Model Calibration and Uncertainty Analyses in Multiscale Modeling using Machine Learning Approaches

Engineering structures and components used in a nuclear power plant are always subjected to numerous vibration and cyclic loadings. These cyclic loading causes variations in the material properties of the structure and leads to crack formation and structural damage. The macroscale response of a material depends on the crystal orientation in the underlying microstructure. Estimating the variation in material properties due to the randomness of the microstructure is essential in any materials design process. Uncertainties in the grain texture and material properties subject to these design processes significantly affect the final macroscale properties. It can even lead to material failure if the deviations in the critical properties exceed a specific limit. This leads one to use statistical methods in calculating the effect of uncertainties on the final macroscale response. In this work, we investigate how machine learning approaches can help in the statistical analysis of the Crystal Plasticity Finite Element (CPFE) model and model parameter estimation. First, a strategy coupling kriging to CPFE demonstrates the interest of such a strategy for multiscale modeling with full 3D Finite Element Model ABAQUS. Second, it is demonstrated that optimization can be carried out for FEM analysis thanks to surrogate modeling by coupling the Efficient Global Optimization (EGO) a lgorithm to the CPFE model. Proof-of-concept is shown on selected test cases.