In-plane dynamics of circular cell hexagonally packaged honeycombs with linear elastic and plastic base material with linear strain hardening in two principal axes

The in-plane deformation modes, stress–strain curves and energy absorption characteristics of circular cell hexagonally packaged honeycombs with the linear elastic and plastic base material with linear strain hardening are numerically investigated under crushing velocities 1–250 m/s in two principal axes. Three deformation modes are observed, quasi-static homogeneous mode, transition mode, and dynamic mode. The empirical formulas of critical velocities of deformation mode transition are given. With increasing crushing velocities, the fluctuation of stress becomes more violent in the plateau stress phase of stress–strain curve, which can be seen at low crushing velocities in x2 direction, but doesn't appear in x1 direction at low and even moderate crushing velocities. The densification strain is linear with the t/R ratio for a given crushing velocity, and becomes larger with the increasing velocities approximately in linear relationship under a deformation mode for a given t/R ratio. The law of mean plateau stress is consistent with the one-dimensional shock wave model and the static plateau stress is proportional to the square of relative density. Based on finite element results, three types of empirical expressions of mean plateau stress are given. Crushing force efficiency is approximately independent of t/R ratio and sensitive to the crushing velocity. The crushing force efficiency is nearly constant under quasi-static homogeneous mode, becomes smaller with increasing velocities under transition mode, and then drops and fluctuates up and down around a level under dynamic mode, which corresponds to the shapes of stress–strain curves.