A circular tube undergoes bucking behavior when it is subjected to axial loading. A accurate understanding of the buckling behavior is important to design the energy-absorbing components. The dynamic elastic–plastic buckling of structures shows a complex phenomenon due to various factors such as geometrical parameters, the inertia effect, large deformation, material inelastic behavior. An upper bound analysis can be an attractive approach to predict the dynamic buckling load and energy absorption efficiently. In general, the upper bound analysis obtains the load or energy absorption by means of assumption of the kinematically admissible velocity fields of materials or structures as a method to analyze the material or structure which undergoes plastic deformation. In order to obtain an accurate solution using the upper bound analysis, kinematically admissible velocity fields should be defined considering not only geometrical parameters but also dynamic effect.
Relatively a few studies reported regarding the kinematically admissible velocity fields in the buckling behavior by Alexander, Abramowicz et al. and Grzebieta. In this study, experiments and finite element analyses are carried out for circular tubes with various dimensions and loading conditions to verify these velocity fields. The results from experiment and finite element analysis show that the wrinkling width and height can be represented as the function of the initial diameter and thickness of a circular tube. As the strain rate increases, the wrinkling width and the height decreases maintaining a constant ratio of these two parameters. Detail deformed shapes determinate that the arc part made by bending and the straight part between arc parts are clearly divided and the length of the straight part depends on the strain rate. The reported velocity fields, however, do not describe this buckling mode accurately because of too much simplification of the deformation mode and no consideration of variation of deformation mode according to the strain rate effect of materials. In this study, the kinematically admissible velocity field is newly proposed in order to consider various dimensions and the strain rate effect of material.
The kinematically admissible velocity field suggested can describe the wrinkling width, the wrinkling height and change of deformation mode according to the strain rate effect of material. Upper bound analysis with the suggested velocity field accurately estimates the mean load and energy absorption obtained from results of experiment and finite element analysis for buckling behavior.