This paper proposes a methodology for architecting microstructures with extremal stiffness, yield, and buckling strength using topology optimization. The optimized microstructures reveal an interesting transition from simple lattice like structures for yield-dominated situations to hierarchical lattice structures for buckling-dominated situations. The transition from simple to hierarchical is governed by the relative yield strength of the constituent base material as well as the volume fraction. The overall performances of the optimized microstructures indicate that maximum strength is determined by the buckling strength at low volume fractions and yield strength at higher volume fractions, regardless of the base material's relative yield strength. The non-normalized properties of the optimized microstructures show that higher base material Young's modulus leads to both higher Young's modulus and strength of the architected microstructures. Furthermore, the polynomial order of the maximum strength lines with respect to mass density obtained from the optimized microstructures reduces as base material relative yield strength decreases, reducing from 2.3 for buckling dominated Thermoplastic Polyurethane to 1 for yield dominated steel microstructures.

翻译：本文提出了一种基于拓扑优化的方法，用于设计具有极端刚度、屈服强度和屈曲强度的微结构。优化后的微结构展示出一个有趣的转变：从屈服主导情况下的简单类晶格结构，过渡到屈曲主导情况下的分层晶格结构。这一简单到分层的转变受基体材料的相对屈服强度以及体积分数共同调控。优化微结构的整体性能表明，最大强度由低体积分数下的屈曲强度和高体积分数下的屈服强度决定，而与基体材料的相对屈服强度无关。优化微结构的非归一化特性显示，基体材料杨氏模量越高，架构化微结构的杨氏模量和强度也越高。此外，从优化微结构获得的最大强度与质量密度的多项式阶次随基体材料相对屈服强度的降低而减小，从屈曲主导的热塑性聚氨酯的2.3阶降至屈服主导的钢微结构的1阶。