pith. machine review for the scientific record. sign in

arxiv: 2602.00147 · v2 · submitted 2026-01-29 · ❄️ cond-mat.soft · cond-mat.mtrl-sci· physics.bio-ph

Recognition: 2 theorem links

· Lean Theorem

Plasticity, hysteresis, and recovery mechanisms in spider silk fibers

Renata Oliv\'e , Jos\'e P\'erez-Riguero , Noy Cohen
Authors on Pith no claims yet

Pith reviewed 2026-05-16 09:54 UTC · model grok-4.3

classification ❄️ cond-mat.soft cond-mat.mtrl-sciphysics.bio-ph
keywords spider silkplasticityhysteresisrecovery mechanismsentropic chainselasto-plastic networkcyclic loadingmicrostructural evolution
0
0 comments X

The pith

Spider silk decouples its response into elasto-plastic bonds and entropic chains under cyclic loading.

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

Spider silk fibers exhibit yielding, energy-dissipating loops, and gradual stiffening after repeated stretches. The paper traces these effects to two parallel microstructural networks that evolve during loading and unloading. An elasto-plastic network of inter- and intramolecular bonds supplies initial stiffness until yield, after which load transfers to polypeptide chains that stretch entropically for large extensions. Unloading shortens the chains through entropy until residual stretch remains, after which reorganization and bond reformation lock the fiber into a stiffer equilibrium. The resulting energy-based model reproduces experimental cyclic tests on Argiope bruennichi dragline silk and links the observed recovery directly to these microstructural steps.

Core claim

The response is decoupled into two parallel networks: (1) an elasto-plastic network of inter- and intramolecular bonds governing the initial stiffness and yield stress, and (2) an elastic network of entropic chains that enable large deformations. Unloading is driven by entropic shortening until a traction free state with residual stretch is achieved. Subsequently, the fiber recovers as chains reorganize and bonds reform, locking the microstructure into a new stable equilibrium that increases stiffness in subsequent cycles. The model is validated against experimental data from Argiope bruennichi dragline silk.

What carries the argument

Two parallel networks: an elasto-plastic network of inter- and intramolecular bonds that sets initial stiffness and yield, and an elastic network of entropic polypeptide chains that accommodates large deformations.

If this is right

  • The model reproduces the full loading-unloading-relaxation cycle observed in silk fibers.
  • Recovery restores and enhances stiffness by locking the microstructure into a new equilibrium.
  • Hysteresis arises from bond dissociation during yield followed by entropic chain deformation.
  • The framework supplies a predictive route for designing synthetic fibers with tailored cyclic properties.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Analogous dual-network separation could govern recoverable plasticity in other protein-based or synthetic fibers.
  • Materials engineers might exploit the same bond-chain split to create fibers that self-stiffen after initial use.
  • Varying chain length or bond density in the model could predict how different spider species tune yield and recovery.
  • The separation suggests a general template for tough biomaterials that adapt under repeated mechanical demand.

Load-bearing premise

Unloading is driven purely by entropic shortening of chains until a traction-free state with residual stretch is reached, and subsequent recovery occurs solely through chain reorganization and bond reformation that locks the microstructure into a new stable equilibrium.

What would settle it

Direct observation that residual stretch after unloading deviates from entropic-chain predictions or that stiffness recovery occurs without measurable bond reformation would falsify the proposed decoupling.

Figures

Figures reproduced from arXiv: 2602.00147 by Jos\'e P\'erez-Riguero, Noy Cohen, Renata Oliv\'e.

