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Abstract Inspired by natural designs, microstructures exhibit remarkable properties, which drive interest in creating metamaterials with extraordinary traits. However, imperfections within microstructures and poor connectivity at the microscale level can significantly impact their performance and reliability. Achieving proper connectivity between microstructural elements and detecting structural imperfections within the microstructures pose challenges in multiscale design optimization. While using a connectivity index (CI) to quantify the topological connectivity between microstructures has been explored previously, prior approaches have limitations in identifying microstructures with complex curved geometries between adjacent units. To alleviate this issue, we present a novel CI in this study. The proposed CI goes beyond conventional methods by focusing on surface interfaces and internal microstructural irregularities. Through numerical investigations, we successfully connected distinct types of microstructures well by integrating the introduced CI with the functional gradation scheme. We also demonstrate that the presented CI can serve as a metric to identify sharp changes or imperfections within microstructures. We evaluate the performance of the introduced index against other connectivity indices using diverse microstructural examples. Experimental findings provide valuable insights into the fundamental aspects of imperfection detection and rectification in microstructures within the multiscale design, paving the way for developing more robust and reliable materials in engineering applications. 

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 the property space of unit cells using our design framework demonstrates its capacity to achieve a diverse range of mechanical properties. The analysis of the generated samples shows that they can surpass the most extensive datasets available in the literature in regions where directional elastic properties are not linked by structural symmetry. The proposed method facilitates the generation of a truss dataset, which can be represented in a trainable 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. 

Abstract Inspired by natural designs, microstructures exhibit remarkable properties, which drive interest in creating metamaterials with extraordinary traits. However, imperfections within microstructures and poor connectivity at the microscale level can significantly impact their performance and reliability. Achieving proper connectivity between microstructural elements and detecting structural imperfections within the microstructures pose challenges in multiscale design optimization. While using a connectivity index (CI) to quantify the topological connectivity between microstructures has been explored previously, prior approaches have limitations in identifying microstructures with complex curved geometries between adjacent units. To alleviate this issue, we present a novel CI in this study. The proposed CI goes beyond conventional methods by focusing on surface interfaces and internal microstructural irregularities. Through numerical investigations, we successfully connected distinct types of microstructures well by integrating the introduced CI with the functional-gradation scheme. We also demonstrate that the presented CI can serve as a metric to identify sharp changes or imperfections within microstructures. We evaluate the performance of the introduced index against other connectivity indices using diverse microstructural examples. Experimental findings provide valuable insights into the fundamental aspects of imperfection detection and rectification in microstructures within the multiscale design, paving the way for developing more robust and reliable materials in engineering applications. 

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.