Crashworthiness analysis of bio-inspired fractal tree-like multi-cell circular tubes under axial crushing

This study proposes novel bio-inspired fractal multi-cell circular (BFMC) tubes for energy absorption. The inner structures of the proposed BFMC tubes were constructed based on the fractal tree-like forms found in many biological structures such as giant water lily and dragon blood tree. The crashworthiness performances of the proposed structures with different fractal orders and mass were numerically investigated. The numerical results indicated that the specific energy absorption (SEA) increased with the fractal order and the SEA of the 2nd order BFMC tube was 35.43% higher than that of the conventional multi-cell circular tube. Furthermore, the complex proportional assessment (COPRAS) method was adopted to optimize the performance of the BFMC. The results demonstrated that the proposed structure with four number of tree-like branches and 2nd-order fractal provided the best performance. Finally, a theoretical derivation of the mean crushing force (MCF) was developed for the proposed tubes based on the simplified super folding element theory. The theoretical results of MCF agreed well with the numerical results. The findings of this study provide an effective guide for using the biomimetic approach with the fractal tree-like forms for the design of a multi-cell energy absorber with high energy absorption efficiency.