ABSTRACT
The axial crushing of thin-walled tubes has for a long time been a significant research topic. Alexander [Alexander 60] was among the first to
study the axial crushing of relatively thick circular tubes collapsing in the concertina mode. He established a basic folding mechanism in which the folds went completely inward or outward, and derived a theoretical formula to calculate the mean crushing force, which agreed well with experimental data. Wierzbicki and colleagues [Wierzbicki et al. 92] observed from experiments that the folds did not go completely inward or outward. He introduced the eccentricity factor m to take the observation into consideration, but could determine the value of m only empirically. The theoretical value of m was later derived and experimentally validated [Singace et al. 95]. Theoretical study of the axial crushing of relatively thin circular tubes collapsing in the diamond mode was not as successful. Pugsley [Pugsley 60, Pugsley 79] found that usually only three or four lobes were finally formed around any circumference of the tube after the tube buckled in the wellknown “Yoshimura pattern.” He proposed two basic folding mechanisms and derived corresponding theoretical predictions of the mean crushing force. Singace [Singace 99] proposed the definition of m for the diamond mode and also obtained a theoretical expression of the mean crushing force. Notably, the number of lobes circumferentially could not be determined by either theory.
