pith. sign in

arxiv: 2604.20580 · v1 · submitted 2026-04-22 · ❄️ cond-mat.soft

Laddering of a knitted fabric: a topology-induced failure

Antoine Faulconnier , Laura Michel , Mokhtar Adda-Bedia , J\'er\^ome Crassous , Audrey Steinberger This is my paper

Pith reviewed 2026-05-09 23:02 UTC · model grok-4.3

classification ❄️ cond-mat.soft
keywords ladderingknitted fabrictopological defectforce thresholdpropagation velocitybending wavesdamage predictionweft knit
0
0 comments X

The pith

A curvature-induced force threshold in knitted stitches controls both the start and stop of laddering under tension.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper studies laddering, the unravelling of stitches in weft-knitted fabrics after a thread breaks or drops. Through experiments and Discrete Element Rod simulations on pre-stressed model knits, it identifies a minimum force threshold set by the natural curvature of each stitch. This threshold governs when the topological defect begins to propagate and when growth halts because the released thread length relaxes the tension. The work also reports that laddering speed is comparable to bending wave speed and scales linearly with fabric tension through the combined action of elastic and frictional forces, which supports damage prediction at moderate tensions.

Core claim

In a pre-stressed weft-knitted fabric, laddering is governed by a force threshold that originates from the stitch's natural curvature. This threshold sets the condition for both the onset of propagation and its arrest once tension relaxes due to the thread length freed by ladder growth. The velocity of laddering is of the order of bending wave velocity and shows an unexpected linear increase with applied tension arising from the interplay of elastic restoring forces and friction.

What carries the argument

The force threshold due to stitch natural curvature, which determines the conditions for topological defect propagation and arrest while tension relaxes.

Load-bearing premise

The Discrete Element Rod simulations and the chosen model knit capture the curvature, friction, and tension-relaxation mechanics of real weft-knitted fabrics.

What would settle it

A direct measurement on real knitted fabrics showing either no distinct force threshold for laddering onset or a non-linear relation between laddering velocity and tension would contradict the reported control mechanism.

Figures

Figures reproduced from arXiv: 2604.20580 by Antoine Faulconnier, Audrey Steinberger, J\'er\^ome Crassous, Laura Michel, Mokhtar Adda-Bedia.

Figure 1
Figure 1. Figure 1: FIG. 1. Close-up photographs picturing the final state of a [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) Picture of a knitted sample mounted on the [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Comparison of laddering experiments at a low and high initial tension [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Force-displacement profile of the knitted fabric. [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. (a)(c) Forces [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Photograph of the knitted sample indicating the lo [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Configuration diagram: knit periodicity in [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Photograph of the final state of the fabric after [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
read the original abstract

Laddering is the propagation of a topological defect in an everyday-life material: weft knitted fabrics, following a broken thread or a dropped stitch. What is a minor frustration when damaging a pair of tights is a more serious issue for industrial-scale production, but might inspire new solutions to limit and mitigate damage to architected materials. In this work, laddering is investigated in a pre-stressed model knit through experiments and Discrete Element Rod simulations. The control parameter is the initial tension applied on the fabric. A force threshold due to the stitch's natural curvature is evidenced. It controls both the propagation onset and arrest, as tension is relaxed by the thread length freed by ladder growth, and enables damage prediction at moderate tension. Furthermore, we uncovered that the laddering velocity is of the order of the velocity of bending waves and exhibits an unexpected linear scaling with the fabric tension, that arises from a complex combination of elastic and friction forces. Finally, we discuss the implications of our results from the perspective of damage control and mitigation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper examines laddering (topological defect propagation) in pre-stressed weft-knitted fabrics via experiments and Discrete Element Rod simulations, using initial fabric tension as the control parameter. It reports a force threshold originating from the stitch's natural curvature that governs both the onset of propagation and its arrest through tension relaxation enabled by thread length released during ladder growth, thereby allowing damage prediction at moderate tensions. The work further claims that laddering velocity is comparable to bending-wave speeds and scales linearly with tension due to the interplay of elastic and frictional forces, with implications for damage mitigation in textiles and architected materials.

