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

Yuanyuan Ding,E Buzaud,A Cosculluela,H Couque,E Cadoni

doi:10.1051/epjconf/201818301023

Abstract

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.

Highlights

In the studies of dynamic response of materials under impact and blast loadings, two dynamic effects, i.e. the inertia effect and the strain rate effect, should be taken into consideration
The analysis of stress wave propagation must be based on the premise of the dynamic constitutive of the materials, on the other hand, the propagation of stress waves in the material cannot be neglected when studying the dynamic constitutive of materials at high strain rates
Wang et al [9] proposed a new method combining the Lagrangian analysis with the Hopkinson pressure bar (HPB) technique overcoming the problem that how to simultaneously measure the stress and particle velocity dual information at one Lagrangian position

Summary

Introduction

In the studies of dynamic response of materials under impact and blast loadings, two dynamic effects, i.e. the inertia effect and the strain rate effect, should be taken into consideration. There are two methods to study the dynamic constitutive relationship of material under high strain rate. In the Lagrangian analysis method, the dynamic constitutive relation of materials can be deduced directly from a series of physical quantity measurements regardless of the two coupled dynamic effects, because the interaction of the inertia effect and strain-rate effect is naturally and implicitly considered in the wave propagation technique.

Results

Conclusion