Figure 1
Figure 1. Figure 1: Microstructural evolution of the spider silk network during a uniaxial cyclic loading [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Schematic decomposition of the macroscopic mechanical response of spider silk fibers [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: (a) The unloading and (b) the relaxation mechanisms governing the recovery of the [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Loading of a spider silk fiber: (a) true stress [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Cyclic loading of a spider silk fiber: true stress [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗
read the original abstract

Spider silk is a remarkable biomaterial with exceptional stiffness, strength, and toughness stemming from a unique microstructure. While recent studies show that silk fibers exhibit plasticity, hysteresis, and recovery under cyclic loading, the underlying microstructural mechanisms are not yet fully understood. In this work, we propose a mechanism explaining the loading-unloading-relaxation response through microstructural evolution: initial loading distorts intermolecular bonds, resulting in a linear elastic regime. Upon reaching the yield stress, these bonds dissociate and the external load is transferred to the polypeptide chains, which deform entropically to allow large deformations. Unloading is driven by entropic shortening until a traction free state with residual stretch is achieved. Subsequently, the fiber recovers as chains reorganize and bonds reform, locking the microstructure into a new stable equilibrium that increases stiffness in subsequent cycles. Following these mechanisms, we develop a microscopically motivated, energy-based model that captures the macroscopic response of silk fibers under cyclic loading. The response is decoupled into two parallel networks: (1) an elasto-plastic network of inter- and intramolecular bonds governing the initial stiffness and yield stress, and (2) an elastic network of entropic chains that enable large deformations. The model is validated against experimental data from Argiope bruennichi dragline silk. The findings from this work are three-fold: (1) explaining the mechanisms that govern hysteresis and recovery and linking them to microstructural evolution; (2) quantifying the recovery process of the fiber, which restores and enhances mechanical properties; and (3) establishing a predictive foundation for engineering synthetic fibers with customized properties.

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 / 1 minor

Summary. The manuscript proposes a mechanism and corresponding energy-based constitutive model for the cyclic loading response of spider silk, attributing plasticity and yield to dissociation of inter- and intramolecular bonds, large-strain deformation and unloading to entropic chain retraction, and recovery to chain reorganization plus bond reformation. The response is formulated as two parallel networks (elasto-plastic bond network plus entropic-chain network) and is stated to be validated on Argiope bruennichi dragline silk data, with the model claimed to quantify hysteresis, residual stretch, and stiffening upon recovery.

Significance. If the parallel-network decoupling and the asserted separation of time scales between entropic retraction and bond kinetics can be shown to follow from the energy functional without additional dissipation channels, the work supplies a microstructural rationale for the observed recovery-induced stiffening and offers a predictive route toward designing synthetic fibers whose cyclic properties can be tuned by controlling bond and chain parameters.

major comments (3)
  1. [Abstract] Abstract: the statement that the model is 'validated against experimental data from Argiope bruennichi dragline silk' supplies no information on how the free parameters (yield stress of the bond network, contour length and persistence length of the entropic chains) were determined, what error metric was minimized, or whether any cycles were withheld for out-of-sample testing; without these details the central claim that the model captures the mechanisms rather than merely reproducing the calibration curves cannot be assessed.
  2. [Model development] Model construction (parallel-network decoupling): the unloading path is asserted to terminate at a traction-free residual stretch determined solely by entropic shortening of the chain network; the manuscript must derive from the total energy functional that viscous relaxation or intra-chain friction on the same time scale is negligible, because any such dissipation would shift the residual stretch that serves as the initial condition for the subsequent bond-reformation step.
  3. [Recovery section] Recovery mechanism: the claim that chain reorganization and bond reformation 'lock the microstructure into a new stable equilibrium that increases stiffness in subsequent cycles' is load-bearing for the recovery prediction, yet the manuscript provides no explicit evolution equation or energy barrier for the reformation kinetics that would allow quantitative comparison with the observed stiffening rate.
minor comments (1)
  1. [Abstract] The abstract lists three findings but the numbering in the text should be checked for consistency with the section headings.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We appreciate the referee's thorough review and constructive feedback on our manuscript. We address each of the major comments below, providing clarifications and indicating where revisions will be made to strengthen the paper.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the statement that the model is 'validated against experimental data from Argiope bruennichi dragline silk' supplies no information on how the free parameters (yield stress of the bond network, contour length and persistence length of the entropic chains) were determined, what error metric was minimized, or whether any cycles were withheld for out-of-sample testing; without these details the central claim that the model captures the mechanisms rather than merely reproducing the calibration curves cannot be assessed.

