Optimal Design and Mean Stress Estimation of Modular Metamaterials Inspired by Burr Puzzles

Modular impact-resistant metamaterials inspired by burr puzzles were recently proposed to combine flexibility, efficiency and adaptivity, which were also beneficial for sustainability in engineering protection. However, the optimal design remains to be explored and the mean stress cannot be effectively estimated. To break these limits, a stiffness-enhanced strategy is implemented to enhance the crashworthiness, and the relation between the mechanical behavior of metamaterials and locking points is revealed. The average thickness of all modules in the metamaterial is denoted by t ave , and the thickness ratio of axially loaded to laterally loaded modules is denoted by y . From the experimental and simulation results, the mean stress of the metamaterials significantly increases with t ave and y , while the deformation mode is gradually transformed into an inefficient global buckling mode and impairs the crashworthiness when ψ ≥ 4 . ψ = 3 can be taken as the optimal design of metamaterials, which can increase the specific energy absorption SEA , energy absorption efficiency h and mean stress s m , respectively, by 62.4%, 44.2% and 57.6% compared to the regular design ( ψ = 1 ). On this basis, we develop a universe method to estimate the mean stress of the metamaterials with a relative error less than 9.6%, and a guideline for their design and application in engineering fields is summarized. This research opens a new avenue for broadening the design and applications of modular metamaterials in engineering applications.