de Pablos Juan Luis, Menga Edoardo, Romero Ignacio
IMDEA Materials Institute, Eric Kandel, 2, 28906 Getafe, Spain.
Mechanical Eng. Department, Universidad Politécnica de Madrid, José Gutiérrez Abascal, 2, 28006 Madrid, Spain.
Materials (Basel). 2020 Oct 2;13(19):4402. doi: 10.3390/ma13194402.
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.
对任何复杂模型，尤其是本构关系进行校准，都是一个复杂的问题，它直接影响生成实验数据的成本及其预测能力的准确性。在这项工作中，我们采用两阶段程序来处理这种常见情况。为了评估模型对其参数的敏感性，我们方法的第一步包括构建一个元模型并使用它来识别最相关的参数。第二步，对模型中最具影响力的参数进行贝叶斯校准，以获得最优均值及其相关不确定性。我们声称，这种策略对于广泛的应用非常有效，并且可以指导实验设计，从而减少测试活动和计算成本。此外，将高斯过程与贝叶斯校准结合使用有效地融合了来自实验和数值模拟的信息。所描述的框架应用于校准三种在高应变率和温度下广泛使用的金属材料本构关系，即约翰逊 - 库克模型、泽里利 - 阿姆斯特朗模型和阿累尼乌斯模型。