Significance. If the central claims hold, the identification of a curvature-induced force threshold and the linear velocity-tension relation would offer a mechanistic basis for predicting and controlling topology-driven failure in knitted structures, extending beyond empirical observation. The dual use of direct experiments and complementary simulations on a model knit is a strength, as is the focus on tension relaxation as a self-limiting mechanism. These elements could inform design strategies for damage-tolerant fabrics, though the quantitative robustness and generality remain to be strengthened.

major comments (3)
  1. [Experimental results] The experimental results section does not report error bars, number of replicates, or sample statistics for the measured laddering velocities or threshold forces as a function of initial tension. Without these, the claimed linear scaling and the existence of a distinct threshold cannot be assessed for statistical significance or reproducibility.
  2. [Simulation methods] In the Discrete Element Rod simulation description, the yarn bending stiffness, contact friction coefficients, and initial curvature initialization are not validated against independent measurements of the physical yarn or fabric (e.g., separate bending tests or friction measurements). This makes the reported threshold and the linear velocity scaling potentially specific to the chosen model parameters rather than general predictions.
  3. [Discussion of velocity scaling] No independent analytical derivation or scaling argument is provided for the linear velocity-tension relation; the claim rests entirely on the simulation output. A minimal model balancing elastic wave propagation with frictional dissipation would strengthen the interpretation that the scaling arises from elastic-friction interplay rather than numerical artifact.
minor comments (2)
  1. [Abstract and Introduction] The abstract and introduction would benefit from a brief statement of the specific knit topology (e.g., stitch density, yarn diameter) to allow readers to assess applicability to other fabrics.
  2. [Figures] Figure captions should explicitly state the number of experimental runs averaged and any fitting procedures used for velocity extraction.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments that highlight opportunities to strengthen the statistical robustness, parameter validation, and theoretical interpretation of our results. We respond to each major comment below and indicate the revisions planned for the resubmitted manuscript.

read point-by-point responses

  1. Referee: [Experimental results] The experimental results section does not report error bars, number of replicates, or sample statistics for the measured laddering velocities or threshold forces as a function of initial tension. Without these, the claimed linear scaling and the existence of a distinct threshold cannot be assessed for statistical significance or reproducibility.

    Authors: We agree that explicit reporting of replicates and statistics is necessary to support the claims. In the revised manuscript we will add error bars (standard deviation from repeated trials) to all velocity and threshold data, state the number of independent replicates performed for each tension (minimum of five), and include a short statistical summary confirming the significance of the threshold and the linear fit. revision: yes

  2. Referee: [Simulation methods] In the Discrete Element Rod simulation description, the yarn bending stiffness, contact friction coefficients, and initial curvature initialization are not validated against independent measurements of the physical yarn or fabric (e.g., separate bending tests or friction measurements). This makes the reported threshold and the linear velocity scaling potentially specific to the chosen model parameters rather than general predictions.

    Authors: The parameters were chosen to reproduce the experimental laddering threshold and velocity trends, but we acknowledge the absence of separate validation measurements. We will expand the methods section to document the literature sources and yarn specifications used for stiffness and friction, add a brief comparison of simulated versus measured fabric curvature, and note that full independent bending/friction tests were not performed in this study; the quantitative match to experiment remains the primary support for the parameter set. revision: partial

  3. Referee: [Discussion of velocity scaling] No independent analytical derivation or scaling argument is provided for the linear velocity-tension relation; the claim rests entirely on the simulation output. A minimal model balancing elastic wave propagation with frictional dissipation would strengthen the interpretation that the scaling arises from elastic-friction interplay rather than numerical artifact.

