractals. These lattices provide tunable anisotropy by integrating architectural elements like ``nesting orders (NOs)'' and corresponding ``nesting orientations (NORs),'' along with repetitive self-similar X-cross struts and three four-fold axes of symmetry, resulting in a wide spectrum of lattice designs. Nine mono-nest and twenty multi-nest lattices, along with 252 parametric variations, are realized. The relative density $\bar{\rho}$ and surface area density $\bar{S}$ are calculated. Employing finite element-based numerical homogenization, elastic stiffness tensors are estimated to evaluate the anisotropic measure - Zener ratio $Z$ and elastic modulus $\bar{E}$ for all lattice designs. The mono-nest lattices generated considering higher NOs and respective NORs exhibit a transition from shear dominant to tensile/compression dominant (TCD) anisotropic behavior and their strut size variations show a strong influence on $\bar{\rho}$, $\bar{S}$, and $\bar{E}$. In contrast, multi-nest lattices exhibit isotropic and neo-isotropic characteristics, with strut size mismatch exerting more influence on $Z$. Increasing NOs and NORs result in isotropic or TCD behavior for most multi-nest lattices, with strut size mismatch leading to many isotropic lattices. These bio-inspired nested lattices, coupled with advancements in additive manufacturing, hold potential for diverse applications.