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

到目前为止，绝大多数拓扑优化的进步限制了人们对假设底层材料弹性变形而不会断裂的问题的关注。然而，它是公认的，即使是一个简单的微观结构的变化可以有一个深刻的影响，有效的断裂性能的材料。因此，优化微结构拓扑结构有可能彻底改变材料的发现与前所未有的断裂性能。EARLY概念探索性研究（EAGER）奖支持基础研究，提出一个理论和计算框架，确定其微观结构具有优化的断裂成核和传播行为的线弹性脆性材料。本研究将探索拓扑空间，以在线弹性脆性材料中创建微结构，从而改善断裂行为并增强能量耗散。所产生的见解将有助于科学的进步，为制定一个系统地发现新的几何形状和机制以增强韧性的理论铺平道路。这项研究将促进其他领域的发展，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，并提供机会，教育和培训研究生在理论优化，先进的建模和实验技术。该研究的目的是创建一种变革性和数学上严格的方法，以优化具有最大断裂性能的微观结构。一个配方的拓扑优化，集成断裂成核和传播到材料的机械响应，这两者都可以弹性变形和断裂，将推导和数值实现。一个特定的材料子集，线弹性脆性材料的两个阶段，将在这个项目中解决。推导出的公式将被用来确定最佳的微观结构拓扑结构的线弹性脆性多孔复合材料具有改善的断裂性能。这些优化的拓扑结构将被制造和系统的实验验证。这项工作将产生新的见解的最佳几何形状和主导机制，提高压裂性能。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NSF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.