An Experimental, Computational, and Statistical Strategy for the Bayesian Calibration of Complex Material Models

The study of solids and structures under extreme conditions often relies on simulations that employ complex material models. These, in turn, are formulated using analytical expressions that depend on parameters whose values need to be adjusted for optimally reproducing available experimental results and, especially, out-of-sample predictiveness. In this article we review the process required to calibrate all the parameters of the Johnson-Cook and Zerilli-Armstrong models for a nickel-based superalloy. To this end, we present in an unified fashion the thermomechanical problem, its numerical implementation, a complete experimental campaign that suffices to obtain the material constants, and a Bayesian calibration procedure that can be employed to obtain the optimal values for the model parameters as well as their uncertainty. The advocated methodology is ideally designed to calibrate strain rate-, temperature-, and age-dependent elastoplastic models. The procedure is, however, general enough to be employed as guideline for other complex calibrations.