Bulletin of the American Physical Society
APS March Meeting 2023
Volume 68, Number 3
Las Vegas, Nevada (March 5-10)
Virtual (March 20-22); Time Zone: Pacific Time
Session T09: Textiles and Topology: Physics of Knots and Tangles |
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Sponsoring Units: DSOFT Chair: Alex Klotz, California State University, Long Beach Room: Room 132 |
Thursday, March 9, 2023 11:30AM - 11:42AM |
T09.00001: Tying up the loose ends of tight knots Alexander R Klotz, Matthew Maldonado The ropelength of a physical knot refers to the minimum contour length it can have while respecting a no-overlap constraint. There are proven upper and lower bounds to the scaling of the ropelength with respect to the crossing number of the knot, as well as numerical estimates based on knot-tightening algorithms. The proven bounds are widely separated from numerical estimates, and the knots that have been numerically tightened are typically not complex enough to constrain stronger conjectured bounds. In this work I discuss some recent results examining the ropelength of torus and satellite knots that are significantly more complex than those previously analyzed, with the goal of constraining conjectured ropelength bounds and providing more insight on the crossing-ropelength relationshp. I will also discuss the convex hull volume of tight knots, which has a nontrivial relationship with the contour length. |
Thursday, March 9, 2023 11:42AM - 11:54AM Author not Attending |
T09.00002: Supramolecular structures with topologically tunable properties: circular polycatenanes and two-dimensional sheets Luca Tubiana, Enzo Orlandini, Franco Ferrari Supramolecular materials built of topologically interlocked polymer rings have recently gained considerable interest in supramolecular chemistry, biology, and soft matter. Two typical examples are polycatenanes, linear chains of concatenated rings, and the kDNA, a natural occuring, two dimensional surface of linked DNA rings. Here, through the use of extensive simulations, we show how one can exploit the topology of the local interlockings to store twist in circular polycatenanes, significantly altering their physical properties. By defining the twist and writhe of these ring-o-rings, we show that a relation equivalent to the Calugareanu-White-Fuller theorem for dsDNA holds for circular polycatenanes. We then extend our investigation to the case of 2D sheets of rings, showing the existence of a similar effect that leads to different global properties based on the chirality of the local interlockings. Our results suggest that supramolecular objects with storable and tunable twist can form a new category of highly designable structures with potential applications in supramolecular chemistry and material science. |
Thursday, March 9, 2023 11:54AM - 12:06PM |
T09.00003: Optimal unravelling of tangled filaments Vishal P Patil, Ishant Tiwari, Saad Bhamla Tangled fibers represent an important class of disordered, strongly interacting systems, with relevance across length scales, from tangled DNA to human-scale materials such as yarn and rope. Despite recent work demonstrating the functionality of amorphous tangles, the problem of controlling tangle topology continues to present profound challenges. In particular, the question of how to extract a single filament from a tangle remains poorly understood. Here, we combine detangling experiments and numerical simulations with a topological analysis of tangle mechanics to understand the fiber extraction problem. Our results indicate the existence of optimal fiber extraction protocols, demonstrating that the topological state of disordered filamentary matter can be robustly manipulated. |
Thursday, March 9, 2023 12:06PM - 12:18PM |
T09.00004: Twisting and braiding elastic filament pairs* Julien Chopin, Animesh Biswas, Arshad Kudrolli Twisting and braiding filaments is a fundamental topological transformation relevant to making ropes, tying shoelaces, robotics, and the mechanical properties of entangled polymers. The regime of inextensible, infinitely thin filaments has been studied extensively, especially in the context of knots. Here, we investigate with experiments the elastic energy required to twist a filament-pair while prescribing the initial pre-stretch. First, we show that the torque profile with applied twist is non-monotonic, with a maximum that depends on their initial length, separation distance, and pre-stretch. After the filaments cross and come in contact, the torque is measured to increase quasi linearly while the filaments form a double helix in a central region which grow in length with increasing twist. We develop a nonlinear elasto-geometric model that captures quantitatively the full torque profile, and the evolution of the filament braid with twist. We find that the combined effect of geometrical nonlinearties with large stretching and self-twist make significant contributions, while bending and contact deformation make only perturbative contributions to the overall response. |
Thursday, March 9, 2023 12:18PM - 12:30PM |
