Critical Mechanical Structures: Topology and Entropy

非技术总结该奖项支持软材料的理论研究、推广和教育，以及使用新概念设计新的机械超材料。机械稳定性的概念可以追溯到1864年J.C.Maxwell的研究，它支配着软物质物理学中许多有趣的现象，从颗粒物质的堵塞到新材料的自组装和生物组织的非线性弹性。同时，这一概念也指导了能够发挥前所未有功能的新型机械超材料的设计。机械超材料通过其结构而不是成分获得了新的力学性能。PI将研究机械不稳定性与一种能量非常小的软材料变形之间的相互作用，这种软材料被称为软模。可以识别的结构是整体是刚性的，但具有容易变形的软边，其基本特性是剥离软边会产生也具有软边的新材料。利用最近发展起来的与拓扑学相关的概念，可以识别具有不同力学性质的材料相，这一数学分支涉及在变形下保持的对象的性质。PI将研究这些材料相，它们对缺陷和热驱动振动的健壮程度，以及当材料接近机械不稳定时，软变形如何在不同材料相之间转换材料。PI将利用从这些“受拓扑保护的”机械相和它们之间的转换研究中获得的理解来设计新的机械超材料。PI还将研究当这些新设备足够小以至于热波动很重要时会发生什么，以及通过自组装制造这些结构。这个项目不仅旨在从根本上理解机械不稳定附近的结构物理，而且还为具有坚固性能和功能的新一代机械材料的设计提供指导。此外，该项目还包括提高公众对软物质物理学及其对我们日常生活的贡献的认识的外联活动，以及通过在当地学校进行外联和在物理女生中进行小组讨论来扩大妇女和其他少数群体对物理学的参与的教育活动。技术总结该奖项支持软材料的理论研究、推广和教育，以及使用新概念设计新的机械超材料。软物质物理学中许多令人着迷的现象的中心是软模的集合，软模是耗费很少能量的变形模式，表明机械不稳定。例如，堵塞的颗粒物质的屈服和生物组织的非线性弹性。机械超材料是指通过结构而不是成分获得新型力学性能的材料，如负泊松比、负压缩比、负热膨胀、声子带隙等。有趣的是，在许多情况下，实现这些机械超材料的新特性的关键也是软模的集合，这通常被称为机制。本项目的目标是研究接近机械不稳定性并表现出软模的结构的拓扑和熵。研究的两个主要内容是：(1)机械系统的拓扑转变和可变形拓扑机械超材料的设计原理；(2)对软模的熵效应，它将被用来理解机械超材料的自组装以及具有抗波动机构的小尺度机器和机器人的设计原理。这个项目将使用的方法包括解析理论和数值模拟。这个项目的智力优势来自(1)对关键机械结构的异常机械和声学性质的一般分类，(2)对机械系统中新的拓扑转变的表征，它与物质的量子拓扑态的转变有有趣的相似之处，(3)对软模的热涨落效应的表征，这些软模表现出与拓扑学有趣的相互作用，并指导稳健机制的选择，(4)设计和预测新的开放式结构。该奖项还支持推广活动，以提高公众对软物质物理及其对我们日常生活的贡献的认识，以及通过在本地学校进行推广活动和女性物理学生的小组讨论，扩大妇女和其他少数群体对物理的参与。

NONTECHNICAL SUMMARYThis award supports theoretical research, outreach, and education on soft materials and designing new mechanical metamaterials using new concepts. The concept of mechanical stability, which dates back to the research of J. C. Maxwell in 1864, governs many fascinating phenomena in soft matter physics, from jamming of granular matter to self-assembly of novel materials and nonlinear elasticity of biological tissue. At the same time, this concept also guides the design of new mechanical metamaterials that can perform unprecedented functions. Mechanical metamaterials display novel mechanical properties acquired through their structure instead of their composition.The PI will investigate the interplay between mechanical instability and the deformations of a soft material that cost very little energy, called floppy modes. Structures can be identified that are rigid in the bulk but have soft edges that are easily deformed with a fundamental property that peeling away the soft edges leads to a new material that also has soft edges. Using recently developed concepts related to topology, the branch of mathematics concerned with the properties of objects that are preserved under deformations, material phases with different mechanical properties can be identified. The PI will study these material phases, how robust they are against imperfections and thermally driven vibrations, and how soft deformations can transform a material between different material phases when a material is close to a mechanical instability.The PI will use the understanding gained from the study of these "topologically protected" mechanical phases and the transformations among them to design new mechanical metamaterials. The PI will also study what will happen when these novel devices are made small enough that thermal fluctuations are important, as well as producing these structures via self-assembly.This project not only aims at a fundamental understanding of the physics of structures near mechanical instabilities, but also provides guidance to the design of new generation mechanical materials that have robust properties and functions. Moreover, the project includes outreach activities which increase the awareness of the general public on soft matter physics and its contributions to our daily life, as well as educational activities that broaden participation of women and other minorities in physics through outreach in local schools and group discussions among female physics students. TECHNICAL SUMMARYThis award supports theoretical research, outreach, and education on soft materials and designing new mechanical metamaterials using new concepts. Central to many fascinating phenomena in soft matter physics are a collection of floppy modes, which are modes of deformations that cost little energy and signals mechanical instability. Examples include the yielding of jammed granular matter and the nonlinear elasticity of biological tissue. In the meantime, recently there has been an explosion of investigations on mechanical metamaterials, which are materials that gain their novel mechanical properties, such as negative Poisson's ratio, negative compressibility, negative thermal expansion, phononic band-gap, via their structure instead of their composition. Interestingly, in many cases the key to realize the novel properties of these mechanical metamaterials, is also a collection of floppy modes, which are often called mechanisms.The goal of this project is to investigate the topology and entropy of structures that are close to mechanical instabilities and exhibit floppy modes. The two main thrusts are to investigate: (1) Topological transitions in mechanical systems and design principles of transformable topological mechanical metamaterials, (2) Entropic effects on floppy modes, which will be used to understand self-assembly of mechanical metamaterials as well as design principles of machines and robots at small scales with mechanisms robust against fluctuations. The methods that will be used in this project include analytic theory and numerical simulations.The intellectual merit of this project stems from (1) the general classification of the unusual mechanical and acoustic properties of critical mechanical structures, (2) the characterization of novel topological transitions in mechanical systems, which share intriguing similarities with transitions in quantum topological states of matter, (3) the characterization of thermal fluctuation effects on floppy modes that exhibit interesting interplay with topology and guides the selection of robust mechanisms, (4) the designs and predictions on the self-assembly of novel open structures.This award also supports outreach activities which increase the awareness of the general public on soft matter physics and its contributions to our daily life, as well as educational activities that broaden participation of women and other minorities in physics through outreach in local schools and group discussions among female physics students.