CAREER: Topological Assessment in Granular Materials

摘要：倒一桶沙子展示了沙子的液体般的潜力，然而海滩游客相信同样的材料可以支撑他们的体重。为什么去海滩的人不沉入沙滩深处？虽然我们有经验了解砂、粉末和其他颗粒系统在特定条件下会像流体一样流动或像刚性固体一样支撑载荷，但没有人能够可靠或精确地预测何时、如何或为什么这些系统会变得刚性或流动。这种不确定性是一大类刚性非晶材料的特征。例子包括沙子、玻璃和塑料。因此，通过研究颗粒材料中刚性的起源，首席研究员希望深入了解各种各样的系统。这个项目的重点是应力通过颗粒状材料内部结构的传递与材料的整体力学响应有关。研究小组使用成像技术来测量整个材料中粒子之间的力。主要目标是识别结构，不是粒子的空间排列，而是通过系统传递的力的模式。为了理解这些结构，该团队利用新方法来描述复杂的网络和几何形状。该项目的第二个目标是操纵这些力传递结构来设计具有特定性能的材料。该项目还将有助于实现几个教育目标。具体来说，首席研究员将为参与研究的本科生和博士后青年科学家提供培训和指导，并将实验技术和项目范围内正在进行的研究纳入核心物理课程。此外，首席研究员将举办一个研讨会，为研究导师提供培训，培养一支多样化和高效的青年科学家队伍。技术摘要：本项目旨在了解非晶颗粒材料的多尺度刚性起源。该研究团队将利用光弹性成像技术（一种最先进的空间和力分辨测量技术），结合高分辨率、复合成像技术，来表征双轴压缩或纯剪切下大颗粒填料的结构和内应力状态。该项目的主要目标是确定材料的整体机械响应与材料内应力状态的力分辨测量之间的相关性。先前的观察表明，所有尺度的结构都有助于颗粒材料的机械响应。因此，平均场描述和颗粒尺度指标都不适合预测材料刚度。相比之下，首席研究员正在开发一种基于代数拓扑和网络科学的新型分析方法，该方法可以识别代表所有长度尺度结构的拓扑特征。为了确定这些拓扑特征与大块材料响应之间的相关性，研究团队使用了支持向量机方法。这种机器学习技术在预测胶体玻璃和湿颗粒柱的局部塑性方面是有效的。该项目的第二个目标是制定材料设计策略，以使人们想起拓扑绝缘电子材料的设计，从而可重复地制造具有规定拓扑特性的封装。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。

Non-technical Abstract:Pouring a bucket of sand demonstrates the liquid-like potential of sand, yet beach-goers trust the same material to support their weight. Why do the beach-goers not sink into the sandy depths? Though we have the experience to understand that sands, powders, and other granular systems will flow like a fluid or support load like a rigid solid under certain conditions, nobody can reliably or precisely predict when, how, or why these systems will become rigid or flowing. This uncertainty is characteristic of a broad class of rigid, amorphous materials. Examples include sand as well as glass and plastics. Thus, by studying the origins of rigidity in granular materials, the principal investigator hopes to gain insight into a wide variety of systems. The focus of this project is the transmission of stress through the internal structure of a granular material is related to the bulk mechanical response of the material. The research team uses an imaging technique to measure the forces between particles throughout the material. The primary goal is to identify structures, not in the particles' spatial arrangement, but the patterns of force transmitted through the system. To understand these structures, the team leverages new methods to describe complicated networks and geometries. A secondary goal of the project is to manipulate these force-transmission structures to design materials with specific properties. The project will contribute to several educational goals, as well. Specifically, the principal investigator will provide training and mentorship to undergraduate and postdoctoral junior scientists involved in the research and integrate experimental techniques and ongoing research within the project's scope into the core physics curriculum. Additionally, the principal investigator will develop a workshop that prepares research mentors to train a diverse and effective population of junior scientists.Technical Abstract:The objective of this project is to understand the multi-scale origins of rigidity in amorphous granular materials. The research team will leverage photoelasticimetric imaging, a state of the art spatially- and force-resolved measurement technique, combined with high-resolution, composite imaging to characterize the structure and internal stress state of large granular packings in either biaxial compression or pure shear. The project's primary goal is to identify correlations between the bulk mechanical response of the material and the force-resolved measurements of the material's internal stress state. Prior observations suggest that structures at all scales contribute to the mechanical response of granular materials. Thus, both mean-field descriptions and particle-scale metrics are ill-suited to predicting material rigidity. In contrast, the principal investigator is developing a novel analytic approach based on algebraic topology and the science of networks, which identifies topological features that represent structures at all length-scales. To identify correlations between these topological features and the bulk material response, the research team uses the Support Vector Machines method. This machine learning technique has been effective in predicting local plasticity in colloidal glasses and wet, granular pillars. A secondary goal of the project is to develop strategies for materials design to reproducibly manufacture packings with prescribed topological properties in an approach reminiscent of the design of topologically insulating electronic materials.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.