Collaborative Research: Framework: Data: HDR: Nanocomposites to Metamaterials: A Knowledge Graph Framework

Metastructure Characterization and Reconstruction: We plan to develop a suite of metastructure characterization and reconstruction (generation) methods, that will enable a quantitative approach to analyze metamaterial geometry. Analogous to Microstructure Characterization, metastructure characterization is essential for identifying a small set of uncorrelated features (parameters) that embody significant structural details; thus, providing a reduced-dimension representation that can be leveraged for machine learning of geometry -property relations and parametric based design exploration. For given metastructure characterization, reconstruction or generation tools are needed to create 2D or 3D metamaterial geometries for property/performance simulations and smooth transition to digital fabrication. Our proposed approach is to represent unit cells using shape descriptors (ShapeDNA) that encode geometric features in a sequence of numbers. We will investigate the applicability of several shape descriptors reported in literature but, focus on spectral shape descriptors. To reconstruct a geometry adhering to a prescribed set of spectral descriptors, we propose the use of a variational optimization approach based on the level set method. Issues related to solving this optimization problem – discontinuity and non-convexity of objective function – will be addressed in our research. All algorithms developed in this task will be available on MetaMine through a user-friendly interface as adapted for NanoMine. II. Machine Learning for Geometry-Property Relations: We seek to find mappings from geometry – characterized by its shape descriptors to the material properties of “building blocks” – (e.g., stiffness, density, shear modulus, vibration absorption and acoustic mitigation). The mappings must be flexible to accommodate non-linear material behavior. Machine learning-based tools are widely used for establishing direct geometry-property mappings either using physical data when physics-based simulations are lacking, or using simulation data when simulations are too expensive for material design optimization. In the proposed research, new machine learning-based models will be created by mining the MetaMine database. To model high-dimensional and highly correlated material properties, the multi-response Gaussian Random Process modeling approach developed in our earlier work will be employed to create stochastic constitutive relations with uncertainty quantification associated with the lack of data. III. Database Construction and and Structure Synthesis - Evolving and Optimizing Metamaterial Structures: Metamaterial database collected based on existing designs and experiments can be further expanded by evolving the unit-cell designs and optimization of metamaterial structures for multi-functions through simulation-based design. We will create tools for this purpose at two scale levels: (1) the unit cell (i.e., tile), and (2) the global structure. Methods on the unit cell level will be used to populate the MetaMine database of building blocks for achieving different functions. The shape descriptors approach (described under I) provides a generative model that allows the creation of metamaterial unit cell geometries either belonging to the existing families of metamaterials or significantly different. Existing topology optimization methods for metamaterial design, such as SIMP and level-set, will also be used for exploration and optimization of new unit cell geometries for targeted properties. In addition, we will pair the geometry-property