Smooth-shell metamaterials of cubic symmetry: Anisotropic elasticity, yield strength and specific energy absorption

Abstract Shell-lattices consist of a single, periodic, non-intersecting shell of uniform wall thickness that separates two intertwined void phases. To obtain a comprehensive overview on their small and large strain response, three families of shell-lattices are derived from Simple-Cubic (SC), Face-Centered Cubic (FCC) and Body-Centered Cubic (BCC) tube-lattices using a parameterized surface-smoothening functional. Each family's central element is an approximation of a Triply Periodic Minimal Surface (TPMS). Detailed finite element simulations are carried out for more than 800 shell-lattices covering relative densities ranging from 1% to 80%. It is found that the TMPS-like structures exhibit highly anisotropic elastic and plastic properties that depend on the type of cubic symmetry. However, when averaging the mechanical properties over all possible directions of loading, the performance of the SC, FCC and BCC shell-lattices turns out to be similar, with all structures providing substantially higher stiffness and strength than optimal truss-lattices of equal mass. They also exhibit high specific energy absorption for large strain compression. It is found that the macroscopic deformation mode changes from foam-like crushing (for relative densities below 10%) to bulk-like positive strain hardening (for relative densities above 20%). The spectrum of anisotropic structures obtained through varying the bias parameter of the surface-defining functional also includes elastically-isotropic shell-lattices. The Young's modulus of the isotropic shell-lattices of FCC and BCC symmetry is slightly higher than the average modulus of their TPMS-like counterparts, while the opposite holds true for SC structures. Compression experiments are performed on additively-manufactured stainless steel 316L specimens to validate the conclusions drawn from numerical simulations.