Lagrangian Analysis Method with Least Square Cubic B-spline

The Lagrangian analysis method is re-analyzed. It is shown that when a series of stress profiles (or strain profiles, or particle velocity profiles) are measured to determine the strain-stress relation. In this paper, the stress histories at different Lagrange positions are measured by one dimensional SHPB experiments. The variation histories of various physical quantities are fitted to least square cubic B-spline function with a sufficient accuracy definite condition. The path lines of these quantities are constructed in terms of a least square quadratic polynomial. A program for inert flow of Lagrangian analysis (IFLA) is worked out. Taking the data of experiments as the input for the IFLA, the flow field information is solved. The error analysis shows that such a method has a definite reliability and stability.