    Authors: We agree that additional details on the parameter fitting procedure are necessary to substantiate the validation claim. In the revised manuscript, we will modify the abstract to briefly mention that parameters were determined by minimizing the mean squared error between model predictions and experimental stress-strain curves using the full dataset from Argiope bruennichi dragline silk. We will also add a dedicated subsection in the methods or results detailing the optimization process, including the error metric and justification for not performing out-of-sample testing due to the limited number of experimental cycles available. This will allow readers to better assess the model's predictive capability versus its fitting accuracy. revision: yes

  2. Referee: [Model development] Model construction (parallel-network decoupling): the unloading path is asserted to terminate at a traction-free residual stretch determined solely by entropic shortening of the chain network; the manuscript must derive from the total energy functional that viscous relaxation or intra-chain friction on the same time scale is negligible, because any such dissipation would shift the residual stretch that serves as the initial condition for the subsequent bond-reformation step.

    Authors: The referee correctly identifies that the manuscript asserts the dominance of entropic retraction without an explicit derivation from the energy functional. To address this, we will revise the model development section to include a derivation showing that, under the assumed separation of time scales (where bond dissociation occurs much faster than chain relaxation), the contribution of viscous dissipation terms to the total energy is negligible during unloading. This will be shown by comparing the magnitudes of the entropic and dissipative potentials, confirming that the residual stretch is indeed determined primarily by the entropic chain network. We believe this addition will rigorously support the parallel-network decoupling. revision: yes

  3. Referee: [Recovery section] Recovery mechanism: the claim that chain reorganization and bond reformation 'lock the microstructure into a new stable equilibrium that increases stiffness in subsequent cycles' is load-bearing for the recovery prediction, yet the manuscript provides no explicit evolution equation or energy barrier for the reformation kinetics that would allow quantitative comparison with the observed stiffening rate.

    Authors: We acknowledge that the recovery mechanism description lacks an explicit kinetic equation, which limits quantitative validation of the stiffening rate. In the revised version, we will introduce a simple first-order kinetic model for bond reformation, incorporating an energy barrier derived from the bond dissociation energy in the elasto-plastic network. This will be coupled to the chain reorganization term, enabling direct comparison with experimental recovery data and providing a predictive framework for the observed stiffening. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper motivates a parallel-network model from proposed microstructural mechanisms (bond dissociation followed by entropic chain deformation and recovery via reorganization), then states that the model is validated against experimental cyclic-loading data on Argiope bruennichi silk. No equations, parameter-fitting procedure, or self-citation chain is exhibited in the provided text that would reduce any claimed prediction to a fit performed on the identical target curves. The decoupling into elasto-plastic and entropic networks is presented as a direct consequence of the described mechanisms rather than an ansatz smuggled in or a self-definitional renaming. This is the common honest case of a self-contained phenomenological construction with external validation.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The model rests on the assumption that bond dissociation is the sole source of yield and that chain entropy alone drives unloading and recovery. No new particles or forces are postulated, but several material constants must be chosen or fitted.

free parameters (2)
  • yield stress of inter/intramolecular bonds
    Determines the transition from linear elastic to large-deformation regime; must be fitted to the first loading curve.
  • entropic chain parameters (contour length, persistence length)
    Control the large-strain response and residual stretch after unloading; calibrated to experimental unloading curves.
axioms (2)
  • domain assumption Unloading follows purely entropic chain shortening to a traction-free state with residual stretch.
    Invoked to explain the observed hysteresis loop without additional dissipative mechanisms.
  • domain assumption Recovery occurs by chain reorganization and bond reformation that increases subsequent stiffness.
    Used to account for the stiffening observed in later cycles.

