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

此职业奖支持针织纺织品机械性能的理论研究和教育。纺织品既无处不在，又不为人所知。针织衫重量轻，坚固，可拉伸，灵活。这些特性，加上廉价、可编程的制造技术，使得针织衫在工业和家庭应用中备受推崇。本研究将探讨针线结构与针织物机械性能之间的关系。针脚的微小变化可以极大地改变大块织物的性能。本研究的目的是确定和量化的数学性质之间的关系，针和织物的性质。对这些特性进行逆向工程，只需改变针脚，就能制造出具有定制特性的织物。本研究在织物的曲率与自然界曲率的物理和数学之间起着桥梁的作用。为了进一步解释这种联系，PI将创建弯曲空间的开源虚拟现实模拟。虚拟和增强现实使用户能够可视化，移动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个真正的三维物体进行互动。这些将首先在荣誉物理课程中实现，最终将开放源代码，供任何人使用或进一步开发。本职业奖支持对针织纺织品机械性能的研究。纺织品是连接曲率、拓扑学和日常生活的天然管道。这些固有的分层材料具有丰富的几何和弹性特性，包括：低应变时的软弹性，大应变时的高拉伸刚度，低弯曲模量，高抗全局破坏能力和可编程的局部曲率。这些特性，加上廉价、可编程的制造技术，使得针织衫在工业和家庭应用中备受推崇。每一针线都与相邻的针线纠缠在一起，形成一个局部打结的结构。这些纺织品“结”的拓扑结构产生了物理约束，这些约束负责纺织品的紧急弹性。以往对针织弹性的研究只考虑了单一类型的针织物。然而，局部针脚拓扑结构的改变对针脚的弹性有深远的影响；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，我们缺乏一组令人满意的决定纺织品力学的总体方程。了解针脚的缠结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CAREER项目将创建一个框架，将纺织品拓扑结构与其紧急弹性结合起来。这些研究分为两个目标：(1)研究小组将确定拓扑学上允许的针脚，(2)它们对织物局部几何形状和弹性的影响可以预测。从结理论和3流形拓扑技术将用于创建一套全面的针。这些针脚及其拓扑结构将为弹性模型提供纱线水平的基础。每个针脚的行为和针脚之间的相互作用将被粗粒度转化为织物弹性的二维表面模型。研究小组将使用各向异性几何弹性理论，将纱线的局部特性和针脚的拓扑结构与大块纺织品的机械响应联系起来。这个框架将是管理纺织品行为的第一套本构关系。本研究在织物的曲率与自然界曲率的物理和数学之间起着桥梁的作用。为了进一步解释这种联系，PI将创建弯曲空间的开源虚拟现实模拟。虚拟和增强现实使用户能够可视化，移动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个真正的三维物体进行互动。这些将首先在荣誉物理课程中实现，最终将开放源代码，供任何人使用或进一步开发。数学和物理科学理事会的材料研究部以及工程理事会的土木、机械和制造创新部为该提案提供了资金。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 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.