T09.00005: The effect of yarn mechanics on the non-linear elasticity of knitted textiles Alexander Cachine, Krishma Singal, Sarah E Gonzalez, Michael S Dimitriyev, Elisabetta A Matsumoto Knitted fabrics are composed of single strands of yarn manipulated into complex lattices of slipknots. These fabrics exhibit emergent elastic properties. Their stress-strain relationships indicate the existence of a linear, low-stress regime and a non-linear, high-stress regime. Prior study has determined that the low-stress behavior can largely be explained by the stitch composition of the fabric: which stitches are used, their topology, and how they are patterned. Under high-stress however, the stitches themselves quickly reach their maximum deformation. At this point, the constituent yarn’s material properties, particularly its compressibility and, to a lesser extent, bending modulus, dictate these elastic properties. Additionally, simulations have shown that the property dominating fabric behavior may be influenced by the direction of applied stress on the fabrics. In order to understand the effect of yarn type on fabric behavior, we perform uniaxial applied strain experiments on fabrics of the same structure, but varying constituent yarn types. We further characterize the effects of yarn compression and bending by performing similar experiments in alternate directions on an array of yarn types and analyzing their stress-strain relationship. This will enable us to develop a constitutive model for knitted fabrics based on both the stitch pattern topology and the underlying mechanics of the yarn itself. |
Thursday, March 9, 2023 12:30PM - 12:42PM |
T09.00006: Mechanical Transitions in Knitted Fabrics with Coarsening Patterns Krishma Singal, Michael S Dimitriyev, Elisabetta A Matsumoto Conventional knitted materials rely on periodic patterning of stitches to generate fabrics with emergent bulk elastic properties. Periodically patterning the two most common stitches, the knit stitch and the purl stitch, introduces soft deformation modes in fabrics. The boundaries between knit and purl stitches govern the emergent fabric behavior. Controlling the lengthscale of these boundaries and the periodicity of the stitches enable us to explore directed fabric strain outside of the fabric's bulk stress response. We use Cahn-Hilliard dynamics to model a two-phase separation of knit and purl stitches, allowing us to explore transitions from a completely disordered state to varying stages of coarsening, concluding in a two-domain state. Our preliminary work has shown that cluster size increases bulk fabric rigidity. We explore how clusters guide strain based on their size and orientation relative to the bulk fabric. Since other coarsening statistical systems, such as the Ising model, show phase transitions at percolations, we seek second-order phase transitions that give rise to new elastic anisotropies where one direction of the fabric exhibits high rigidity, and the other, soft deformations. |
Thursday, March 9, 2023 12:42PM - 12:54PM |
T09.00007: Characterizing Jamming in Knitted Fabrics Sarah E Gonzalez, Michael S Dimitriyev, Krishma Singal, Elisabetta A Matsumoto When stretched, most knitted fabrics have a soft mechanical response determined by yarn properties and curvature of the stitches for low stress, which gradually stiffens for higher stress as the yarn is increasingly compressed. However, when knit fabrics have tight stitches, the yarn is highly compressed even when the fabric is unstretched. This creates an initially stiff response that then softens to the usual linear response, before stiffening again. This new stiff regime at low-stress is a result of geometric confinement of yarn and can be considered a fiber-analogue of "jamming." Once a significant enough force is applied such that the stitches collectively move apart and the confinement is overcome, the fabric can begin to stretch. This jamming can be seen in force-extension experiments on stockinette fabric when it exhibits an initially large tensile modulus at low stress. Utilizing computational simulations of knit fabrics, we investigate yarn and manufacturing parameters that affect the presence and intensity of jamming. To study the interplay between confinement and mechanics, we map the distribution of non-local contact interactions, known as the contact set. Changes in the location and geometry of the contact set provide a morphological indicator of jamming. |
Thursday, March 9, 2023 12:54PM - 1:06PM |
T09.00008: Laddering Propagation in Weft Knit Fabrics Helen E Read, Kausalya Mahadevan, Katia Bertoldi We use weft knit fabrics every day, as their compliance makes them ideal for clothes that are easy to put on and can conform to our bodies. However, the same structure that grants weft knits their stretchiness can also cause them to fail catastrophically; the breaking of a single yarn can lead to large visible holes which are caused by unsupported loops that propagate vertically and create a laddering effect. Using experiments to investigate this phenomenon, we first identify biaxial loading conditions that lead to laddering in plain knit architectures. Then, we explore strategies that we can use to manipulate this laddering effect. These include cut location along the stitch and horizontal transfers. As such, our study provides a framework not only to understand, but also to manipulate failure modes in soft wearables. |
Thursday, March 9, 2023 1:06PM - 1:18PM |
