Collaborative Research: Cellular Metamaterials that Localize Stress - Towards a Topological Protection against Fracture

设计能够承受恶劣载荷条件的工程结构的主要挑战之一是开发能够智能地控制应力以避免或延缓断裂的开始和扩展的材料。实现这一目标的大多数传统方法包括改善材料的微观结构成分以增加韧性。该奖项回顾了具有蜂窝结构的晶格材料背景下的断裂，其中不仅可以通过调整材料组成来寻求保护，还可以通过改变蜂窝结构的形态来寻求保护。重点将放在一类特殊的晶格材料上，在这种材料中，可能会将外部载荷引起的应力集中在已知的、所需的位置，从而提供防止或延迟损伤过程开始的能力。从这项研究中获得的知识将有助于在从基础设施工程到航空航天工业的各种工程应用中提高结构系统的寿命和可靠性。该项目还将支持为本科生设计创新的应力分析演示工具包，以及为高中生和公众演示结构分析的基本原理。该项目的目标是研究细胞超材料中的拓扑结构在管理内应力和防止断裂方面的潜力。该项目以麦克斯韦晶格为中心，这种晶格可以包含拓扑偏振态，包括沿着内部磁区壁或界面的自应力的拓扑保护态。当这些晶格被加载和变形时，应力往往主要集中在这些界面上，即使在区域中存在裂纹的情况下也是如此。因此，可以避免或显著延缓通常在裂纹尖端观察到的有害应力集中和随后的破裂。该项目将评估这种依赖于晶格整体结构的属性是如何在从具有完美铰链的理想晶格到具有结构韧带的现实晶格的过程中得到保留的。这一目标将通过基于数字图像相关性的实验表征来实现，同时伴随着将拓扑断裂保护扩展到连续介质极限的理论发展。还将致力于确定材料本身受到故障影响的拓扑保护的深度，将使用声发射监测对其进行试验性评估。这一裁决反映了NSF的法定使命，并已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。

One of the main challenges in designing engineering structures that can withstand severe loading conditions is the development of materials that can intelligently manage stresses to avoid or retard the onset and propagation of fracture. Most traditional approaches towards this goal involve improvements in the microstructural composition of the material to increase toughness. This award revisits fracture in the context of lattice materials featuring a cellular architecture, where protection can be sought not only by adjusting the material composition but also through changes in the morphology of the cellular structure. The focus will be on a special class of lattice materials in which it may be possible to concentrate the stresses due to external loading at known, desirable locations, providing the ability to prevent or delay the onset of damage processes. The knowledge gained from this research will contribute towards the longevity and reliability of structural systems across engineering applications, from infrastructural engineering to the aerospace industry. The project will also support design of innovative demonstration kits on stress analysis for undergraduate students and demonstrations of basic principles of structural analysis for high-school students and the public.The objective of this project is to investigate the potential of topology in cellular metamaterials in managing internal stresses and protecting against fracturing. The project is centered on Maxwell lattices that can contain topologically polarized states, including topologically protected states of self-stress along internal domain walls or interfaces. When these lattices are loaded and deformed, the stress tends to focus predominantly on these interfaces, even in the presence of cracks in the domain. As a result, the detrimental stress concentration and subsequent fracturing, which is typically observed at crack tips can be avoided or significantly retarded. The project will assess how this property, which depends on the bulk architecture of the lattice, is preserved in going from ideal lattices endowed with perfect hinges to realistic lattices featuring structural ligaments. This objective will be achieved through an experimental characterization based on digital image correlation accompanied by theoretical development that will extend the topological fracture protection to the continuum limit. Efforts will be also devoted to determining how deep into the topological protection the material itself is affected by failure, an assessment of which will be sought experimentally using acoustic emission monitoring.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.