Non-Iterative Characteristics Analysis for High-Pressure Ramp Loading

TL;DR

This paper introduces a non-iterative, recursive method for analyzing high-pressure ramp loading experiments, significantly reducing computation time and eliminating the need for initial guesses, while maintaining accuracy.

Contribution

The authors develop a direct recursive technique to deduce stress-density relations from ramp loading data, avoiding iterative optimization and its associated issues.

Findings

Recursive method matches iterative analysis results

Calculation is orders of magnitude faster

Robust against typical experimental data conditions

Abstract

In the canonical ramp compression experiment, a smoothly-increasing load is applied to the surface of the sample, and the particle velocity history is measured at two or more different distances into the sample, at interfaces where the surface of the sample can be probed. The velocity histories are used to deduce a stress-density relation, usually using iterative Lagrangian analysis to account for the perturbing effect of the impedance mismatch at the interface. In that technique, a stress- density relation is assumed in order to correct for the perturbation, and is adjusted until it becomes consistent with the deduced stress-density relation. This process is subject to the usual difficulties of nonlinear optimization, such as the existence of local minima (sensitivity to the initial guess), possible failure to converge, and relatively large computational effort. We show that, by considering the interaction of successive characteristics reaching the interfaces, the stress-density relation can be deduced directly by recursion rather than iteration. This calculation is orders of magnitude faster than iterative analysis, and does not require an initial guess. Direct recursion may be less suitable for very noisy data, but it was robust when applied to trial data. The stress-density relation deduced was identical to the result from iterative Lagrangian analysis.