We demonstrate an approach to the calibration of material models in a simulation code that combines the principles of physics and probabilistic Bayesian analysis. The focus is on the parameters and their uncertainties in the simulation-code submodels, as well as the numerical errors introduced in solving the dynamical equations. Bayesian analysis provides the underpinning for quantifying the uncertainties in models inferred from experimental results, which possess their own degree of uncertainty. The aim is to construct an uncertainty model that is based on inferences drawn from comparing the code's predictions to relevant experimental results. In the context of this framework, it is possible to design new experiments that can best provide data for reducing prediction uncertainty.
In the Taylor impact test, a metal cylinder is propelled into a rigid wall and the profile of the deformed cylinder is measured. We show how such profile data can be used to update the parameters in a plastic strain-strain model used in a simulation code to predict the Taylor cylinder profile. Our example is based on data taken on samples of HSLA 100, which is the steel to be used in containment vessels. As the Bayesian updating process includes a full uncertainty analysis, it allows one to estimate the uncertainties in predictions of future dynamic experiments involving the same material. The technique demonstrated here can be generalized to analyze a hierarchy of experiments. In such an analysis, progressively more complex experiments may contribute to improved knowledge of the physics submodels incorporated in the simulation code.
Keywords: physics simulation codes, Bayesian calibration, Bayesian analysis, uncertainty estimation, Taylor impact test, plastic flow, Zerilli-Armstrong model, hierarchy of experiments, validation
Presentation same as given at Radiographic Simulation and Analysis Workshop (pdf, 548 KB)
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Send e-mail to author at kmh@hansonhub.com