An improvement of the Lagrangian analysis method based on particle velocity profiles

In general, techniques used in studies on dynamic behaviour of materials could be classified into two categories, namely the split Hopkinson pressure bar technique (SHPB) and the wave propagation technique (WPT). Lagrangian analysis method is one of the most famous methods in WPT. The traditional Lagrangian analysis based on the particle velocity wave-profiles measurements should consider a boundary condition, because it involves integral operations. However, the boundary stress data in some cases cannot be detected or determined by the experimental measures. To tackle this situation, this paper presents a modified Lagrangian analysis method which does not involve the boundary stress computation. Starting from the path-lines method and utilizing the zero-initial condition, the material constitutive stress-strain curves under high strain-rates is deduced from only observing the particle velocity curve measurements. The dynamic stress/strain wave-profiles of the PMMA material, as a paradigm, are numerically studied using the proposed method, which are well in agreement with the theoretical result using the method of characteristics, which confirms the reliability and validity of the presented method.