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Cellular materials widely exist in natural biologic systems such as honeycombs, bones, and woods. With advances in additive manufacturing, research on cellular metamaterials is emerging due to their unique mechanical performance. However, the design of on-demand cellular metamaterials usually requires solving a challenging inverse design problem for exploring complex structure–property relations of microstructured representative volume elements (RVEs) in the design domain. Here, we propose an experience-free and systematic methodology for exploring a parametrized system for microstructures of cellular mechanical metamaterials using a multiobjective genetic algorithm (GA). Globally, by considering the importance of the initial population selection for a population-based heuristic optimization method, we study the impact of the populations initialized by the different sampling methods on the optimal solutions. Locally, we develop our method by using a micro-GA with a new searching strategy, which requires the standard genetic algorithm to be conditionally run for a sufficient number of times with a small population size during the global searching process. We have applied our method to explore optimal solutions for applications mapped on two different parameter spaces of the cellular mechanical metamaterials with periodic and nonperiodic RVEs effectively and accurately. 

Microstructure-sensitive material design has become popular among materials engineering researchers in the last decade because it allows the control of material performance through the design of microstructures. In this study, the microstructure is defined by an orientation distribution function (ODF). A physics-informed machine learning approach is integrated into microstructure design to improve the accuracy, computational efficiency, and explainability of microstructure-sensitive design. When data generation is costly and numerical models need to follow certain physical laws, machine learning models that are domain-aware perform more efficiently than conventional machine learning models. Therefore, a new paradigm called Physics-Informed Neural Network (PINN) is introduced in the literature. This study applies the PINN to microstructure-sensitive modeling and inverse design to explore the material behavior under deformation processing. In particular, we demonstrate the application of PINN to small-data problems driven by a crystal plasticity model that needs to satisfy the physics-based design constraints of the microstructural orientation space. For the first problem, we predict the microstructural texture evolution of Copper during a tensile deformation process as a function of initial texturing and strain rate. The second problem aims to calibrate the crystal plasticity parameters of Ti-7Al alloy by solving an inverse design problem to match PINN-predicted final texture prediction and the experimental data. 

This work discusses new methodologies for identifying the grain boundaries in color images of metallic microstructures and the quantification of their grain topology. Grain boundaries have a large impact on the macro-scale material properties. Particularly, this work employs the experimental microstructure data of Titanium-Aluminum alloys, which can be used for various aerospace components owing to their outstanding mechanical performance in elevated temperatures. The grain topology of these metallic microstructures is quantified using the concept of shape moment invariants. In order to capture the grains using the shape moment invariants, it is necessary to identify the grain boundaries and separate them from their respective grains. We present two methodologies to detect the grain boundaries. The first method is the tolerance-based neighbor analysis. The second method focuses on creating three-dimensional space of pixel intensity values based on the three color channels and measuring the Euclidean distance to separate different grains. Additionally, since the grain boundaries may not possess the same material properties as the grain itself, this work investigates the effect of including the grain boundaries when determining the homogenized material properties of the given microstructure. To generate adequate statistical information, microstructures are reconstructed from the experimental data using the Markov Random Field (MRF) method. Upon separating the grains, we use the shape moment invariants to quantify the shapes of different grains. Using the shape moment invariants and the experimental material property values, three neural network functions are developed to investigate the effects of grain boundaries on material property predictions.