Physical properties of twisted structures. II. Industrial yarns, cords, and ropes

Pan, Ning; Brookstein, David

doi:10.1002/app.2261

Cited by 39 publications

(34 citation statements)

References 78 publications

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“…The complexity of cross-sectional packing in this archetypal material geometry has long been a subject of study, particularly from the viewpoint of the mechanical properties of manufactured textiles (14,17) and wire ropes (13). The problem is best visualized from the perspective of the planar cross-section of a twisted bundle, as shown in Fig.…”

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confidence: 99%

Non-Euclidean geometry of twisted filament bundle packing

Bruss

Grason

2012

Proc. Natl. Acad. Sci. U.S.A.

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Densely packed and twisted assemblies of filaments are crucial structural motifs in macroscopic materials (cables, ropes, and textiles) as well as synthetic and biological nanomaterials (fibrous proteins). We study the unique and nontrivial packing geometry of this universal material design from two perspectives. First, we show that the problem of twisted bundle packing can be mapped exactly onto the problem of disc packing on a curved surface, the geometry of which has a positive, spherical curvature close to the center of rotation and approaches the intrinsically flat geometry of a cylinder far from the bundle center. From this mapping, we find the packing of any twisted bundle is geometrically frustrated, as it makes the sixfold geometry of filament close packing impossible at the core of the fiber. This geometrical equivalence leads to a spectrum of close-packed fiber geometries, whose low symmetry (five-, four-, three-, and twofold) reflect non-Euclidean packing constraints at the bundle core. Second, we explore the ground-state structure of twisted filament assemblies formed under the influence of adhesive interactions by a computational model. Here, we find that the underlying non-Euclidean geometry of twisted fiber packing disrupts the regular lattice packing of filaments above a critical radius, proportional to the helical pitch. Above this critical radius, the ground-state packing includes the presence of between one and six excess fivefold disclinations in the cross-sectional order.self-assembly | topological defects | geometric frustration P acking problems arise naturally in a multitude of contexts, from models of crystalline and amorphous solids to structure formation in tissues of living organisms. Though often easy to state, packing problems are notoriously difficult to solve. The cannonball stacking of spheres, for example, conjectured by Kepler to be the densest packing in three-dimensional space (1), was only proven so in 1999, and even then with the aid of a computer algorithm (2). In some cases, like the densest packing of spheres, the face-centered cubic lattice-or its two-dimensional analogue, the densest packing of discs, the hexagonal lattice-the optimal structure is a regular, periodic partition of space. In many problems, however, perfect lattice packings are prohibited, and optimal structures necessarily lack the translational and rotational symmetry of periodic order. A well-known example is the problem of finding the densest packing of N discs on a sphere of a given radius, known alternately as the Tammes or the generalized-Thomson problem (3). In this problem, spherical topology requires a variation in the local packing symmetry: All states possess at minimum 12 discs whose nearest-neighbor geometry is fivefold coordinated (4). Beyond its relevance to structural studies of such diverse materials as spherical viral capsids (5) and colloid-stabilized emulsions (6, 7), the problems involving point or disc packing on spheres serve as an important example of systems where topological de...

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confidence: 99%

Non-Euclidean geometry of twisted filament bundle packing

Bruss

Grason

2012

Proc. Natl. Acad. Sci. U.S.A.

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“…In other words, on the one hand there are variables such as inter-fiber friction and lateral contractions due to fiber twisting that reduce the tensile strength of the yarn, while on the other hand there are rope unwinding mechanisms that, similar to waviness release in natural tendon, amplify ductility [4,30,32,33]. Such a mechanism is bound to give rise to complications, with the yarn strength predicted to be smaller than the constituent fiber strength.…”

Section: Introductionmentioning

confidence: 88%

“…Although the effects of yarn twist remain debatable, its application does result in a more intimate interaction between fibers than in a loose yarn made of parallel fibers. This, of course (as well as the filament length which is not considered here) influences the strength and modulus of a yarn, as well as the strength variability [31][32][33]. Various theoretical models of Young's modulus and strength of twisted yarns have recently been reviewed by Sui et al [30].…”

Section: Introductionmentioning

confidence: 97%

Gelatin yarns inspired by tendons — Structural and mechanical perspectives

Selle

Bar‐On

Marom

et al. 2015

Materials Science and Engineering: C

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“…Pre-twist of the yarn Helical strands are widely used in traditional engineering such as textiles [8,13] and wire ropes [3,4,15]. Because of their superior mechanical properties of both the relatively high tensile stiffness and low bending stiffness, they are used as fiber reinforcements in matrices and transmissible tension members.…”

Section: List Of Symbolsmentioning

confidence: 99%

Residual twist in a double-layer strand and its correlation with bending fatigue

Morimoto¹,

Ashida³

2015

Acta Mech

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We propose a method to characterize an undeformed double-layer strand with residual stress by considering the deviation from the self-equilibrium configuration where torque is balanced without any external forces. We first derive the residual twist defined as the deviation of internal twisting moment in the strand from the self-equilibrium configuration. The residual twist gives a measure of the effective torsional rigidity of the strand, determined by the geometrical, material, and mechanical parameters from the microstructural viewpoint. Then, we correlate the residual twist with the fatigue life of (3+8)-glass strands embedded in a rubber matrix under cyclic bending. We show that the residual twist correlates with the number of cycles to failure for specific (3+8)-glass strands having the identical twist direction.

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Physical properties of twisted structures. II. Industrial yarns, cords, and ropes

Cited by 39 publications

References 78 publications

Non-Euclidean geometry of twisted filament bundle packing

Non-Euclidean geometry of twisted filament bundle packing

Gelatin yarns inspired by tendons — Structural and mechanical perspectives

Residual twist in a double-layer strand and its correlation with bending fatigue

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