Curvature-Guided Mechanics and Design of Spinodal and Shell-Based Architected Materials

Abstract: Additively manufactured (AM) architected materials have enabled unprecedented control over mechanical properties of engineered materials. While lattice architectures have played a key role in these advances, they suffer from stress concentrations at sharp joints and bending-dominated behavior at high relative densities, limiting their mechanical efficiency. Additionally, high-resolution AM techniques often result in low-throughput or costly fabrication, restricting manufacturing scalability of these materials. Aperiodic spinodal architected materials offer a promising alternative by leveraging low-curvature architectures that can be fabricated through techniques beyond AM. Enabled by phase separation processes, these architectures exhibit tunable mechanical properties and enhanced defect tolerance by tailoring their curvature distributions. However, the relation between curvature and their anisotropic mechanical behavior remains poorly understood. In this work, we develop a theoretical framework to quantify the role of curvature in governing the anisotropic stiffness and strength of shell-based spinodal architected materials. We introduce geometric metrics that predict the distribution of stretching and bending energies under different loading conditions, bridging the gap between curvature in doubly curved shell-based morphologies and their mechanical anisotropy. We validate our framework through finite element simulations and microscale experiments, demonstrating its utility in designing mechanically robust spinodal architectures. This study provides fundamental insights into curvature-driven mechanics, guiding the optimization of next-generation architected materials for engineering applications.