Axial crushing of novel hierarchical multi-cell square tubes

Inspired by the concept of hierarchy, two types of hierarchical multi-cell square tubes (HMSA and HMSB) are proposed. The crashworthiness of HMSA and HMSB tubes with various wall thicknesses and hierarchical orders is numerically studied. It has been found that the peak crushing force of HMSA and HMSB tubes is smaller than that of single square tubes, which is preferred to minimize the possible injury or damage caused by the initial peak force. Moreover, the mean crushing force, energy absorption, crushing force efficiency and specific energy absorption of HMSA and HMSB tubes increase with the hierarchical order and wall thickness. Compared with single square tubes, the specific energy absorption of the 3rd order HMSA and HMSB tubes increases by more than 1.5 and 1.7 times, respectively. Moreover, the 3rd order HMSB tubes show slightly greater specific energy absorption than that of the 3rd order HMSA tubes. In addition, theoretical models are developed which can well predict the mean crushing force of two new types of tubes.