EAGER: Integrating Fracture Nucleation and Propagation into Optimization: Towards Materials with Optimal Fracture Properties

迄今为止，绝大多数拓扑优化的进展都局限于底层材料的弹性变形而不会破裂的问题。然而，已经确定的是，即使是简单的微观结构变化也会对材料的有效断裂性能产生深远的影响。因此，微观结构拓扑的优化有可能彻底改变具有前所未有断裂性能的材料的发现。这项早期概念探索性研究基金（EAGER）支持基础研究，以提出理论和计算框架，识别微结构优化断裂成核和扩展行为的线弹性脆性材料。本研究将探索在线弹性脆性材料中创建微结构的拓扑空间，从而改善断裂行为和增强能量耗散。所产生的见解将有助于科学的进步，为系统地发现新的几何形状和增强韧性的机制，制定理论铺平道路。这项研究将推动其他领域的进步，如民用和航空航天结构以及医疗植入物，最终为国家健康和繁荣的广泛应用做出贡献。该项目还将丰富多学科课程，并为研究生提供理论优化、高级建模和实验技术方面的教育和培训机会。这项研究的目的是创造一种革命性的、数学上严谨的方法，以优化微结构，最大限度地提高断裂性能。将推导并实现一种拓扑优化公式，该公式将断裂成核和扩展集成到材料的力学响应中，该材料既可以发生弹性变形，也可以发生断裂。一个特定的材料子集，具有两相的线弹性脆性材料，将在这个项目中解决。该公式将用于确定具有改善断裂性能的线弹性脆性多孔复合材料的最佳微观结构拓扑。这些优化的拓扑结构将被制作并通过实验系统地验证。这项工作将为提高压裂性能的最佳几何形状和主导机制提供新的见解。该项目还将为操纵裂缝的新能力奠定基础，并为广泛的应用开辟可能性。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。

To date, the vast majority of topology optimization advancements have restricted attention to problems where the underlying materials are assumed to deform elastically without ever fracturing. However, it is well established that even a simple variation in microstructure can have a profound influence on the effective fracture properties of materials. Hence, optimization of microstructural topology has the potential to revolutionize the discovery of materials with unprecedented fracture properties. This EArly-concept Grant for Exploratory Research (EAGER) award supports fundamental research to put forth a theoretical and computational framework that identifies linear elastic brittle materials whose microstructures have optimized fracture nucleation and propagation behaviors. This research will explore the topological space to create microstructures in linear elastic brittle materials that lead to improved fracture behaviors and enhanced energy dissipation. The insights generated will contribute to the progress of science by paving the way required to formulate a theory that systematically discovers novel geometries and mechanisms toward enhanced toughness. This research will allow advancement in other fields, such as civil and aerospace structures and medical implants, ultimately contributing towards a broad range of applications for national health and prosperity. The project will also enrich the multidisciplinary course curriculum and provide opportunities to educate and train graduate students in theoretical optimization, advanced modeling, and experimental techniques. The objective of the research is to create a transformative and mathematically rigorous approach to optimize microstructures with maximized fracture properties. A formulation of topology optimization that integrates fracture nucleation and propagation into the mechanical response of materials, which can both deform elastically and fracture, will be derived and implemented numerically. A specific subset of materials, linear elastic brittle materials with two phases, will be addressed in this project. The derived formulation will be employed to identify optimal microstructural topologies in linear elastic brittle porous composite materials with improved fracture properties. These optimized topologies will be fabricated and systematically validated by experiments. This work will generate new insights about the optimal geometries and dominating mechanisms that enhance fracture performance. The project will also build the foundation of a new ability to manipulate cracks and opens up possibilities for a wide range of applications.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.