Dynamic buckling of an imperfect elastoplastic beam subjected to an impulsive load analyzed using transport equations

In this study, we use transport equations to investigate the dynamic buckling of an imperfect elastoplastic beam, including the effect of axial stress waves, when subjected to an impulsive load. Thus, the governing equations for the elastoplastic behavior of the material are extracted using mass, energy, and momentum transport equations. We assume that the passage of the shock wave through the control volume creates five phases with four boundary discontinuities, i.e., the initial elastic phase, initial plastic phase, fluid phase, secondary plastic phase, and secondary elastic phase. Transport equations are used in integral form as well as non-physical variables to eliminate the discontinuity conditions in the governing equations. These equations are also used for continuum modeling of the elastoplastic behavior of the beam under an impulsive load and a continuous model is presented. Finally, the time histories of stress, strain, and velocity wave propagation along the beam are presented, and the results are validated based on comparisons with known solutions.