pith-pipeline@v0.9.0 · 5600 in / 1547 out tokens · 38350 ms · 2026-05-16T09:54:39.633764+00:00 · methodology

discussion (0)

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

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

62 extracted references · 62 canonical work pages

  1. [1]

    R., Perez-Rigueiro, J., and Guinea, G

    Elices, M., Plaza, G. R., Perez-Rigueiro, J., and Guinea, G. V . (2011) The hidden link be- tween supercontraction and mechanical behavior of spider silks.Journal of the Mechanical Behavior of Biomedical Materials 4, 658 – 669

    work page 2011

  2. [2]

    Y ., Narayanan, J., Li, L., Lim, M

    Du, N., Liu, X. Y ., Narayanan, J., Li, L., Lim, M. L. M., and Li, D. (2006) Design of superior spider silk: from nanostructure to mechanical properties.Biophysical journal 91, 4528–4535

    work page 2006

  3. [3]

    C., and Frische, S

    V ollrath, F., Holtet, T., Thogersen, H. C., and Frische, S. (1996) Structural organization 19 of spider silk.Proceedings of the Royal Society of London. Series B: Biological Sciences 263, 147–151

    work page 1996

  4. [4]

    M., Denny, M

    Gosline, J. M., Denny, M. W., and DeMont, M. E. (1984) Spider silk as rubber.Nature 309, 551–552

    work page 1984

  5. [5]

    (2008) The elaborate structure of spider silk: structure and function of a natural high performance fiber.Prion 2, 154–161

    Roemer, L., and Scheibel, T. (2008) The elaborate structure of spider silk: structure and function of a natural high performance fiber.Prion 2, 154–161

    work page 2008

  6. [6]

    L., Cherry, B

    Yarger, J. L., Cherry, B. R., and van der Vaart, A. (2018) Uncovering the structure-function relationship in spider silk.Nature Reviews Materials 3, 18008

    work page 2018

  7. [7]

    W., and Morosoff, N

    Work, R. W., and Morosoff, N. (1982) A Physico-Chemical Study of the Supercontraction of Spider Major Ampullate Silk Fibers.Textile Research Journal 52, 349–356

    work page 1982

  8. [8]

    Cohen, N., Levin, M., and Eisenbach, C. D. (2021) On the Origin of Supercontraction in Spider Silk.Biomacromolecules 22, 993–1000

    work page 2021

  9. [9]

    V ., Elices, M., Perez-Rigueiro, J., and Plaza, G

    Guinea, G. V ., Elices, M., Perez-Rigueiro, J., and Plaza, G. R. (2005) Stretching of su- percontracted fibers: a link between spinning and the variability of spider silk.Journal of Experimental Biology 208, 25–30

    work page 2005

  10. [10]

    R., Guinea, G

    Plaza, G. R., Guinea, G. V ., Perez-Rigueiro, J., and Elices, M. (2006) Thermo-hygro- mechanical behavior of spider dragline silk: Glassy and rubbery states.Journal of Polymer Science Part B: Polymer Physics 44, 994–999

    work page 2006

  11. [11]

    M., and Puglisi, G

    Fazio, V ., De Tommasi, D., Pugno, N. M., and Puglisi, G. (2022) Spider silks mechanics: Predicting humidity and temperature effects.Journal of the Mechanics and Physics of Solids 164, 104857

    work page 2022

  12. [12]

    Perez-Rigueiro, J., Elices, M., and Guinea, G. V . (2003) Controlled supercontraction tai- lors the tensile behaviour of spider silk.Polymer 44, 3733–3736

    work page 2003

  13. [13]

    (2023) The underlying mechanisms behind the hydration-induced and mechan- ical response of spider silk.Journal of the Mechanics and Physics of Solids 172, 105141

    Cohen, N. (2023) The underlying mechanisms behind the hydration-induced and mechan- ical response of spider silk.Journal of the Mechanics and Physics of Solids 172, 105141. 20

    work page 2023

  14. [14]

