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REVIEW 4 major objections 6 minor 1 cited by

Harnessing Discrete Differential Geometry: A Virtual Playground for the Bilayer Soft Robotics

T0 review · 4 major / 6 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read Two coupled elastic rods can simulate bilayer soft robots, matching experiments in gripping, crawling, jumping, and swimming.

desk verdict A plausible DER-based bilayer soft robot simulator with a solid Timoshenko validation, but a likely factor-of-two error in the interface coupling and unsupported quantitative claims make it conditional. read the letter →

arxiv 2502.00714 v1 pith:PLFJJTIB submitted 2025-02-02 cs.RO cond-mat.soft

Jiahao Li , Dezhong Tong , Zhuonan Hao , Yinbo Zhu , Hengan Wu , Mingchao Liu , Weicheng Huang This is my paper · ORCID
classification cs.ROcond-mat.soft
keywords softroboticsbilayerstructuresdiscreteelasticroddifferentialgeometrystrainmismatchfrictionalcontactfluiddraglocomotionsimulation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper argues that a bilayer soft robot can be simulated as two discrete elastic rods held together by penalty springs, capturing the full range of dynamic behaviors at lower cost than a finite element treatment. The authors build a simulation environment around the Discrete Elastic Rod (DER) model, coupling the two centerlines with energy penalties that enforce near-equal translation and rotation at the interface. They validate the model against Timoshenko's classical bilayer bending formula and against experiments for four robot archetypes. The payoff would be a fast, predictive virtual playground for designing bilayer soft robots that interact with their environment.

What carries the argument

The central object is the Discrete Elastic Rod (DER) model applied to two slender layers, each discretized into nodes with edge vectors and material frames. Stretching energy is quadratic in edge strain, while bending and twisting energy are quadratic in material curvatures and discrete twist. The load-bearing mechanism is the coupling element: a penalty energy $C_T$ projects the relative displacement of the two centerlines onto an averaged material frame and penalizes deviation from the total thickness $h$, while a second penalty energy $C_R$ penalizes relative bending and twisting between the edge frames using the same curvature-binormal construction as the single-rod bending energy. A smooth log-barrier normal force with a smoothed Coulomb friction law handles contact, and an anisotropic quadratic drag model captures fluid interaction for swimming. Time integration is implicit, solved by Newton-Raphson iteration.

What would settle it

A concrete check would be to measure local through-thickness and interfacial shear strain in a bilayer ribbon under dynamic bending and twisting using digital image correlation or embedded markers, and compare those local strains with the simulation's predictions. If the measured local interface tractions deviate systematically from the penalty-spring forces while the integrated curvature still matches, the coupling model would be shown to miss the mechanics it claims to capture.

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Extended reading notes

Core claim

The central claim is that the mechanical essence of a bilayer actuator is a pair of Kirchhoff rods whose centerlines are held together by penalty energies: one term penalizing relative translation of the two centerlines in the material frame, and one term penalizing relative bending and twisting. With these couplings, the Discrete Elastic Rod formulation reproduces planar bending matching the Timoshenko prediction, 3D helical morphing, and the experimentally observed kinematics of gripping, inchworm and dual-leg crawling, jumping, and jellyfish-like swimming when frictional contact and fluid drag are added. The paper also claims superior convergence compared with finite element methods, particularly in contact interactions, and releases the simulator as a general tool for bilayer soft robotics.

Load-bearing premise

The load-bearing premise is that two one-dimensional rod centerlines connected by penalty springs with stiffnesses $K_T/EA=100$ and $K_R/EI=1000$ transfer stress across a real adhesive interface faithfully enough to reproduce local bending and twisting, even though only integrated bending curvature is validated.

Editorial extensions

If this is right

  • Bilayer soft robot designs could be simulated without full 3D finite element meshes, enabling rapid iteration over geometry and actuation parameters.
  • The same simulator covers dry behaviors such as gripping, crawling, and jumping, and wet behaviors such as swimming by switching the contact and drag models on or off.
  • Strain mismatch can be scripted over time, so hygroscopic, photothermal, and shape-memory-alloy-driven actuators can all be represented as time-varying reference strains in one environment.
  • Because the coupling permits different discretizations and stiffnesses for the two layers, asymmetric and heterogeneous bilayers can also be explored.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the penalty coupling is faithful, the same environment could be extended to multi-layer laminates by stacking three or more rods with pairwise penalties, opening up programmable morphing beyond bilayers.
  • Because the model resolves only centerlines, it predicts bulk deformation but not stress concentrations near adhesive edges; a hybrid approach that hands off local interface stresses to a shell or continuum model would be a natural next test.
  • The validation compares integrated curvature and whole-body kinematics; a direct measurement of interface shear or twist during dynamic motion would be a sharper test of the penalty stiffness assumptions.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. This paper presents a Discrete Elastic Rod (DER) simulation framework for bilayer soft robots. Two Kirchhoff rods, representing the centerlines of an active and a passive layer, are coupled at the interface by penalty springs that penalize relative translation and rotation; an implicit time integrator is combined with frictional contact and fluid drag models. The framework is checked against Timoshenko's 2D bilayer bending formula and a qualitative 3D helix example, then used to simulate gripping, crawling, jumping, and swimming. The paper claims that the environment is accurate, efficient, and predictive for bilayer soft robotics, with open-source code provided.

