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Hierarchical structure has gained great popularity in recent years, due to its significant promotion on structural strength and stiffness. In this study, the concept of high-order vertex-based hierarchy structure (VHS) was incorporated based on the new-rising multi-cell square tubes by replacing every vertex with scaled itself, layer by layer. The theoretical solution of VHS structure subjected to static compression has been conducted, based on the classical Super Folding Element. Mean crushing force ( MCF, P ) and energy absorption E have been calculated theoretically. The innovative finding lies that the relationship of the mean load between case lever  i  to lever  i +1 has been determined. The relationship of the mean load between case lever  i  to lever i+1 mainly related to the cell number and length scale. All these achievements shield a light in aid to design novel thin-walled and light-weight energy absorption device.

Theoretical analyses of mechanical performance of higher-order vertex-based hierarchical square cell structure subjected to compression