    M., and Puglisi, G

    Fazio, V ., Pugno, N. M., and Puglisi, G. (2023) Water to the ropes: A predictive model for the supercontraction stress of spider silks.Extreme Mechanics Letters 61, 102010

    work page 2023

  15. [15]

    Xu, G., Gong, L., Yang, Z., and Liu, X. Y . (2014) What makes spider silk fibers so strong? From molecular-crystallite network to hierarchical network structures.Soft Matter 10, 2116–2123

    work page 2014

  16. [16]

    C., Yu, M., Zheng, S., Yu, L., Liu, J., He, Y ., Dun- stan, D

    Liu, D., Tarakanova, A., Hsu, C. C., Yu, M., Zheng, S., Yu, L., Liu, J., He, Y ., Dun- stan, D. J., and Buehler, M. J. (2019) Spider dragline silk as torsional actuator driven by humidity.Science Advances 5

    work page 2019

  17. [17]

    Cohen, N., and Eisenbach, C. D. (2022) Humidity-Driven Supercontraction and Twist in Spider Silk.Phys. Rev. Lett. 128, 098101

    work page 2022

  18. [18]

    (2021) Designing of spider silk proteins for human induced pluripotent stem cell-based cardiac tissue engineering

    Esser, T., Trossmann, V ., Lentz, S., Engel, F., and Scheibel, T. (2021) Designing of spider silk proteins for human induced pluripotent stem cell-based cardiac tissue engineering. Materials Today Bio 11, 100114

    work page 2021

  19. [19]

    S., Trossmann, V

    Koeck, K. S., Trossmann, V . T., and Scheibel, T. (2024) 3D Printed and Recombinant Spi- der Silk Particle Reinforced Collagen Composite Scaffolds for Soft Tissue Engineering. Advanced Functional Materials 35

    work page 2024

  20. [20]

    (2021) Spidroin-Based Biomaterials in Tissue Engineering: General Approaches and Potential Stem Cell Therapies.Stem Cells International 2021, 1–16

    Zhang, Q., Li, M., Hu, W., Wang, X., and Hu, J. (2021) Spidroin-Based Biomaterials in Tissue Engineering: General Approaches and Potential Stem Cell Therapies.Stem Cells International 2021, 1–16

    work page 2021

  21. [21]

    (2018) Fracture toughness and fatigue behavior of spi- der silk and S-glass epoxy composites: An FEM approach.Materials Today: Proceedings 5, 2627–2634

    Archana, T., Anand Kumar, S., Elangovan, R., Rammohan, Y ., Dumpala, R., Ratna Sunil, B., and Kumar, R. (2018) Fracture toughness and fatigue behavior of spi- der silk and S-glass epoxy composites: An FEM approach.Materials Today: Proceedings 5, 2627–2634

    work page 2018

  22. [22]

    (2016) Spider silk as a blueprint for greener materials: a review

    Lefevre, T., and Auger, M. (2016) Spider silk as a blueprint for greener materials: a review. International Materials Reviews 61, 127–153. 21

    work page 2016

  23. [23]

    G., Lewis, J

    Qin, Z., Compton, B. G., Lewis, J. A., and Buehler, M. J. (2015) Structural optimization of 3D-printed synthetic spider webs for high strength.Nature Communications 6, 7038

    work page 2015

  24. [24]

    Keten, S., Xu, Z., Ihle, B., and Buehler, M. J. (2010) Nanoconfinement controls stiffness, strength and mechanical toughness of beta-sheet crystals in silk.Nature Materials 9, 359– 367

    work page 2010

  25. [25]

    M., Redaelli, A., and Buehler, M

    Nova, A., Keten, S., Pugno, N. M., Redaelli, A., and Buehler, M. J. (2010) Molecular and Nanostructural Mechanisms of Deformation, Strength and Toughness of Spider Silk Fibrils.Nano Lett. 10, 2626–2634

    work page 2010

  26. [26]

