Research Initiation Award: Theoretical and Computational Methods for Robust Retrieval of Effective Electromagnetic Properties of Random Composite Materials

研究启动奖为历史悠久的黑人学院和大学的初级和职业生涯中期教师提供支持，这些教师正在建立新的研究计划或重新定向和重建现有的研究计划。预计该奖项有助于进一步提高教师的研究能力和有效性，改善所在机构的研究和教学，并让本科生参与研究经验。霍华德大学的奖项支持旨在优化具有电磁(EM)能力的随机复合材料工程的研究。这些能力包括电磁干扰屏蔽和电磁可观测性增强，和/或电磁感应能力。这开启了商业和国防技术的广泛应用，如电气/电子设备、通信系统、石油和天然气工业以及军事和执法。复合材料的宏观性能取决于各组分的几何形状、分布、体积分数和性质。虽然周期性分布复合材料有效电磁性能的数值提取技术已经建立得比较成熟且易于实现，但对于随机分布复合材料的数值提取技术还没有得到充分的探索。这项研究的目的是发展一种严谨的理论和精确高效的数值方法，以提供随机复合材料在静态和动态情况下的有效电磁性质的尺度相关界。所提出的EM均匀化理论将被结合到构造全频率稳定的公式中，该公式将在使用有限元和区域分解方法的蒙特卡罗模拟中求解。还将开发一种随机模拟方法来表征材料的随机性和几何不确定性，以提高电磁特性检索的效率。所提出的理论和方法将导致用于表征和分析随机复合材料的最先进的均化工具的发展。这反过来将使基于理论指导和计算支持的随机复合材料中的新设计方法成为可能。该项目包括广泛的教育和外展活动，包括让历史上在这一研究领域中代表性不足的学生参与，并制作视频剪辑和演示以向公众传播结果。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Research Initiation Awards provide support for junior and mid-career faculty at Historically Black Colleges and Universities who are building new research programs or redirecting and rebuilding existing research programs. It is expected that the award helps to further the faculty member's research capability and effectiveness, improves research and teaching at the home institution, and involves undergraduate students in research experiences. Howard University’s award supports research that seeks to optimize the engineering of random composite materials that have electromagnetic (EM) capabilities. Such capabilities include EM interference shielding and EM observability enhancing, and/or EM sensing capabilities. This opens a wide range of applications in commercial and defense technologies, such as electrical/electronic devices, communication systems, oil and gas industries, and military and law enforcement. The macroscopic properties of composite materials depend on the geometry, distribution, volume fraction, and property of each constituent. While the numerical extraction techniques for the effective EM properties of periodically distributed composite materials are relatively well established and straightforward to implement, those for the randomly distributed composite materials have not been fully explored. The objective of this proposed research is to develop a rigorous theory and accurate and efficient numerical methods to provide the scale-dependent bounds of the effective EM properties of random composites in both static and dynamic cases. The proposed EM homogenization theory will be incorporated in the construction of an all-frequency stable formulation, which will be solved in Monte-Carlo simulations using finite element and domain decomposition methods. A stochastic simulation method will also be developed to characterize the material randomness and geometrical uncertainty and achieve an improved efficiency in the EM property retrieval. The proposed theories and methods will lead to the development of state-of-the-art homogenization tools for the characterization and analysis of random composite materials. This in turn would enable new design methodologies in random composites based on the theoretical guidance and computational support. The project includes an extensive education and outreach activities, including the involvement of students historically underrepresented in this field of research, and the development of video clips and demonstrations to disseminate the results to the public.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.