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1. Symmetry-Induced Mechanical Metamaterials Design Framework and Dataset Generation

   https://doi.org/10.1115/DETC2024-141866  

   Abu-Mualla, Mohammad; Huang, Jida (August 2024, American Society of Mechanical Engineers)

   Abstract The surge in machine learning research and recent advancements in 3D printing technologies have significantly enriched materials science and engineering, particularly in the domain of mechanical metamaterials, which commonly consist of periodic truss materials. Despite the extensive exploration of their tailorable properties, truss-based metamaterial design has predominantly adhered to cubic and orthotropic unit-cells, a limitation arising from the conventional design method, where the type of symmetry related to the designed truss-based material is determined after the design process is done. To overcome this issue, this work introduces a groundbreaking 3D truss material designing framework that departs from this constraint by employing six distinctive material symmetries (cubic, hexagonal, tetragonal, orthotropic, trigonal, and monoclinic) within the design process. This innovative approach represents a versatile paradigm shift compared to previous design approaches. Furthermore, we are able to integrate anisotropy into the design framework, thus enhancing the property space exploration capability of the proposed design framework. Probing materials property space using our design framework demonstrates its capacity to achieve a diverse range of mechanical properties, surpassing even the most extensive datasets available in the literature. The proposed method facilitates the generation of a comprehensive truss dataset, which can be represented in a trainable continuous format suitable for machine learning and data-driven approaches. This advancement paves the way for the development of robust inverse design tools for truss materials, marking a significant contribution to the mechanical metamaterial community. 

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2. Design of Low Density Architectured Metamaterials With High Compressive and Torsional Stiffness

   https://doi.org/10.1115/IMECE2023-110261  

   Liu, Xiangbei; Jeon, Joseph J; Tiplea, Anisia G; Li, Yan; Song, Bo (October 2023, American Society of Mechanical Engineers)

   Abstract Metamaterials are architected cellular networks with solid struts, plates, or shells that constitute the edges and faces of building cells. Certain metamaterial designs can balance light weight and high stiffness requirements, which are otherwise mutually exclusive in their bulk form. Existing studies on these materials typically focus on their mechanical response under uniaxial compression, but it is unclear whether a strut-based metastructure design with high compressive stiffness can exhibit high torsional stiffness simultaneously. Designing lightweight metastructures with both high compressive and torsional stiffnesses could save time and cost in future material development. To explore the effect of unit cell design, unit cell number, and density distribution on both compressive and torsional stiffnesses, a computational design space was presented. Seven different unit cells, including three basic building blocks: body-centered cubic (BCC), face-centered cubic (FCC), and simple cubic (SC) were analyzed. All samples had a relative density of approximately 7%. It was found that a high compressive stiffness required a high concentration of struts along the loading direction, while a high torsional stiffness needed diagonal struts distributed on the outer face. Increasing unit cell numbers from 1 to 64 affected stiffness by changing the stress distribution globally. Non-uniform metastructure designs with strengthened vertical and diagonal struts towards the outer surface exhibited higher stiffness under either compressive or torsional loading. This study provides valuable guidelines for designing and manufacturing metamaterials for complex mechanical environments. 

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3. METASET: An Automated Data Selection Method for Scalable Data-Driven Design of Metamaterials

   https://doi.org/10.1115/DETC2020-22681  

   Chan, Yu-Chin; Ahmed, Faez; Wang, Liwei; Chen, Wei (October 2020, International Design Engineering Technical Conferences and Computers and Information in Engineering Conferences)

   null (Ed.)

   Abstract Data-driven design of mechanical metamaterials is an increasingly popular method to combat costly physical simulations and immense, often intractable, geometrical design spaces. Using a precomputed dataset of unit cells, a multiscale structure can be quickly filled via combinatorial search algorithms, and machine learning models can be trained to accelerate the process. However, the dependence on data induces a unique challenge: An imbalanced dataset containing more of certain shapes or physical properties than others can be detrimental to the efficacy of the approaches and any models built on those sets. In answer, we posit that a smaller yet diverse set of unit cells leads to scalable search and unbiased learning. To select such subsets, we propose METASET, a methodology that 1) uses similarity metrics and positive semi-definite kernels to jointly measure the closeness of unit cells in both shape and property space, and 2) incorporates Determinantal Point Processes for efficient subset selection. Moreover, METASET allows the trade-off between shape and property diversity so that subsets can be tuned for various applications. Through the design of 2D metamaterials with target displacement profiles, we demonstrate that smaller, diverse subsets can indeed improve the search process as well as structural performance. We also apply METASET to eliminate inherent overlaps in a dataset of 3D unit cells created with symmetry rules, distilling it down to the most unique families. Our diverse subsets are provided publicly for use by any designer. 

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4. Prediction of tensile performance for 3D printed photopolymer gyroid lattices using structural porosity, base material properties, and machine learning

   https://doi.org/10.1016/j.matdes.2023.112126  

   Peloquin, Jacob; Kirillova, Alina; Rudin, Cynthia; Brinson, LC; Gall, Ken (June 2023, Materials & Design)

   Advancements in additive manufacturing (AM) technology and three-dimensional (3D) modeling software have enabled the fabrication of parts with combinations of properties that were impossible to achieve with traditional manufacturing techniques. Porous designs such as truss-based and sheet-based lattices have gained much attention in recent years due to their versatility. The multitude of lattice design possibilities, coupled with a growing list of available 3D printing materials, has provided a vast range of 3D printable structures that can be used to achieve desired performance. However, the process of computationally or experimentally evaluating many combinations of base material and lattice design for a given application is impractical. This research proposes a framework for quickly predicting key mechanical properties of 3D printed gyroid lattices using information about the base material and porosity of the structure. Experimental data was gathered to train a simple, interpretable, and accurate kernel ridge regression machine learning model. The performance of the model was then compared to numerical simulation data and demonstrated similar accuracy at a fraction of the computation time. Ultimately, the model development serves as an advancement in ML-driven mechanical property prediction that can be used to guide extension of current and future models. 

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5. Designing Connectivity-Guaranteed Porous Metamaterial Units Using Generative Graph Neural Networks

   https://doi.org/10.1115/1.4066128  

   Wang, Zihan; Bray, Austin; Naghavi_Khanghah, Kiarash; Xu, Hongyi (February 2025, Journal of Mechanical Design)

   Abstract Designing 3D porous metamaterial units while ensuring complete connectivity of both solid and pore phases presents a significant challenge. This complete connectivity is crucial for manufacturability and structure-fluid interaction applications (e.g., fluid-filled lattices). In this study, we propose a generative graph neural network-based framework for designing the porous metamaterial units with the constraint of complete connectivity. First, we propose a graph-based metamaterial unit generation approach to generate porous metamaterial samples with complete connectivity in both solid and pore phases. Second, we establish and evaluate three distinct variational graph autoencoder (VGAE)-based generative models to assess their effectiveness in generating an accurate latent space representation of metamaterial structures. By choosing the model with the highest reconstruction accuracy, the property-driven design search is conducted to obtain novel metamaterial unit designs with the targeted properties. A case study on designing liquid-filled metamaterials for thermal conductivity properties is carried out. The effectiveness of the proposed graph neural network-based design framework is evaluated by comparing the performances of the obtained designs with those of known designs in the metamaterial database. Merits and shortcomings of the proposed framework are also discussed. 

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