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CAREER: What a Tangled Web We Weave - Topology and Mechanics of Textiles

职业生涯：我们编织的网络多么错综复杂——纺织品的拓扑和力学

基本信息

批准号：
1847172
负责人：
Elisabetta Matsumoto
金额：
$ 66.07万
依托单位：
Georgia Tech Research Corporation
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2019
资助国家：
美国
起止时间：
2019-05-01 至 2025-04-30
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1847172&HistoricalAwards=false
关键词：
CAREER What Tangled Web Weave

项目摘要

NON-TECHNICAL SUMMARYThis CAREER award supports theoretical research and education on mechanical properties of knitted textiles. Textiles are simultaneously ubiquitous and not well understood. Knits are lightweight, strong, stretchable and flexible. These properties, coupled with cheap, programmable manufacturing techniques make knits prized for industrial and domestic applications. This research will probe the relationship between the structure of the stitches and the mechanical properties of knitted textiles. Small changes in stitches can vastly alter the properties of the bulk fabric. The goal of this research is to identify and quantify the relationship between mathematical properties of the stitch and fabric properties. Reverse engineering these properties enables fabrics with bespoke properties to be created merely by changing their stitches.This research acts as a conduit between curvature in fabrics and the physics and mathematics of curvature in nature. To further explain this connection, the PI will create open source virtual reality simulations of curved space. Virtual and augmented reality enable users to visualize, move through and interact with objects and concepts that they could not in the real world. The PI and her research team will create a series of virtual reality modules to introduce vector fields and vector calculus to introductory physics and mathematics students. Virtual reality capitalizes upon kinesthetic learning and 3D visualization to enable students to interact with one of the first truly three-dimensional objects they encounter in the standard physics curriculum. These will be implemented first in the honors physics course and will eventually be made open source for anyone to use or develop further.TECHNICAL SUMMARYThis CAREER award supports research into mechanical properties of knitted textiles. Textiles are a natural conduit between curvature, topology and everyday life. These innately hierarchical materials have a wealth of emergent geometric and elastic properties, including: soft elasticity at low strain, high extensional rigidity at large strain, low bending modulus, high resistance to global failure, and programmable local curvature. These properties, coupled with cheap, programmable manufacturing techniques make knits prized for industrial and domestic applications. Each knitted stitch is entangled with its neighbors, creating a locally knotted structure. The topology of these textile "knots" creates physical constraints that are responsible for the emergent elasticity of textiles. Previous studies into knitted elasticity have considered only a single type of knitted fabric. However, manipulating the local stitch topology has a profound impact on the elasticity; it can increase or decrease the extensional rigidity, change the crossover between soft elasticity and nonlinear behavior, and even create local topography. Unlike many coarse-grained physical systems, a satisfactory set of overarching equations that determine the mechanics of textiles is lacking. Understanding the entanglement topology of knitted stitches is key to creating a predictive model of elastic and geometric responses of textiles. This CAREER project will create a framework which unites textile topology with its emergent elasticity. These are broken into two aims: (1) the research team will identify topologically allowed knitted stitches, from which (2) their effect on the local geometry and elasticity of the fabric can be predicted. Techniques from knot theory and 3-manifold topology will be used to create a comprehensive set of stitches. These stitches and their topology will provide the yarn-level basis for an elasticity model. The behavior of each stitch and interactions between stitches will be coarse-grained into a 2D surface model of fabric elasticity. The research team will use anisotropic geometric elasticity theory to relate the local properties of the yarn and the topology of the stitches to the mechanical response of the bulk textile. This framework will be the first set of constitutive relations that govern textile behavior. This research acts as a conduit between curvature in fabrics and the physics and mathematics of curvature in nature. To further explain this connection, the PI will create open source virtual reality simulations of curved space. Virtual and augmented reality enable users to visualize, move through and interact with objects and concepts that they could not in the real world. The PI and her research team will create a series of virtual reality modules to introduce vector fields and vector calculus to introductory physics and mathematics students. Virtual reality capitalizes upon kinesthetic learning and 3D visualization to enable students to interact with one of the first truly three-dimensional objects they encounter in the standard physics curriculum. These will be implemented first in the honors physics course and will eventually be made open source for anyone to use or develop further.The Division of Materials Research in the Mathematical and Physical Sciences Directorate and the Civil, Mechanical, and Manufacturing Innovation Division in the Engineering Directorate contribute funds to this proposal.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.

