Bioinspired Nested-Isotropic Lattices with Tunable Anisotropy for Additive Manufacturing

Abstract: 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 correspondingnesting 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.