Confidence-Based Uncertainty Quantification and Model Validation for Simulations of High-Speed Impact Problems

Abstract

Validation exercises for computational models of materials under impact must contend with sparse experimental data and with uncertainties due to microstructural stochasticity and variabilities in thermo-mechanical properties of the material. This paper develops statistical methods for determining confidence levels for validation of computational models subject to aleatoric and epistemic uncertainties and sparse stochastic experimental results. To demonstrate the method, the classical problem of Taylor impact of a copper bar is simulated. The simulations are performed to cover the range of variabilities in the nominal yield strength A, the hardening constant B, and the hardening exponent n in a Johnson-Cook model for copper. To quantify uncertainties in the simulations, we construct probability density functions of ratios of two quantities of interest the final bar diameter to the original diameter and the final length to the original length. The uncertainties in the experimental data are quantified by constructing target output distributions for these QoIs from the sparse experimental results reported in literature. The simulation and the experimental output distributions are compared to compute the median of the model prediction error and the model confidences at user-specified error level. These metrics show that the simulation models predict the final length of the bar more accurately than the diameter. The calculated confidence levels are consistent with expectations from the physics of the problem and the assumptions in the computational model. Thus, this paper develops and demonstrates physically meaningful metrics for validating simulation models under input uncertainties and limited stochastic experimental data.