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

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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.