Elastic effects on deformation of impulsively loaded elastoplastic beams

Abstract

Velocity trajectories for simple lumped mass models of an impulsively loaded elastoplastic beam and a cantilever are used to compare rigid-plastic and elastoplastic solutions. Accuracy of a rigid-plastic approximation depends on both the energy ratio R and similarity of the initial momentum distribution to the shape of a stable dynamic plastic mode. For the discrete model of a beam, the region of initial velocities where early elastic effects result in errors of 20% for the rigid-plastic approximation extends to R = 77 for an initial momentum distribution that is close to a plastic mode; this occurs because the beam has multiple stable plastic modes. These modes are “attractors” for the elastoplastic motion and elastic effects can switch convergence from one to another.