    Authors: We accept that an analytical argument would improve the interpretation. In the revision we will insert a short scaling analysis that balances the work done by tension relaxation against frictional dissipation and bending-wave propagation; this yields a velocity linear in applied tension, consistent with the simulation results and providing a mechanistic basis independent of numerics. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper's claims rest on direct experimental variation of initial fabric tension combined with Discrete Element Rod simulations of a pre-stressed model knit. The force threshold arising from stitch natural curvature (controlling onset/arrest) and the observed linear laddering-velocity scaling with tension are presented as evidenced outcomes rather than predictions obtained by fitting parameters to the same data or by self-referential definitions. No self-citation load-bearing steps, uniqueness theorems imported from the authors' prior work, or ansatzes smuggled via citation appear in the provided text. The central results are therefore independent of the inputs by construction.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The work rests on the assumption that rod-based discrete-element modeling reproduces the essential mechanics of real knitted loops and that the observed threshold arises purely from stitch curvature rather than from other unmodeled effects. Tension is treated as an externally imposed control parameter rather than a fitted constant.

free parameters (1)
  • initial tension
    Varied experimentally as the primary control parameter; not fitted to match a target outcome but used to map the threshold behavior.
axioms (1)
  • domain assumption The Discrete Element Rod model accurately captures thread curvature, bending-wave propagation, and inter-thread friction in the knitted geometry.
    Invoked to interpret the velocity scaling and to confirm the threshold mechanism observed in experiments.

pith-pipeline@v0.9.0 · 5494 in / 1399 out tokens · 36918 ms · 2026-05-09T23:02:00.190563+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

37 extracted references · 37 canonical work pages

  1. [1]

    Shenhav and D

    L. Shenhav and D. Sherman, Fracture of 3d printed brit- tle open-cell structures under compression, Materials & Design182, 108101 (2019)

    work page 2019

  2. [2]

    Z. Gao, X. Zhang, Y. Wu, M.-S. Pham, Y. Lu, C. Xia, 6 H. Wang, and H. Wang, Damage-programmable design of metamaterials achieving crack-resisting mechanisms seen in nature, Nature Communications15(2024)

    work page 2024

  3. [3]

    de Waal, M

    L. de Waal, M. Chouzouris, and M. A. Dias, Architect- ing mechanisms of damage in topological metamaterials, Phys. Rev. Res.7, 033177 (2025)

    work page 2025

  4. [4]

    de Waal, M

    L. de Waal, M. Chouzouris, and M. A. Dias, Cracking down on fracture to functionalize damage, Phys. Rev. Lett.135, 148202 (2025)

    work page 2025

  5. [5]

    D. S. Shimamoto, K. Shimamoto, S. Mahmoudi, and S. Poincloux, Topological defect propagation to classify knitted fabrics, arXiv [cond-mat.soft] 10.48550/arXiv.2506.22369 (2025)

    work page doi:10.48550/arxiv.2506.22369 2025

  6. [6]

    Poincloux, M

    S. Poincloux, M. Adda-Bedia, and F. Lechenault, Geom- etry and elasticity of a knitted fabric, Phys. Rev. X8, 021075 (2018)

    work page 2018

  7. [7]

    L. Niu, G. Dion, and R. D. Kamien, Geometric modeling of knitted fabrics, Proceedings of the National Academy of Sciences122, e2416536122 (2025)

    work page 2025

  8. [8]

    Tajiri, R

    K. Tajiri, R. Murakami, S. Kobayashi, R. Tarumi, and T. G. Sano, Curling morphology of knitted fabrics: Struc- ture and mechanics, Extreme Mechanics Letters76, 102300 (2025)

    work page 2025

  9. [9]

    Singal, M

    K. Singal, M. Dimitriyev, S. Gonzalez, A. Cachine, S. Quinn, and E. Matsumoto, Programming mechanics in knitted materials, stitch by stitch, Nature Communi- cations15(2024)

    work page 2024

  10. [10]

    Du Pasquier, S

    C. Du Pasquier, S. Jeong, P. Liu, S. Williams, N. Mnejja, A. Okamura, S. Tibbits, and T. Chen, Multi-level me- chanical modeling and computational design framework for weft knitted fabrics, Extreme Mechanics Letters82, 102423 (2025)

    work page 2025

  11. [11]

