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 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.