Our lab investigates the mechanics of materials through the development of fundamental theoretical frameworks integrated with state-of-the-art computational methods, including physics-informed machine learning and isogeometric analysis. We explore these domains across multiple scales from architected metamaterials to thin materials subjected to non-mechanical stimuli.

By coupling theory, computation, and AI-driven modeling, we aim to understand and control the interplay between mechanics, physics, and geometry in advanced materials. Our goal is the design and discovery of novel materials with unprecedented dynamic functionalities, paving the way for next-generation technologies in areas such as wave-based sensing, protective devices, and thermal transport management.

The feasible applicability of this novel cross-coupling requires accurately calculating it on given metamaterial designs. Homogenization is a powerful tool for deriving effective constitutive relations, including cross-coupling, that govern the macroscopic behavior of heterogeneous media like metamaterials. Green’s function-based theories have been used as they can precisely consider the whole material domain in the homogenization process, not just a representative volume element. However, their challenge is the difficulty in determining Green’s function of the heterogeneous medium in homogenization, particularly for real-world, i.e., finite-size and non-periodic cases. Therefore, we formulated a new homogenization theory via the Hashin-Shtrikman principle, relying on the infinite-body Green’s function of a homogeneous comparison medium, i.e., free from the difficulty of determining Green’s function.

Physics-informed neural networks learn directly from physics equations, thus mitigating data dependency. However, their intrinsic continuity requirement restricts application in metamaterial design problems due to the non-differentiable material domain. We addressed this challenge by replacing the strong-form physics-equation residual with a weak form and introducing an interactive process that integrates the weak-form physics-informed loss with design objectives, eliminating the need for pre-trained surrogate models or analytical sensitivity derivations.

As an interdisciplinary work, we employed this stimuli-responsive shell theory for bio-mechanics. As the normal operation of the eye depends on morphogenetic processes for its eventual shape, developmental flaws can lead to ocular defects. However, the mechanisms of ocular morphogenesis are not well understood. Using our shell theory, we showed that the constrained growth in the inner optic vesicle by the extracellular matrix induces effective torques and that elastic instabilities caused by these torques govern the optic cup morphogenesis from optic vesicles. The optic cup morphogenesis is driven by two elastic instabilities analogous to the snap-through in spherical shells. The second instability is sensitive to the initial geometry of the optic vesicle. If the optic vesicle is too slender, it buckles and breaks axisymmetry, thus preventing normal development of the optic cup, which has been observed for glaucoma in newborn infants.