Inverse design of tubular energy absorbers formed from the least-symmetric crystallographic DDC surface

Thin-walled origami tubes are distinguished by their superior energy absorption capacity during axial crushing, a property largely attributed to their intricate crease patterns. To develop optimized tubes for enhanced energy absorption performance, we propose a strategy for the inverse design of tubular energy absorbers formed from the least-symmetric crystallographic developable double corrugation (LS-DDC) surface. To this end, first, the phase space of all flat-foldable configurations is systematically mapped based on the kinematics of the LS-DDC surface. To account for the various transformations of unit fragments into origami structures, constrained equations are derived based on the inherent constraints of enclosed structures. The solution space for various configurations is delineated using both traversal techniques and the particle swarm optimization (PSO) method. A comparative performance analysis was conducted among the proposed LS-DDC tube and two conventional tubes: the isosceles trapezoidal origami bellow (ITOB) tube and the arc-Miura-ori (AMO) tube. Both the AMO and LS-DDC tubes demonstrate superior energy-absorbing performance compared to the ITOB tube. The choice between the AMO and LS-DDC tubes can be made based on specific application requirements. While the AMO tube exhibits a slightly higher mean crushing force than the LS-DDC tube, the LS-DDC tube possesses a substantially higher crushing force efficiency than the AMO tube. Finally, we present the inverse design process, which identifies the optimal input parameters for energy absorption. This framework enables the transformation of diverse crease patterns into various origami structures with enhanced energy absorption, broadening their applicability and revitalizing the potential of origami-inspired designs.