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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 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.