Architecting materials for extremal stiffness, yield and buckling strength

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 proposed microstructures indicate that optimal strength is determined by the buckling strength at low volume fractions and yield strength at high volume fractions, regardless of the base material's relative yield strength.