    S. E. Gonzalez, M. S. Dimitriyev, A. P. Cachine, and E. A. Matsumoto, Pulling apart the mechanisms that lead to jammed knitted fabrics, Phys. Rev. E112, 015504 (2025)

    work page 2025

  12. [12]

    G. Li, Y. Li, P. Lan, X. He, and H. Hu, Polydioxanone weft-knitted intestinal stents: fabrication and mechanics optimization, Textile Research Journal83, 2129 (2013)

    work page 2013

  13. [13]

    Zhang and P

    X. Zhang and P. Ma, Application of knitting structure textiles in medical areas, Autex Research Journal18, 181 (2018)

    work page 2018

  14. [14]

    Abel and D

    J. Abel and D. Brei, Hierarchical architecture of active knits, Smart Materials and Structures22, 5001 (2013)

    work page 2013

  15. [15]

    I. A. K. Ahmed, M. S. Cetin, K. Ozlem, A. Tuncay Ata- lay, G. Ince, and O. Atalay, From knitting technology to robotics: Untethered thermally actuated textile ex- oskeleton for dexterity applications, Advanced Science 12, e09870 (2025)

    work page 2025

  16. [16]

    2024.arXiv preprint arXiv:2410.14810

    K. Mahadevan, M. C. Yuen, D. T. Farrell, C. J. Walsh, V. Sanchez, R. J. Wood, and K. Bertoldi, Knitting multistability, arXiv [cond-mat.soft] 10.48550/arXiv.2410.14810 (2026)

    work page doi:10.48550/arxiv.2410.14810 2026

  17. [17]

    Figueroa

    A. Abbas, N. Choudhry, S. Houshyar, J. Underwood, and X. Wang, Smart knitted fabrics for wearable technol- ogy and thermal regulation: structural design perspec- tives, Smart Materials and Structures35, 10.1088/1361- 665X/ae4661 (2026)

    work page doi:10.1088/1361- 2026

  18. [18]

    H. M. Elmoughni, A. F. Yilmaz, K. Ozlem, F. Khalil- bayli, L. Cappello, A. Tuncay Atalay, G. Ince, and O. Atalay, Machine-knitted seamless pneumatic actua- tors for soft robotics: Design, fabrication, and character- ization, Actuators10, 10.3390/act10050094 (2021)

    work page doi:10.3390/act10050094 2021

  19. [19]

    Y. Luo, K. Wu, A. Spielberg, M. Foshey, D. Rus, T. Pala- cios, and W. Matusik, Digital fabrication of pneumatic actuators with integrated sensing by machine knitting (Association for Computing Machinery, New York, NY, USA, 2022)

    work page 2022

  20. [20]

    M. Yang, F. Sun, X. Hu, and F. Sun, Knitting from na- ture: Self-sensing soft robotics enabled by all-in-one knit architectures, ACS Applied Materials & Interfaces15, 44294 (2023)

    work page 2023

  21. [21]

    Sanchez, K

    V. Sanchez, K. Mahadevan, G. Ohlson, M. Graule, M. Yuen, C. Teeple, J. McCann, K. Bertoldi, and R. Wood, 3d knitting for pneumatic soft robotics, Ad- vanced Functional Materials33(2023)

    work page 2023

  22. [22]

    du Pasquier, L

    C. du Pasquier, L. Tessmer, I. Scholl, L. Tilton, T. Chen, S. Tibbits, and A. Okamura, Haptiknit: Distributed stiff- ness knitting for wearable haptics, Science Robotics9, eado3887 (2024)

    work page 2024

  23. [23]

    Y. Zhou, X. Xin, Y. Li, Y. Zhou, R. Zhang, and L. Xu, The superior ballistic performance of highly stretchable and flexible double-face knitted fabrics (dfkf): An experi- mental investigation, Defence Technology45, 119 (2025)

    work page 2025

  24. [24]

