A new Lagrangian analysis method used to study dynamic performance of concrete with multiple velocity gauges in attenuating waves

Lagrangian analysis method derives the specific internal energy, strain, and stress and particle velocity histories from either stress or particle velocity records from a series of gauges embedded in material. However, if only particle velocity is obtained, the existing Lagragian analysis methods need to know stress at initial Lagrangian position. In this paper, a new Lagrangian analysis method for multiple particle velocity gauges (termed path-line time stepping) is presented. The method can derives the stress from particle velocity records without any initial conditions. Besides, the method is applied to measure waves in concrete. And the verification of the analysis for attenuating waves is studied by numerical simulation that reproduced the stress-strain histories.