Critical Mechanical Structures: Topology and Entropy

关键机械结构：拓扑和熵

基本信息

批准号：
1609051
负责人：
Xiaoming Mao
金额：
$ 28.5万
依托单位：
Regents of the University of Michigan - Ann Arbor
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2016
资助国家：
美国
起止时间：
2016-05-15 至 2020-04-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1609051&HistoricalAwards=false
关键词：
Critical Mechanical Structures Topology Entropy

项目摘要

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.

非技术摘要这一奖项支持有关软材料的理论研究，外展和教育，并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年的J. C. Maxwell的研究，它控制着软物质物理学中许多引人入胜的现象，从颗粒物的干扰到新型材料的自组装和生物组织的非线性弹性。同时，该概念还指导了可以执行前所未有的功能的新机械超材料的设计。机械超材料显示通过其结构而不是其组成获得的新型机械性能。PI将研究机械不稳定性与软材料的变形之间的相互作用，而软材料的变形很小，所得到的能量很少，称为软模式。可以鉴定出块状刚性但具有柔软边缘的结构，这些柔软的边缘很容易与剥离软边缘剥离的基本特性变形，从而导致一种新材料也具有柔软的边缘。使用与拓扑相关的最近开发的概念，可以鉴定出与变形下保留的对象的性质有关的数学分支，可以确定具有不同机械性能的材料阶段。 PI将研究这些物质阶段，它们对缺陷和热驱动振动的稳健性以及当材料接近机械不稳定性时，软变形如何在不同的材料相之间转化材料。PI将利用从对这些“拓扑保护”的机械阶段的研究中获得的理解，以及它们之间的变化，以设计新的机械化机械质量。 PI还将研究这些新型设备变得足够小时会发生什么，以使热波动很重要，并通过自组装生产这些结构。该项目不仅旨在对机械不稳定性的结构的基本理解，而且还为具有强大属性和功能强大的新机械材料的设计提供了指导。此外，该项目包括推广活动，这些活动提高了公众对软物质物理学的认识及其对我们日常生活的贡献，以及通过在当地学校的外展和小组讨论中的妇女和其他少数群体在物理学中扩大妇女和其他少数群体在女性物理学生中的参与的教育活动。技术摘要这一奖项支持有关软材料的理论研究，外展和教育，并使用新概念设计新的机械超材料。软物质物理学中许多迷人现象的中心是软盘模式的集合，这些模式是变形的模式，几乎没有能量，并且信号是机械不稳定的。例子包括被困住的颗粒物和生物组织的非线性弹性的屈服。同时，最近对机械超材料的研究爆炸了，这些材料是获得新型机械性能的材料，例如负泊松的比率，负压缩性，负热膨胀，语音带隙，通过其结构而不是其组成。有趣的是，在许多情况下，实现这些机械超材料的新型特性的关键也是软盘模式的集合，通常称为机制。该项目的目的是研究与机械不稳定性和展示软盘模式接近的结构的拓扑和熵。这两个主要目的是研究：（1）机械系统和设计原理的拓扑过渡，（可转换拓扑机械材料，（2）对软盘模式的熵效应，这将用于理解机械超材料的自组装机械和机器人的设计原理以及机器的设计原理以及机器上的小尺度机械尺度，以抗化力。该项目将使用的方法包括分析理论和数值模拟。该项目的智力优点源于（1）关键机械结构的不寻常的机械和声学特性的一般分类，（2）在机械系统中的新型拓扑过渡的表征，机械系统在机械系统中具有与量子范围相似性的相似之处（3）的特性，（3）的特性（3），（3）的特性（3），（3）（3）（3）（3）（3）（3），（3）的特性，（3），（3）（3）（3），（3）（3）（3）（3）（3）的特性（3）。展示与拓扑结构的有趣相互作用，并指南选择了可靠的机制，（4）对新型开放结构自组装的设计和预测。该奖项还支持外展活动，这些奖项提高了公众对软物质物理学及其对我们日常生活的贡献的认识，以及在妇女和其他教育中的教育活动，并通过物理学进行了培训，并在物理学中进行了培训。