Energy absorption and recoverability of Moore space-filling thin-walled structures

This paper proposes novel thin-walled structures inspired by Moore space-filling curves. Nine designs, featuring three fractal hierarchies (1st, 2nd, and 3rd orders) with three different relative densities (20%, 30%, and 40%), were used as cross-sectional configurations of the thin-walled structures. Specimens were manufactured using a material extrusion additive manufacturing technique, fused filament fabrication, with a carbon fiber-reinforced composite. Quasi-static compression tests from in-plane direction were conducted to investigate the influences of fractal hierarchy and relative density on the energy absorption capacity. Finite element models were developed to compare with the experiments and to further explore the 4th order structures. A certain level of compliance and snap-in instability were observed in all the structures. These properties show great potential for such thin-walled structures to absorb more energy by enduring large strain. Among them, the 2nd order structures exhibited the best energy absorption capacity. Furthermore, loading and unloading compression tests were performed on the 2nd and 3rd order structures (relative density of 20%) to evaluate their resilience toward displacement and damages. The residual strain and dissipated energy ratio demonstrated that the 2nd order structure outperformed the 3rd order structure owing to its less compliant feature. The integration of Moore curves with thin-walled structures contributes to great compliance and snap-in instability, offering a new approach to designing lightweight energy absorption structures.