    (2024) Deformation and failure mechanisms in spider silk fibers

    Olive, R., and Cohen, N. (2024) Deformation and failure mechanisms in spider silk fibers. Journal of the Mechanics and Physics of Solids 182, 105480

    work page 2024

  27. [27]

    R., Blackledge, T

    Madurga, R., Plaza, G. R., Blackledge, T. A., Guinea, G. V ., Elices, M., and Perez- Rigueiro, J. (2016) Material properties of evolutionary diverse spider silks described by variation in a single structural parameter.Scientific Reports 6, 18991

    work page 2016

  28. [28]

    R., Perez-Rigueiro, J., Riekel, C., Perea, G

    Plaza, G. R., Perez-Rigueiro, J., Riekel, C., Perea, G. B., Agullo-Rueda, F., Burgham- mer, M., Guinea, G. V ., and Elices, M. (2012) Relationship between microstructure and mechanical properties in spider silk fibers: identification of two regimes in the microstruc- tural changes.Soft Matter 8, 6015–6026

    work page 2012

  29. [29]

    D., Hess, S., V ollrath, F., and Meier, B

    van Beek, J. D., Hess, S., V ollrath, F., and Meier, B. H. (2002) The molecular structure of spider dragline silk: Folding and orientation of the protein backbone.Proc Natl Acad Sci USA 99, 10266

    work page 2002

  30. [30]

    Y ., Li, Y ., and Xu, H

    Du, N., Yang, Z., Liu, X. Y ., Li, Y ., and Xu, H. Y . (2011) Structural Origin of the Strain- Hardening of Spider Silk.Adv. Funct. Mater. 21, 772–778

    work page 2011

  31. [31]

    Z., and V ollrath, F

    Madsen, B., Shao, Z. Z., and V ollrath, F. (1999) Variability in the mechanical properties of spider silks on three levels: interspecific, intraspecific and intraindividual.International Journal of Biological Macromolecules 24, 301–306. 22

    work page 1999

  32. [32]

    (2005) Extended wet-spinning can modify spider silk properties.Chem

    Liu, Y ., Shao, Z., and V ollrath, F. (2005) Extended wet-spinning can modify spider silk properties.Chem. Commun.2489–2491

    work page 2005

  33. [33]

    V ., Perez-Rigueiro, J., and Plaza, G

    Elices, M., Guinea, G. V ., Perez-Rigueiro, J., and Plaza, G. R. (2005) Finding inspiration in argiope trifasciata spider silk fibers.JOM 57, 60–66

    work page 2005

  34. [34]

    (2025) Employing spinning conditions to control the mechanical response of spider silk fibers.International Journal of Solids and Structures 322, 113592

    Olive, R., and Cohen, N. (2025) Employing spinning conditions to control the mechanical response of spider silk fibers.International Journal of Solids and Structures 322, 113592

    work page 2025

  35. [35]

    (1994) Molecular Modeling of Spider Silk Elasticity.Macromolecules 27, 7378–7381

    Termonia, Y . (1994) Molecular Modeling of Spider Silk Elasticity.Macromolecules 27, 7378–7381

    work page 1994

  36. [36]

    (2025) Modeling of protein networks reveals factors affecting stiffness, yield stress, and strain stiffening in silk fibers.Acta Biomaterialia 208, 402–410

    Cohen, N., and Zhang, F. (2025) Modeling of protein networks reveals factors affecting stiffness, yield stress, and strain stiffening in silk fibers.Acta Biomaterialia 208, 402–410

    work page 2025

  37. [37]

    R., Arnedo, M

    Elices, M., Plaza, G. R., Arnedo, M. A., Perez-Rigueiro, J., Torres, F. G., and Guinea, G. V . (2009) Mechanical Behavior of Silk During the Evolution of Orb-Web Spinning Spiders. Biomacromolecules 10, 1904–1910

    work page 2009

  38. [38]

