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

到目前为止，绝大多数的拓扑优化进展都限制了人们对底层材料假设为弹性变形而永远不会破裂的问题的关注。然而，众所周知，即使是微观结构的简单变化也会对材料的有效断裂性能产生深远的影响。因此，微结构拓扑的优化有可能使具有前所未有断裂性能的材料的发现发生革命性的变化。这一早期概念探索性研究(AGER)奖支持基础研究，以提出一个理论和计算框架，识别其微观结构优化了断裂形核和扩展行为的线弹性脆性材料。这项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。产生的见解将为科学进步铺平道路，为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课程，并提供教育和培训研究生理论优化、高级建模和实验技术的机会。这项研究的目标是创造一种变革性的和数学上严格的方法来优化微结构，使其具有最大的断裂性能。将裂纹形核和扩展与材料的力学响应相结合，推导出一种既能弹性变形又能断裂的拓扑优化公式，并进行数值实现。本项目将讨论一种特定的材料子集，即两相线弹性脆性材料。推导出的公式将被用来识别具有改善断裂性能的线弹性脆性多孔复合材料的最佳微结构拓扑。这些优化的拓扑结构将被制作出来，并通过实验系统地验证。这项工作将对提高骨折性能的最佳几何形状和主导机制产生新的见解。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。

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.