Significance. If the claims are substantiated, the framework would be a useful open-source platform for simulating bilayer soft robots without full FEM meshes, including contact-rich locomotion, and the Timoshenko benchmark gives an independent check on the 2D bending mechanics. Concrete strengths are the provided code repository, the 2D benchmark against a classical analytical solution, a simplified 2D beam model in Appendix A, and demonstrations spanning four distinct robot behaviors. However, the evidence as presented does not yet support the stronger claims: the 2D validation lacks quantitative error metrics, the 3D validation is purely qualitative, the locomotion parameters appear fitted to reproduce the experiments, and the interface coupling in Eq. (19) appears to enforce the wrong rest separation, which would make the reference state pre-stressed and undermine the physical interpretation of the validation.

major comments (4)
  1. [Section 2, Eq. (19)] The translation penalty energy in Eq. (19) sets the rest separation between the two rod centerlines to h = h1 + h2. Since the centerlines are the midplanes of the two layers, their undeformed separation is h1/2 + h2/2 = h/2. With the Table 1 parameters (h1 = h2 = 1 mm), the reference configuration therefore carries a residual penalty energy of order (1/2)K_T(1 mm)^2 and a nonzero initial force, so the 'non-translation constraint' as printed does not describe a stress-free adhesive interface. Because the lever arm between the active and passive centerlines enters the bending response compared in Eq. (30), either the printed equation is wrong, or the code uses the correct h/2 and the validation is not produced by the model as written. This must be clarified and the 2D validation re-run or re-interpreted before the central physical-fidelity claim can be assessed.
  2. [Abstract and Section 3.1] The abstract and Section 1 claim that the DER approach offers 'superior convergence compared to conventional methods like FEM, particularly in handling contact interactions,' but no FEM comparison, mesh-convergence study, time-step study, or runtime comparison is presented anywhere in the manuscript. Figure 3 reports only a visual match of simulation points to the Timoshenko curve, without error bars or numerical error values. This convergence claim should either be substantiated with a quantitative benchmark or removed and replaced by a more modest statement about computational efficiency.
  3. [Section 3.2] The 3D validation is qualitative: it shows before/after snapshots of a helical bilayer but provides no comparison with an analytical solution, an experimental measurement, or quantitative quantities such as pitch, curvature, and twist. Calling this a 'validation' overstates what is demonstrated. The authors should either add quantitative measures and a comparison target or relabel the subsection as a demonstration of 3D morphing capability.
  4. [Sections 4.2 and 4.4, Table 1] The crawling simulations use forward/backward friction coefficients of 0.3/0.6, and the swimming simulation uses drag coefficients C_d^∥ = 0.01 and C_d^⊥ = 1.0, with no parameter-identification procedure, no sensitivity analysis, and no independent measurement supporting these values. The text repeatedly claims 'strong quantitative agreement' and 'quantitative agreement' with experiments, but no numerical displacement/velocity comparisons, error bars, or fit statistics are reported in Figures 5-9. As presented, the locomotion demonstrations are illustrative reproductions, not validated predictions, and the manuscript should be revised to make that distinction explicit.
minor comments (6)
  1. [Section 4.4] The text says the drag force is 'computed using Eq. (24)', but Eq. (24) is the contact force; the drag force is defined in Eq. (27).
  2. [Section 3] There are two subsections both titled '3.2 3D validation: helical deformation'; the second one should be renumbered.
  3. [Table 1] The table lists 'Top layer nodes M' and 'Bottom layer nodes N', whereas Section 2 defines i for the top layer with N nodes and j for the bottom layer with M nodes; the notation should be made consistent.
  4. [Section 2] The subsection heading 'F riotnal contact force' contains a typo and should read 'Frictional contact force'.
  5. [Section 2, Eq. (24)] The log-barrier expression appears to have a missing delimiter; the parentheses around the term involving (d_i - d_hat) and d_i should be checked and typeset unambiguously.
  6. [Supporting Information] The paper refers to 'Supporting Information Movie-S1' in several places, but no video is included in the manuscript; either include the movie as supplementary material or cite a permanent repository link.

Circularity Check

2 steps flagged · score 6.0 of 10

Locomotion demos are fitted parameters presented as predictions; the core DER/Timoshenko validation remains independent.

