Prediction with quantified uncertainty of temperature and rate dependent material behavior

The increasing reliance on computer simulations in decision-making motivates the need to formulate a commonly accepted definition for "predictive maturity." The concept of predictive maturity involves quantitative metrics that should be capable of tracking progress (or lack thereof) as additional knowledge becomes available and is integrated into the simulations. Two examples are the addition of new experimental datasets for model calibration and implementation of better physics models in the codes. This publication discusses the attributes that a metric of predictive maturity should exhibit by emphasizing that they must go beyond the goodness-of-fit of the model to the available test data. Predictive maturity must also consider the degree to which physical experiments cover the domain of applicability. We propose a Predictive Maturity Index (PMI). Physical datasets are used to illustrate how the PMI quantifies the maturity of the non-linear, Preston-Tonks-Wallace model of plastic deformation applied to Beryllium, a light-weight, high-strength metal. The question "does collecting additional data improve predictive power?" is answered by computing the PMI iteratively as additional experimental datasets become available. The results obtained reflect that coverage of the validation domain is as important to predictive maturity as goodness-of-fit. The example treated also indicates that the stabilization of predictive maturity can be observed, provided that enough physical experiments are available.