非技术总结该职业奖支持针织面料机械性能的理论研究和教育。纺织品无处不在，但却没有得到很好的理解。针织品重量轻、结实、可伸缩、可弯曲。这些特性，再加上廉价、可编程的制造技术，使针织产品在工业和家庭应用中备受青睐。本研究将探讨针织面料的组织结构与其力学性能之间的关系。针迹的微小变化可以极大地改变散装面料的性能。这项研究的目的是识别和量化针迹的数学特性和织物特性之间的关系。逆向工程这些特性使得只需改变缝合就能创造出具有定制特性的织物。这项研究充当了织物曲率与自然界中曲率的物理和数学之间的桥梁。为了进一步解释这种联系，PI将创建开放源代码的弯曲空间虚拟现实模拟。虚拟和增强现实使用户能够可视化、穿行并与他们在现实世界中无法实现的对象和概念进行交互。PI和她的研究团队将创建一系列虚拟现实模块，向物理和数学入门学生介绍矢量场和矢量微积分。虚拟现实利用动觉学习和3D可视化，使学生能够与他们在标准物理课程中遇到的第一批真正的三维对象之一进行交互。这些将首先在荣誉物理课程中实施，并最终开放源代码供任何人使用或进一步开发。TECHNICAL SUMMARY这个职业奖项支持针织纺织品机械性能的研究。纺织品是曲率、拓扑学和日常生活之间的天然通道。这些固有的层次化材料具有丰富的新出现的几何和弹性特性，包括：低应变下的柔软弹性、大应变下的高拉伸刚性、低弯曲模数、高抗整体破坏能力和可编程的局部曲率。这些特性，再加上廉价、可编程的制造技术，使针织产品在工业和家庭应用中备受青睐。每一针都与其相邻的针脚缠绕在一起，形成一种局部打结的结构。这些纺织品“结”的拓扑结构产生了物理约束，这些约束导致了纺织品的紧急弹性。以前对针织弹性的研究只考虑了单一类型的针织面料。然而，操纵局部缝合拓扑对弹性有深刻的影响，它可以增加或减少拉伸刚度，改变软弹性和非线性行为之间的交叉，甚至产生局部地形。与许多粗粒度的物理系统不同，缺乏一套令人满意的确定纺织品力学的总体方程。了解针织线迹的缠绕拓扑结构是建立纺织品弹性和几何响应预测模型的关键。这个职业项目将创建一个框架，将纺织拓扑学与其新出现的弹性统一起来。这些目标分为两个目标：(1)研究小组将确定拓扑允许的针织缝合，(2)可以预测它们对织物局部几何形状和弹性的影响。来自纽结理论和3-流形拓扑的技术将被用来创建一套全面的针脚。这些缝线及其拓扑结构将为弹性模型提供纱线级别的基础。每一针的行为和针之间的相互作用将被粗粒度化为织物弹性的2D表面模型。研究小组将使用各向异性几何弹性理论将纱线的局部属性和针脚的拓扑与散装纺织品的机械响应联系起来。这一框架将是管理纺织品行为的第一套本构关系。这项研究在面料的曲率和自然界的曲率的物理和数学之间起到了沟通的作用。为了进一步解释这种联系，PI将创建开放源代码的弯曲空间虚拟现实模拟。虚拟和增强现实使用户能够可视化、穿行并与他们在现实世界中无法实现的对象和概念进行交互。PI和她的研究团队将创建一系列虚拟现实模块，向物理和数学入门学生介绍矢量场和矢量微积分。虚拟现实利用动觉学习和3D可视化，使学生能够与他们在标准物理课程中遇到的第一批真正的三维对象之一进行交互。这些将首先在荣誉物理课程中实施，最终将开放源代码供任何人使用或进一步开发。数学和物理科学局的材料研究部和工程局的土木、机械和制造创新部为这一计划提供资金。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。