  1. fitted input called prediction [Section 4.2 (Crawling), inchworm-like robot; Table 1]
    "We applied different friction coefficients for forward motion ( μ = 0 .3) and backward motion ( μ = 0 .6) to simulate directional movement. This frictional asymmetry is consistent with experimental observations [40]. ... Quantitative agreement between experiments and numerical predictions is demonstrated in Fig. 6 and Fig. 7."

    The directional asymmetry is an input, not an output: with backward friction (0.6) larger than forward friction (0.3), the gait is mechanically biased to move forward. The paper does not measure these coefficients or derive them from the bilayer actuation model; it applies them to simulate directional movement. Consequently, the claimed quantitative agreement for the crawling gait is partly a restatement of the imposed asymmetry, not an independent prediction of the DER bilayer model. The Timoshenko 2D validation is unaffected, so this is partial, not total, circularity.

  2. fitted input called prediction [Section 4.4 (Swimming), jellyfish-like robot; Table 1]
    "By incorporating implicit drag forces, computed using Eq. (24) [38, 39], we accurately model the interaction between the robot and the surrounding fluid. ... Fig. 9 presents a sequence of snapshots comparing the swimming motion of the bilayer soft robot in simulation and experiments, demonstrating a strong agreement between the two. ... Drag coefficient C ∥ d - - - - - 0.01; Drag coefficient C ⊥ d - - - - - 1.0."

    The drag anisotropy C∥d=0.01 and C⊥d=1.0 is listed as an input in Table 1 and is not measured or derived in the paper. In resistive-force models of slender swimmers, the tangential/normal drag ratio controls both thrust direction and speed, so setting these coefficients to match the observed swimming motion makes the strong agreement in Fig. 9 substantially by construction. The underlying DER elasticity and contact equations remain independent of this fit, so the circularity is partial.

full rationale

The Section 2 discrete elastic rod formulation is a standard DDG derivation, and the 2D validation against the external Timoshenko formula (Eq. 30, Ref. [14]) is an independent, parameter-free benchmark. The 3D helix test is qualitative and is not presented as a quantitative prediction. The identified circularity is confined to the robotic demonstration sections: the crawling friction asymmetry and swimming drag coefficients are calibrated inputs, so the claimed quantitative agreement in those demos reduces in part to the chosen parameters. I do not classify the interface rest-length question in Eq. (19) as circularity; it is a modeling consistency and correctness concern rather than a derivation that reduces to its own inputs. No load-bearing self-citation or imported uniqueness theorem is present, and the core bilayer mechanics claim retains independent content.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The ledger records the numbers and model choices the simulation depends on that are not derived from the cited experimental literature: penalty stiffnesses, friction asymmetry, and drag coefficients are chosen in the paper, and the DER, contact, and drag models are imported from prior work as domain assumptions.

free parameters (6)
  • Penalty stiffness KT/EA = 100
    Chosen ad hoc in Table 1; no convergence study versus penalty stiffness is reported, though the coupling strength affects all bilayer results.
  • Penalty stiffness KR/EI = 1000
    Chosen ad hoc; controls rotational locking of the interface; no sensitivity study is provided.
  • Friction coefficient forward motion = 0.3
    For crawling robots, forward/backward friction asymmetry (0.3 vs 0.6) is selected to reproduce directional crawling from [40]; this makes the crawling demo a fit, not a prediction.
  • Friction coefficient backward motion = 0.6
    See above; the asymmetry is tuned to match the observed directional gait.
  • Drag coefficient parallel C_d^parallel = 0.01
    Chosen in Table 1 for the swimming demo; no identification from fluid mechanics is given.
  • Drag coefficient perpendicular C_d^perp = 1.0
    Chosen in Table 1 for swimming; the anisotropy ratio strongly affects thrust and is not measured.
assumptions (5)
  • domain assumption Kirchhoff rod theory: cross-sections remain planar and shear deformation is neglected in the rod formulation
    Invoked in Sec. 2 'Degrees of freedom' and in the stretching, bending, and twisting elements; limits validity to slender rods.
  • domain assumption Bonding at the bilayer interface can be represented by penalty springs between centerlines with averaged material frames
    Eqs. (19) and (21) enforce non-translation and non-rotation via finite penalty stiffness; assumes perfect rigid bonding in the limit of infinite stiffness.
  • domain assumption Incremental potential contact with log-barrier and smoothed friction is applicable
    Eqs. (24) to (26) rely on the methods from [36,37] and on chosen barrier and velocity parameters.
  • domain assumption Fluid interaction reduces to local anisotropic quadratic drag
    Eq. (27); ignores added mass, vortex shedding, and free-surface effects; the validity for these swimming robots is not assessed.
  • standard math Standard discrete elastic rod energy definitions are correct
    Sec. 2 uses the established discrete curvature, twist, and stretching definitions from Bergou et al. [31,32].

