Effect of geometric deviations on the strength of additively manufactured ultralight periodic shell-based lattices

Lightweight shell-based lattice structures with various multifunctional applications can be fabricated with limited manufacturing constraints, thanks to the advancements of additive manufacturing technologies. However, there is always a geometric deviation between the 3D digital model and the additively manufactured lattice structure. In some cases, the geometric deviations may be as small as the machine accuracy, but they would cause a significant decrease in the strength of the lattice. In other cases, the lattice may not be so sensitive to geometric deviations. The sensitivity of lattice structures to the geometric deviations depends on their constituent material, loading condition, relative density, and the geometry of the unit-cell. To understand this, buckling failure should be considered beside yielding. This paper presents a local failure analysis of the ultralight shell-based lattices and explores the effects of the aforementioned factors on their strength and failure mechanism under compression. The main finding of this research is that unlike the high-relative density lattices, which are not sensitive to geometric deviations, in the design of ultralight shell-based lattices (with relative densities lower than 26 %), beside the loading conditions, the constituent material and relative density should be considered, as well. For example, for a 10 % relative density lattice designed for a triaxial compressive macroscopic state of stress, if the base material is stainless steel, the minimal surface is the optimal unit-cells, while if it is made of pyrolytic carbon, a constant mean curvature surface with a certain value of mean curvature other than zero is optimal. However, for shell-based lattices with relative densities higher than 26 %, the geometric deviation does not influence the lattice strength and thus the optimal geometry can be designed without regard to the base material and relative density.