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 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.