Computational and Machine Learning-Reinforced Modeling and Design of Materials under Uncertainty

The component-level performance of materials is fundamentally determined by the underlying microstructural features. Therefore, designing high-performance materials using multi-scale models plays a significant role to improve the predictability, reliability, proper functioning, and longevity of components for a wide range of applications in the fields of aerospace, electronics, energy, and structural engineering. This thesis aims to develop new methodologies to design microstructures under inherent material uncertainty by incorporating machine learning techniques. To achieve this objective, the study addresses gradient-based and machine learning-driven design optimization methods to enhance homogenized linear and non-linear properties of polycrystalline microstructures. However, variations arising from the thermo-mechanical processing of materials affect microstructural features and properties by propagating over multiple length scales. To quantify this inherent microstructural uncertainty, this study introduces a linear programming-based analytical method. When this analytical uncertainty quantification formulation is not applicable (e.g., uncertainty propagation on non-linear properties), a machine learning-based inverse design approach is presented to quantify the microstructural uncertainty. Example design problems are discussed for different polycrystalline systems (e.g., Titanium, Aluminium, and Galfenol). Though conventional machine learning performs well when used for designing microstructures or modeling material properties, its predictions may still fail to satisfy design constraints associated with the physics of the system. Therefore, the physics-informed neural network (PINN) is developed to incorporate problem physics in the machine learning formulation. In this study, a PINN model is built and integrated into materials design to study the deformation processes of Copper and a Titanium-Aluminum alloy.