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.

翻译：本研究受皮质骨骨单位、黄金螺旋及分形等生物结构的启发，提出了一种面向增材制造的创新型嵌套各向同性晶格。通过集成“嵌套阶次(NOs)”与“嵌套取向(NORs)”等架构元素，结合重复自相似X形支柱及三重四重对称轴，该晶格可实现各向异性的可调谐控制，从而生成多样化的晶格结构。研究实现了九种单嵌套晶格、二十种多嵌套晶格及其252种参数变体，并计算了相对密度 \( \bar{\rho} \) 与比表面积 \( \bar{S} \)。基于有限元数值均匀化方法，估算了所有晶格设计的弹性刚度张量，以评估各向异性度量——齐纳比 \( Z \) 与弹性模量 \( \bar{E} \)。考虑高阶NOs及其对应NORs的单嵌套晶格呈现出从剪切主导型向拉/压主导型(TCD)各向异性行为的转变，且支柱尺寸变化对 \( \bar{\rho} \)、\( \bar{S} \) 与 \( \bar{E} \) 具有显著影响。相比之下，多嵌套晶格表现出各向同性与新各向同性特征，其中支柱尺寸失配对 \( Z \) 的影响更为突出。增加NOs与NORs使多数多嵌套晶格趋向各向同性或TCD行为，而支柱尺寸失配则诱导出大量各向同性晶格。这些仿生嵌套晶格与增材制造技术的进步相结合，在多样化的应用场景中具有广阔前景。