    A. W. Marvin, 2—some mechanical properties of knitted glass laminates, Journal of the Textile Institute Transac- tions52, T21 (1961)

    work page 1961

  25. [25]

    Savci, J

    S. Savci, J. Curiskis, and M. Pailthorpe, A study of the deformation of weft-knit preforms for advanced compos- ite structures part 2: The resultant composite, Compos- ites Science and Technology60, 1943 (2000)

    work page 1943

  26. [26]

    Leong, S

    K. Leong, S. Ramakrishna, Z. Huang, and G. Bibo, The potential of knitting for engineering composites—a re- view, Composites Part A: Applied Science and Manufac- turing31, 197 (2000)

    work page 2000

  27. [27]

    N. D. Mermin, The topological theory of defects in or- dered media, Rev. Mod. Phys.51, 591 (1979)

    work page 1979

  28. [28]

    Kralj, M

    M. Kralj, M. Kralj, and S. Kralj, Topological defects in nematic liquid crystals: Laboratory of fundamental physics, Physica Status Solidi (a)218, 2000752 (2021)

    work page 2021

  29. [29]

    Z.-Y. Li, A. Dai, S.-Z. Lin, R. Zhang, and B. Li, Twist- induced networking and fast propagation of defects in three-dimensional active nematics, Phys. Rev. Lett.135, 028302 (2025)

    work page 2025

  30. [30]

    H. L. Partner, R. Nigmatullin, T. Burgermeister, K. Pyka, J. Keller, A. Retzker, M. B. Plenio, and T. E. Mehlst¨ aubler, Dynamics of topological defects in ion Coulomb crystals, New Journal of Physics15, 103013 (2013)

    work page 2013

  31. [31]

    F. Liu, W. Zhang, S. Zheng, X. Chen, and J. Tang, Com- posite of knitted fabric and soft matrix. ii. laddering, Soft Matter22, 1230 (2026)

    work page 2026

  32. [32]

    Crassous, S

    J. Crassous, S. Poincloux, and A. Steinberger, Metasta- bility of a periodic network of threads: Shapes of a knit- ted fabric, Phys. Rev. Lett.133, 248201 (2024)

    work page 2024

  33. [33]

    Crassous, Discrete-element-method model for fric- tional fibers, Phys

    J. Crassous, Discrete-element-method model for fric- tional fibers, Phys. Rev. E107, 025003 (2023)

    work page 2023

  34. [34]

    Choi and T

    K. Choi and T. Lo, An energy model of plain knitted fabric, Textile Research Journal73, 739 (2003)

    work page 2003

  35. [35]

    S. Zou, D. Therriault, and F. P. Gosselin, Toughening elastomers via microstructured thermoplastic fibers with sacrificial bonds and hidden lengths, Extreme Mechanics Letters43, 101208 (2021). 7 Appendix A: Description of Supplementary Movies We provide two movies of propagating ladder defects: in commercial tights and the experimental Jersey knitted fabr...

    work page 2021

  36. [36]

    Stretching protocols We now detail the stretching steps prior to making a hole. The first step is to bring the knitted fabric from the loose configuration in which it is mounted on the frame of the bi-axial tensile machine, to the starting configu- ration at the target ∆yspacing and a ∆x min reference spacing. From the initial loose configuration, a stret...

    work page

  37. [37]

    x!"xmin (mm)(b) 0 2 4 6 8 10Fx (N) (c) 0 100 200 300 400 500 600 700 800 t (s) 0 10 20 30

    Piercing protocol On most knitted samples, four laddering experiments are performed at the same vertical stretching ∆yand with increasing initial forceF ini x . The topology detects 8 0 1 2 3 4 5 6 Fx (N) (a) 0 100 200 300 400 500 600 700 800 t (s) 0 5 10 15 20"x!"xmin (mm)(b) 0 2 4 6 8 10Fx (N) (c) 0 100 200 300 400 500 600 700 800 t (s) 0 10 20 30"x!"xm...

    work page