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1. A Data-Driven Approach for Multi-Lattice Transitions

   Baldwin, Martha; Meisel, Nicholas A.; McComb, Christopher (January 2022, 2022 International Solid Freeform Fabrication Symposium)

   Additive manufacturing is advantageous for producing lightweight components while maintaining function and form. This ability has been bolstered by the introduction of unit lattice cells and the gradation of those cells. In cases where loading varies throughout a part, it may be necessary to use multiple lattice cell types, also known as multi-lattice structures. In such structures, abrupt transitions between geometries may cause stress concentrations, making the boundary a primary failure point; thus, transition regions should be created between each lattice cell type. Although computational approaches have been proposed, smooth transition regions are still difficult to intuit and design, especially between lattices of drastically different geometries. This work demonstrates and assesses a method for using variational autoencoders to automate the creation of transitional lattice cells. In particular, the work focuses on identifying the relationships that exist within the latent space produced by the variational autoencoder. Through computational experimentation, it was found that the smoothness of transition regions was higher when the endpoints were located closer together in the latent space. 

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2. Machine learning assisted design of new lattice core for sandwich structures with superior load carrying capacity

   https://doi.org/10.1038/s41598-021-98015-7  

   Challapalli, Adithya; Li, Guoqiang (December 2021, Scientific Reports)

   Abstract Herein new lattice unit cells with buckling load 261–308% higher than the classical octet unit cell were reported. Lattice structures have been widely used in sandwich structures as lightweight core. While stretching dominated and bending dominated cells such as octahedron, tetrahedron and octet have been designed for lightweight structures, it is plausible that other cells exist which might perform better than the existing counterparts. Machine learning technique was used to discover new optimal unit cells. An 8-node cube containing a maximum of 27 elements, which extended into an eightfold unit cell, was taken as representative volume element (RVE). Numerous possible unit cells within the RVE were generated using permutations and combinations through MATLAB coding. Uniaxial compression tests using ANSYS were performed to form a dataset, which was used to train machine learning algorithms and form predictive model. The model was then used to further optimize the unit cells. A total of 20 optimal symmetric unit cells were predicted which showed 51–57% higher capacity than octet cell. Particularly, if the solid rods were replaced by porous biomimetic rods, an additional 130–160% increase in buckling resistance was achieved. Sandwich structures made of these 3D printed optimal symmetric unit cells showed 13–35% higher flexural strength than octet cell cored counterpart. This study opens up new opportunities to design high-performance sandwich structures. 

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3. Topological and geometric analysis of cell states in single-cell transcriptomic data

   https://doi.org/10.1093/bib/bbae176  

   Huynh, Tram; Cang, Zixuan (April 2024, Briefings in Bioinformatics)

   Abstract Single-cell RNA sequencing (scRNA-seq) enables dissecting cellular heterogeneity in tissues, resulting in numerous biological discoveries. Various computational methods have been devised to delineate cell types by clustering scRNA-seq data, where clusters are often annotated using prior knowledge of marker genes. In addition to identifying pure cell types, several methods have been developed to identify cells undergoing state transitions, which often rely on prior clustering results. The present computational approaches predominantly investigate the local and first-order structures of scRNA-seq data using graph representations, while scRNA-seq data frequently display complex high-dimensional structures. Here, we introduce scGeom, a tool that exploits the multiscale and multidimensional structures in scRNA-seq data by analyzing the geometry and topology through curvature and persistent homology of both cell and gene networks. We demonstrate the utility of these structural features to reflect biological properties and functions in several applications, where we show that curvatures and topological signatures of cell and gene networks can help indicate transition cells and the differentiation potential of cells. We also illustrate that structural characteristics can improve the classification of cell types. 

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4. Elucidating correlated defects in metal organic frameworks using theory-guided inelastic neutron scattering spectroscopy

   https://doi.org/10.1039/D2MH00914E  

   Cavalcante, Lucas S.; Dettmann, Makena A.; Sours, Tyler; Yang, Dong; Daemen, Luke L.; Gates, Bruce C.; Kulkarni, Ambarish R.; Moulé, Adam J. (January 2023, Materials Horizons)

   Metal organic frameworks (MOFs) that incorporate metal oxide cluster nodes, exemplified by UiO-66, have been widely studied, especially in terms of their deviations from the ideal, defect-free crystalline structures. Although defects such as missing linkers, missing nodes, and the presence of adventitious synthesis-derived node ligands (such as acetates and formates) have been proposed, their exact structures remain unknown. Previously, it was demonstrated that defects are correlated and span multiple unit cells. The highly specialized techniques used in these studies are not easily applicable to other MOFs. Thus, there is a need to develop new experimental and computational approaches to understand the structure and properties of defects in a wider variety of MOFs. Here, we show how low-frequency phonon modes measured by inelastic neutron scattering (INS) spectroscopy can be combined with density functional theory (DFT) simulations to provide unprecedented insights into the defect structure of UiO-66. We are able to identify and assign peaks in the fingerprint region (<100 cm −1 ) which correspond to phonon modes only present in certain defective topologies. Specifically, this analysis suggests that our sample of UiO-66 consists of predominantly defect-free fcu regions with smaller domains corresponding to a defective bcu topology with 4 and 2 acetate ligands bound to the Zr 6 O 8 nodes. Importantly, the INS/DFT approach provides detailed structural insights ( e.g. , relative positions and numbers of acetate ligands) that are not accessible with microscopy-based techniques. The quantitative agreement between DFT simulations and the experimental INS spectrum combined with the relative simplicity of sample preparation, suggests that this methodology may become part of the standard and preferred protocol for the characterization of MOFs, and, in particular, for elucidating the structure defects in these materials. 

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5. Data-Driven Multiscale Topology Optimization Using Multi-Response Latent Variable Gaussian Process

   https://doi.org/10.1115/DETC2020-22595  

   Wang, Liwei; Tao, Siyu; Zhu, Ping; Chen, Wei (August 2020, Proceedings of the ASME 2020 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 11A: 46th Design Automation Conference (DAC)

   null (Ed.)

   Abstract The data-driven approach is emerging as a promising method for the topological design of the multiscale structure with greater efficiency. However, existing data-driven methods mostly focus on a single class of unit cells without considering multiple classes to accommodate spatially varying desired properties. The key challenge is the lack of inherent ordering or “distance” measure between different classes of unit cells in meeting a range of properties. To overcome this hurdle, we extend the newly developed latent-variable Gaussian process (LVGP) to creating multi-response LVGP (MRLVGP) for the unit cell libraries of metamaterials, taking both qualitative unit cell concepts and quantitative unit cell design variables as mixed-variable inputs. The MRLVGP embeds the mixed variables into a continuous design space based on their collective effect on the responses, providing substantial insights into the interplay between different geometrical classes and unit cell materials. With this model, we can easily obtain a continuous and differentiable transition between different unit cell concepts that can render gradient information for multiscale topology optimization. While the proposed approach has a broader impact on the concurrent topological and material design of engineered systems, we demonstrate its benefits through multiscale topology optimization with aperiodic unit cells. Design examples reveal that considering multiple unit cell types can lead to improved performance due to the consistent load-transferred paths for micro- and macrostructures. 

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