Transient Impact Analysis of Elastic-plastic Beam with Strain-Rate Sensitivity

Abstract The impact response of an elastic-plastic beam is highly complicated in nonlinear transient dynamics especially when the material's plasticity is strain rate dependent. To reduce the efforts required for the computational analysis, an analytical-numerical model (hybrid model) is proposed for the analysis of the transient response of the beam to sphere impact. The model couples two sub-models, a combined discretization model and a refined contact model. Both the sub-models incorporate the material strain rate dependence. The combined discretization model discretizes the beam in length direction by a dynamic substructure technique and in thickness direction by a finite difference technique to capture the beam wave propagations along the length and the stress variations along the thickness. The refined contact model extends the BD model[ 1 ] to sphere-beam impacts by introducing a new representative contact strain rate and a new unloading law to avoided the force discontinuity at the inception of unloading. The hybrid model is validated by the laboratory test performed for low-velocity impacts and by the three-dimensional finite element (FE) analysis implemented for moderate-velocity and moderate high-velocity impacts. The validations show that the hybrid model is accurate, highly efficient and suitable for the parametric study, especially for the study of impact-induced wave effects. By using the hybrid model, tests and FE analyses, the influences of the material strain rate sensitivity are investigated by comparing to the results of elastic plastic impact simulations ignoring the effect of strain rate. It is found that the influence of the strain rate dependence on the contact force-indentation relation is significant even in the low-velocity impacts. The influences of the strain rate dependence on the contact duration and maximum contact force are small, even for the impact velocity up to 30 m/s. The influences of the strain rate dependence on other impact responses are small in the low-velocity impacts, and increase with increasing of the impact velocity. A parametric analysis is conducted to investigate the effects of the impact conditions on the contact duration and coefficient restitution. Their map structures are complicated, depending upon the mass ratio and the impact position. A jumping/falling phenomenon for the variations of the contact duration and coefficient of restitution is found, which are caused by the multiple impacts.