T09.00009: Structure-Property Investigation of Knit Patterns on Mechanical, Thermal, and Moisture Properties Jay H Park, S M Fijul Kabir, Ihsan Uluturk, Seijiro Yoshihara, Joshua Lee, Scott Stapleton While recent advances in material science has expanded functionlaities of textiles, little is known about how the textile structure alone changes the response. Fabric, a 2D form of textile, is characterized with exceptionally intricate structures involves interlacing (weaving), intermeshing or interloping (kitting), fiber entangling (nonwoven), intertwining (braiding). The present work explores the structure-property relationships of different knit structures with same fiber and yarn properties; how different loop formation techniques (intermeshing or interloping) impact on the moisture and heat transfer properties of fabrics, determinants of comfortability, crucial and fundamental properties of wearable textiles. Herein, 12 types of polyester-based knit performance textiles including basic and complex knits were produced and investigated for i) bi-axial mechanical response, ii) vertical (AATCC TM197-2011e2) and horizontal moisture wicking (AATCC TM198-2011e), as well as iii) heat transfer properties using sweating guarded hotplate method (ASTM-1868). The mechanical responses have been corroborated by digital image correlation (DIC) and textile-based modelling. Results shows wicking properties of basic knit structures are better relative to complex structures; however, opposite is found in case of heat transfer. Wick runs faster along the wale (lengthwise) direction for most of the cases; nonetheless, higher wicking in course direction and few even wicking (same in both directions) are also observed, which are related to the tightness of the structure, interloping techniques, loop density, and fabric density. On the other hand, heat transfer is related to thickness of the fabric, fabric density, chances of developing entrapped air in the structure during wearing, volume and distribution of entrapped air. This paper also aims to quantify still air volume and distribution using X-ray tomography, and relates these attributes to the thermal resistance of the fabric and fit regression model to predict thermal properties, which has not been reported yet to best of the authors' knowledge. The research has high implication in technical design of apparel to tune comfort properties simply changing the fabric structure. |
Thursday, March 9, 2023 1:18PM - 1:30PM Author not Attending |
T09.00010: Hydrodynamics of Brownian colloids in soluble surfactant layers Mehdi Molaei, Stephen Crane, Nicholas G Chisholm, Kathleen J Stebe The Brownian motion of passive colloids embedded on fluid interfaces is governed by fluctuation dissipation theorem. This enables the measurement of interfacial dynamics by the tracking of single colloidal particles and measuring their correlated behaviors. |
Thursday, March 9, 2023 1:30PM - 1:42PM |
T09.00011: "Liquid network" theory of supramolecular soft matter networks Michael S Dimitriyev, Gregory M Grason Macromolecules can self-assemble into a variety of ordered nanostructures, including the triply-periodic double-gyroid and double-diamond network phases. These phases consist of complex, intercatenated, labyrinthine domains, yet are supramolecular soft crystals with long-range order. Interruptions to their crystal symmetries, e.g. due to defects or composition gradients, result in collective changes in domain morphology as a result of thermodynamic forces and constraints on molecular packing. Motivated by experiments and self-consistent field calculations of block copolymer melts, we propose a "liquid network" theory that coarse-grains the collective behavior of such supramolecular networks into an effective mechanical network model. Unlike canonical models of mechanical networks, our theory describes networks whose struts possess a length-independent line tension, and is thus characterized by the mathematics of so-called Steiner networks. We show that our model reproduces key observations of experiments and simulations, namely significant non-affinity of node displacements and highly correlated bond angles. Finally, we discuss structural transformations under shear and deformation pathways that facilitate transitions between different network phases. |
Thursday, March 9, 2023 1:42PM - 1:54PM |
T09.00012: Topological edge modes and Weyl hypersurfaces in hyperbolic Maxwell lattices Francesco Serafin, Xiaoming Mao, Zeb Rocklin, Kai Sun We generalize topological mechanics to lattices with negative intrinsic curvature. We find that the mechanical stability of the lattice, quantified by Maxwell's counting, now depends on the spatial symmetries of the lattice while the eigenspace of deformations splits into sectors which can be under-, over- or critically constrained. Distortions of hyperbolic Maxwell lattices can lead to edge-localization of the zero-energy deformations and to partial or complete lattice polarization. We impose periodic boundary conditions by compactifying the lattice's unit cell into surfaces of high genus g>1, and compute topological indices using curved-space Bloch states. The lattice's curvature translates into a constraint between the Bloch wave functions, leading to precise correlations in the directions of localization of edge modes. Finally, we find that in certain hyperbolic lattices, the Brillouin zone contains not only Weyl points and lines but also higher dimensional Weyl hypersurfaces and define their topological charge. |
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