Analytical modelling of dynamic plastic buckling of an axially loaded strain-rate sensitive bar

Abstract

Dynamic plastic buckling of a bar is analytically studied based on some simplifying assumptions. The bar is simply supported and subjected to an axial step-force at its ends. The material is assumed to have linearly strain hardening and the strain-rate effect is considered by employing Malvern's over-stress model. Shanley's assumption of no unloading when plastic buckling occurs is adopted. A linear differential equation of motion of the bar is thus established. A stability condition is then derived by means of the method of amplifying function. Expressions of buckling half-wavelength and critical buckling load are obtained. The results are compared with those of a strain-rate insensitive bar. It is found that the strain-rate effect has a significant influence on the dynamic plastic buckling of bars.