Elastically isotropic open-cell uniform thickness shell lattices with optimized elastic moduli via shape optimization

Shell lattices are composed of smooth, non-intersecting and periodic thin shells. Their open-cell topology facilitates the manufacturing and multifunctional applications. This work proposes a shape optimization framework to obtain uniform thickness shell lattices with superior elastic moduli and isotropic elasticity. A B-spline parameterized Monge patch model is used to represent the mid-surface within the 1/48 unit cell, which maintains the cubic symmetry and simplifies the sensitivity evaluation. Two groups of elastically isotropic shell lattices are obtained, including Primitive (P) and I-graph-wrapped package (IWP). The highest achievable bulk, Young's, shear moduli of P/IWP family lattices are nearly 70%/80%, 40%/60%, 40%/60% of the Hashin-Shtrikman upper bounds at 10% relative density. Besides, the Young's/bulk modulus maximization is further introduced into the optimization to seek potential stiffness improvement, yielding similar optimized lattices with close stiffness for arbitrary initial designs. The highest achievable moduli are slightly improved by 3~5% than those without moduli maximization. In general, P-family lattices possess comparable Young's, shear and higher bulk moduli to the stiffest truss lattices, while IWP-family lattices possess superior stiffness. This work proposes a systematic design approach to obtain elastically isotropic uniform thickness shell lattices, which can be applied to the other lattice families with Monge patch representations.