Mechanics of Lattice Functionally Graded Materials

This dissertation investigates the design, modeling, and optimization of architected lattice structures and sustainable composite materials. The work is motivated by the need for lightweight, high-performance materials in modern engineering applications, including aerospace, automotive, civil, and biomedical fields, while also addressing the growing importance of sustainable and recycled material integration. The research focuses on bridging the gap between classical analytical models, numerical simulations, and data-driven optimization. Classical scaling laws, such as the Gibson--Ashby model, provide a foundation for predicting the mechanical properties of cellular solids, but they are limited in addressing functionally graded structures, structural irregularities, and dynamic behaviors. To overcome these limitations, this dissertation develops extended analytical frameworks, validated through finite element simulations and, where applicable, experimental data. Key contributions include: - Development of analytical models for three-dimensional lattices and functionally graded honeycombs, incorporating correction factors to account for grading and randomness. - Modeling of transient wave propagation in graded lattice structures, including reduced-order, physics-informed approaches that capture dynamic responses efficiently. - Implementation of a physics-informed, machine learning–driven optimization framework for sustainable composite design, enabling the integration of recycled materials while balancing mechanical performance, economic, and regulatory constraints. - Methodological exploration of micromechanical methods (MOC, GMC, HFGMC) to establish computational expertise and support data-driven modeling approaches. By combining analytical, numerical, and data-driven methods, the dissertation provides a comprehensive framework for the design of advanced architected materials and sustainable composites. The work demonstrates both fundamental insights and practical tools for engineering applications, addressing critical gaps in modeling, dynamic analysis, and optimization. This research lays the foundation for future studies in architected materials, multi-objective design, and sustainable manufacturing, providing guidelines for both theoretical understanding and practical implementation.