Theoretical-Computational Framework for Modeling of Composite Materials with Thin Coatings and Two-Dimensional Reinforcements

薄涂层和二维增强板是现代复合材料的重要组成部分。在航空航天、汽车、生物医学和许多其他对美国经济特别重要的行业中，它们被用于防止损坏、增加耐久性和提高部件和结构的性能。例如，在陶瓷或金属中使用石墨烯纳米片或聚合物纳米涂层可以产生具有优异机械强度的轻质复合材料，这对于制造便携式电子设备、医疗植入物和太阳能电池是必不可少的。尽管在过去的十年中取得了显著的进展，然而，薄层和超薄层材料的准确预测建模仍然是一项具有挑战性的任务。该奖项支持的研究将提供一个有效的理论和计算框架，这将有可能促进基于模拟的复合材料系统的设计和优化，并显着提高其分析的准确性。此外，该项目将支持努力吸引和激励学生从事基于仿真的工程研究，并在复合力学、表面科学和计算方法等跨学科领域培养研究生和本科生。它还将利用机构项目支持各级学生的教育和外展活动，特别关注妇女和低收入学生。表面化学的最新进展和相关技术的发展使复合材料的设计和创造具有前所未有的机械性能。特别令人感兴趣的是具有薄涂层或二维增强的复合材料。本研究的目的是开发新的方法，通过零厚度界面和特殊设计的跳跃条件来模拟涂层和/或增强材料。研究方法将包括建立新的高阶界面模型，发展新的界面形态分类，并建立它们与低维板壳理论的联系。界面模型将被整合到以高正则基函数为特征的新的有限元和边界元公式中。最后，这些实现将在合作者对现实问题的实验数据的帮助下进行验证。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Thin coatings and two-dimensional reinforcing sheets are key elements of modern composite materials. They are used for prevention of damage, increase in durability, and enhancement in performance of components and structures in aerospace, automotive, biomedical, and many other industries that are of particular importance to the US economy. For example, the use of graphene nanoplatelets or polymer nano coatings in ceramics or metals produces lightweight composites with superior mechanical strength that are indispensable for fabrication of portable electronic devices, medical implants, and solar cells. Despite remarkable progress made in the last decade, however, accurate predictive modeling of materials with thin and ultrathin layers remains a challenging task. This award supports research that will deliver an efficient theoretical and computational framework that will potentially facilitate simulation-based design and optimization of composite material systems and significantly enhance the accuracy of their analysis. In addition, the project will support efforts to attract and inspire students to pursue research in simulation-based engineering and train graduate and undergraduate students in the cross-disciplinary areas of composite mechanics, surface science, and computational methods. It will also leverage institutional programs to support education and outreach to students at all levels, with special focus on women and low-income students. Recent advances in surface chemistry and related technological developments enable the design and creation of composite materials with unprecedented mechanical properties. Of particular interest are composites with thin coatings or two-dimensional reinforcements. The objective of this research is to develop novel methodologies to model the coatings and/or reinforcements through interfaces of zero thickness and specially designed jump conditions. The research approach will consist of formulating novel higher-order interface models, developing new classification of interface morphologies, and establishing their connections with lower-dimensional plate and shell theories. The interface models will be integrated into new finite element and boundary element formulations characterized by high-regularity basis functions. Lastly, these implementations will be validated with the help of experimental data available from collaborators on real-world problems.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.