Data-driven analysis of spinodoid topologies: anisotropy, inverse design, and elasticity tensor distribution

Spinodoid topologies are bicontinuous porous microstructures inspired by the natural spinodal decomposition process. They offer a vast design space and are capable of representing anisotropic topologies, which makes them suitable for use in biomedical applications. This work focuses on some fundamental aspects in spinodoid microstructures. As the first, the extent of anisotropy is computed by a universal index and its correlation with spinodoid design parameters, including relative density and the three cone angles, is investigated. In order to do this, the k-means clustering method is utilized to group the topologies based on their level of anisotropy. Within each cluster, the relationship between the statistical features of the design parameters and the extent of anisotropy is analyzed in detail. As one of the findings, it is revealed that topologies created by larger cone angles will lie in low anisotropy category. Although the sensitivity analysis indicates that all the cone angles are equally important in determining the elasticity tensor elements, our findings demonstrate that there are some discrepancies in the probability density function of cone angles in topologies with high anisotropy. In addition, the results show that lower relative densities tend to lead to higher anisotropy in the structures regardless of cone angle values. In the second stage of this work, a data-driven framework for inverse design is proposed. This approach involves generating high-quality samples and utilizing an efficient data-driven framework capable of handling unequal queries. It can identify multiple spinodoid candidates for a desired elasticity tensor, rather than just one. This approach has great advantages, especially in manufacturing, where different topologies may have varying manufacturing costs. This provides designers with more choices to select from. In the final stage, we estimated the statistical distribution of the elasticity tensor components for the generated spinodoid topologies. By measuring the Mahalanobis distance between a query and the estimated distribution, one can determine whether the query belongs to the property space of spinodoid topologies or not. This approach allows for assessing the similarity or dissimilarity of a query to the distribution of the generated spinodoid topologies.