    (2006) The spinning processes for spider silk.Soft Matter 2, 448–451

    Chen, X., Shao, Z., and V ollrath, F. (2006) The spinning processes for spider silk.Soft Matter 2, 448–451

    work page 2006

  39. [39]

    J., Holland, C., Shao, Z., and V ollrath, F

    Young, R. J., Holland, C., Shao, Z., and V ollrath, F. (2021) Spinning conditions affect structure and properties of Nephila spider silk.MRS Bulletin 46, 915–924

    work page 2021

  40. [40]

    V ., and Perez- Rigueiro, J

    Jiang, P., Wu, L., Hu, M., Tang, S., Qiu, Z., Lv, T., Elices, M., Guinea, G. V ., and Perez- Rigueiro, J. (2023) Variation in the Elastic Modulus and Increased Energy Dissipation In- duced by Cyclic Straining of Argiope bruennichi Major Ampullate Gland Silk.Biomimet- ics 8

    work page 2023

  41. [41]

    (2007) Mechanical Properties of Spider Dragline Silk: Humidity, Hysteresis, and Relaxation.Biophysical Journal 93, 4425–4432

    Vehoff, T., Glisovic, A., Schollmeyer, H., Zippelius, A., and Salditt, T. (2007) Mechanical Properties of Spider Dragline Silk: Humidity, Hysteresis, and Relaxation.Biophysical Journal 93, 4425–4432. 23

    work page 2007

  42. [42]

    (2015) Energy absorption of spider orb webs during prey capture: A mechanical analysis.Journal of Bionic Engineering 12, 453–463

    Yu, H., Yang, J., and Sun, Y . (2015) Energy absorption of spider orb webs during prey capture: A mechanical analysis.Journal of Bionic Engineering 12, 453–463

    work page 2015

  43. [43]

    D., Puglisi, G., and Saccomandi, G

    Tommasi, D. D., Puglisi, G., and Saccomandi, G. (2010) Damage, Self-Healing, and Hys- teresis in Spider Silks.Biophysical Journal 98, 1941–1948

    work page 2010

  44. [44]

    (2020) Dynamic response of spider orb webs subject to prey impact.International Journal of Mechanical Sciences 186, 105899

    Jiang, Y ., and Nayeb-Hashemi, H. (2020) Dynamic response of spider orb webs subject to prey impact.International Journal of Mechanical Sciences 186, 105899

    work page 2020

  45. [45]

    (2020) A new constitutive model for dragline silk.In- ternational Journal of Solids and Structures 202, 99–110

    Jiang, Y ., and Nayeb-Hashemi, H. (2020) A new constitutive model for dragline silk.In- ternational Journal of Solids and Structures 202, 99–110

    work page 2020

  46. [46]

    P., Kulkarni, A., and Markert, B

    Patil, S. P., Kulkarni, A., and Markert, B. (2022) Mechanical Properties of Dragline Silk Fiber Using a Bottom-Up Approach.Journal of Composites Science 6, 95

    work page 2022

  47. [47]

    L., Arnedo, M., Ruiz-Leon, Y ., Gonzalez- Nieto, D., Rojo, F

    Blamires, S., Lozano-Picazo, P., Bruno, A. L., Arnedo, M., Ruiz-Leon, Y ., Gonzalez- Nieto, D., Rojo, F. J., Elices, M., Guinea, G. V ., and Perez-Rigueiro, J. (2023) The Spider Silk Standardization Initiative (S3I): A powerful tool to harness biological variability and to systematize the characterization of major ampullate silk fibers spun by spiders fro...

    work page 2023

  48. [48]

    B., Fossey, S

    Oroudjev, E., Soares, J., Arcidiacono, S., Thompson, J. B., Fossey, S. A., and Hansma, H. G. (2002) Segmented nanofibers of spider dragline silk: Atomic force mi- croscopy and single-molecule force spectroscopy.Proceedings of the National Academy of Sciences 99, 6460–6465

    work page 2002

  49. [49]

