Analytical and numerical models to predict the shape of incident pulse in split-Hopkinson bar experiments

In typical split-Hopkinson pressure bar experiments (SHPB), the striker bar impacts the incident bar via discs made from soft materials such as copper. These discs, also called pulse shapers, are used (i) to eliminate the high frequency components of the incident pulse, (ii) to obtain a finite rise time of the incident pulse and (iii) to obtain a constant strain rate. Although these pulse shapers have been used for over decades in SHPB experiments, no analytical solutions or simple models are available that can predict the incident pulse as a function of the striker velocity, pulse shaper geometry and material parameters. Assuming that the pulse shaper is a rigid-linearly hardening material, we derive the analytical solution for the incident pulse when the rise time of the incident pulse is less than twice the time taken for a longitudinal wave to travel along the length of the striker. For larger rise times, we additionally assume that the striker is rigid to obtain a simple numerical model to predict the incident pulse in the presence of a pulse shaper. Both these models are validated against numerical simulations and experiments to demonstrate their accuracy.