The calibration of any sophisticated model, and in particular a constitutive relation, is a complex problem that has a direct impact in the cost of generating experimental data and the accuracy of its prediction capacity. In this work, we address this common situation using a two-stage procedure. In order to evaluate the sensitivity of the model to its parameters, the first step in our approach consists of formulating a meta-model and employing it to identify the most relevant parameters. In the second step, a Bayesian calibration is performed on the most influential parameters of the model in order to obtain an optimal mean value and its associated uncertainty. We claim that this strategy is very efficient for a wide range of applications and can guide the design of experiments, thus reducing test campaigns and computational costs. Moreover, the use of Gaussian processes together with Bayesian calibration effectively combines the information coming from experiments and numerical simulations. The framework described is applied to the calibration of three widely employed material constitutive relations for metals under high strain rates and temperatures, namely, the Johnson–Cook, Zerilli–Armstrong, and Arrhenius 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.