    T., and Jelinski, L

    Grubb, D. T., and Jelinski, L. W. (1997) Fiber Morphology of Spider Silk: The Effects of Tensile Deformation.Macromolecules 30, 2860–2867

    work page 1997

  50. [50]

    V ., Perez-Rigueiro, J., Plaza, G

    Guinea, G. V ., Perez-Rigueiro, J., Plaza, G. R., and Elices, M. (2006) V olume Constancy during Stretching of Spider Silk.Biomacromolecules 7, 2173–2177. 24

    work page 2006

  51. [51]

    Jiang, P., Wu, L.-H., Lv, T.-Y ., Tang, S.-S., Hu, M.-L., Qiu, Z.-m., Guo, C., and Jose, P.-R. (2023) Memory effect of spider major ampullate gland silk in loading-unloading cycles and the structural connotations.Journal of the Mechanical Behavior of Biomedical Mate- rials 146, 106031

    work page 2023

  52. [52]

    V ., Perez-Rigueiro, J., and Jiang, P

    Hong, Y .-q., Zhang, X.-r., Wu, L.-H., Lv, T.-Y ., Guinea, G. V ., Perez-Rigueiro, J., and Jiang, P. (2025) Analysis of spider silk in loading-unloading cycles using Raman spec- troscopy based on molecular bioinformatics of spidrion.Polymer 317, 127910

    work page 2025

  53. [53]

    S., and Boyce, M

    Bergstrom, J. S., and Boyce, M. C. (1998) Constitutive modeling of the large strain time- dependent behavior of elastomers.Journal of the Mechanics and Physics of Solids 46, 931–954

    work page 1998

  54. [54]

    Flory, P. J. (1942) Thermodynamics of High Polymer Solutions.The Journal of Chemical Physics 10, 51–61

    work page 1942

  55. [55]

    A., Correia, J

    Bernard, C. A., Correia, J. P. M., Ahzi, S., and Bahlouli, N. (2016) Numerical implemen- tation of an elastic-viscoplastic constitutive model to simulate the mechanical behaviour of amorphous polymers.International Journal of Material Forming 10, 607–621

    work page 2016

  56. [56]

    K., and Kim, J

    Cho, C., Poornesh, K. K., and Kim, J. (2015) Micromechanically motivated constitutive model to characterize the hygrothermomechanical response of polymer electrolyte mem- brane.Journal of Mechanical Science and Technology 29, 1145–1150

    work page 2015

  57. [57]

    F., and Bouklas, N

    Fontenele, F. F., and Bouklas, N. (2023) Understanding the inelastic response of collagen fibrils: A viscoelastic-plastic constitutive model.Acta Biomaterialia 163, 78–90

    work page 2023

  58. [58]

    M., Srivastava, V ., and Chester, S

    Anand, L., Ames, N. M., Srivastava, V ., and Chester, S. A. (2009) A thermo-mechanically coupled theory for large deformations of amorphous polymers. Part I: Formulation.Inter- national Journal of Plasticity 25, 1474–1494

    work page 2009

  59. [59]

    Cohen, N., and Eisenbach, C. D. (2019) A microscopically motivated model for the 25 swelling-induced drastic softening of hydrogen-bond dominated biopolymer networks. Acta Biomaterialia 96, 303 – 309

    work page 2019

  60. [60]

    (1991) A Padé approximant to the inverse Langevin function.Rheologica Acta 30, 270–273

    Cohen, A. (1991) A Padé approximant to the inverse Langevin function.Rheologica Acta 30, 270–273

    work page 1991

  61. [61]

    Cohen, N., and McMeeking, R. M. (2019) On the swelling induced microstructural evo- lution of polymer networks in gels.Journal of the Mechanics and Physics of Solids 125, 666 – 680

    work page 2019

  62. [62]

    Bažant, P., and Oh, B. H. (1986) Efficient Numerical Integration on the Surface of a Sphere.ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Ange- wandte Mathematik und Mechanik 66, 37–49

    work page 1986