Robust implementation of Physical Regime Sensitivity and demonstration on Richtmyer-Meshkov instability experiments

We present a robust analytic implementation of Physical Regime Sensitivity (PRS), which quantifies sensitivity of an experiment or application to regimes of a material model’s independent variables rather than to model parameters. The new PRS implementation is tested on impact-driven Richtmyer-Meshkov Instability (RMI) strength experiments on tantalum. Sequential PRS hydrocode simulations perturbed strength in local regimes of independent variables like strain rate to quantify the resulting effects on experimentally measured maximum spike velocities in the instabilities. The numeric behavior of the sensitivity calculation is investigated regarding mesh convergence and the parameters controlling the strength perturbation. The sensitivities generally converge with mesh size at least as quickly as the underlying RMI simulations. A wide range of perturbation amplitudes produced similar normalized sensitivities, indicating the perturbation is not changing physical behavior in the simulation. Adjusting the range (width) over which the strength is perturbed allows for resolving fine sensitivity features covering narrow regimes of independent variables or more broad regimes for general interpretation. For interpreting RMI, PRS shows that the maximum spike velocity of the instability is most sensitive to a narrow regime of strain rates near 107/s, which occurs inside the spike as strength effects arrest the instability. The PRS analyses revealed that a modification to the experimental metric used to assess strength would better isolate the strength effects in the regimes of most interest. Using the new metric to generate pressure PRS curves revealed that sensitivities to strength at near-zero pressure were 3.5 times greater than at the high-pressure shock state, supporting the practice of using RMI to isolate strain rate effects when combined with high-pressure experiments. It is also shown that a simple, calibrated constant strength model can reproduce PRS sensitivities of a complex, multivariate Preston-Tonks-Wallace strength model quite well, which supports the robustness of PRS and its utility for experimental design and interpretation prior to the availability of a sophisticated material strength model.