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Cite this review

Pith. "Pith review of Harnessing Discrete Differential Geometry: A Virtual Playground for the Bilayer Soft Robotics." pith.science (2026). https://pith.science/paper/PLFJJTIB

@misc{pith2026250200714,
  author       = {Pith},
  title        = {Pith review of: Harnessing Discrete Differential Geometry: A Virtual Playground for the Bilayer Soft Robotics},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PLFJJTIB}},
  note         = {Machine review of arXiv:2502.00714}
}
read the original abstract

Soft robots have garnered significant attention due to their promising applications across various domains. A hallmark of these systems is their bilayer structure, where strain mismatch caused by differential expansion between layers induces complex deformations. Despite progress in theoretical modeling and numerical simulation, accurately capturing their dynamic behavior, especially during environmental interactions, remains challenging. This study presents a novel simulation environment based on the Discrete Elastic Rod (DER) model to address the challenge. By leveraging discrete differential geometry (DDG), the DER approach offers superior convergence compared to conventional methods like Finite Element Method (FEM), particularly in handling contact interactions -- an essential aspect of soft robot dynamics in real-world scenarios. Our simulation framework incorporates key features of bilayer structures, including stretching, bending, twisting, and inter-layer coupling. This enables the exploration of a wide range of dynamic behaviors for bilayer soft robots, such as gripping, crawling, jumping, and swimming. The insights gained from this work provide a robust foundation for the design and control of advanced bilayer soft robotic systems.

Figures

Figures reproduced from arXiv: 2502.00714 by the authors.

Figure 1
Figure 1. Examples of bilayer soft robots and structures. (A) The helix bilayer hydrogel inspired from the chiral pea pod [11]. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Schematic representation of a bilayer structure. (A) Diagram of a bilayer system that composed of an top layer [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Model validation of bilayer structure. (A) Schematic diagram illustrating planar bending behavior of bilayer [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: (A) The state of bilayer structures before deformation, in which the top layer has a natural configuration of a [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: Gripping demonstration using a bilayer gripper to grasp a ping pong ball. A sequence of snapshots illustrate the [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: Crawling demonstration using a inchworm-like robot. A sequence of snapshots illustrate the dynamic crawling [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]
Figure 7
Figure 7. Figure 7: Crawling demonstration using a dual-leg robot. A sequence of snapshots illustrate the dynamic crawling process [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]
Figure 8
Figure 8. Figure 8: Jumping demonstration using an insect larvae-inspired robot. A sequence of snapshots illustrate the dynamic [PITH_FULL_IMAGE:figures/full_fig_p011_8.png]
Figure 9
Figure 9. Figure 9: Swimming demonstration using an jellyfish-like robot. A sequence of snapshots illustrate the dynamic swimming [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]

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Forward citations

Cited by 1 Pith paper

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Reference graph

Works this paper leans on

42 extracted references · 39 canonical work pages · cited by 1 Pith paper

  1. [1]

    , " * write output.state after.block =

    ENTRY address author booktitle chapter edition editor eid howpublished institution isbn issn journal key month note number organization pages publisher school series title type url volume year label INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 'before.all := #1 'mid.sentence := #2 'after.sentence :...

  2. [2]

    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in capitalize " " * FUNCT...

  3. [3]

    W. Wang, C. Y. Yu, P. A. A. Serrano, S.-H. Ahn, Composites Part B: Engineering 2019, 164 198

    work page 2019

  4. [4]

    B. Shin, J. Ha, M. Lee, K. Park, G. H. Park, T. H. Choi, K.-J. Cho, H.-Y. Kim, Science Robotics 2018, 3, 14 eaar2629

    work page 2018

  5. [5]

    J. Li, M. Wang, Z. Cui, S. Liu, D. Feng, G. Mei, R. Zhang, B. An, D. Qian, X. Zhou, et al., Journal of Materials Chemistry A 2022, 10, 47 25337

    work page 2022

  6. [6]

    L. Xu, F. Xue, H. Zheng, Q. Ji, C. Qiu, Z. Chen, X. Zhao, P. Li, Y. Hu, Q. Peng, et al., Nano Energy 2022, 103 107848

    work page 2022

  7. [7]

    Y. Hu, J. Liu, L. Chang, L. Yang, A. Xu, K. Qi, P. Lu, G. Wu, W. Chen, Y. Wu, Advanced Functional Materials 2017, 27, 44 1704388

    work page 2017

  8. [8]

    C. Yin, F. Wei, S. Fu, Z. Zhai, Z. Ge, L. Yao, M. Jiang, M. Liu, ACS Applied Materials & Interfaces 2021, 13, 39 47147

    work page 2021

Show all 42 references
  1. [9]

    Huang, Z

    X. Huang, Z. J. Patterson, A. P. Sabelhaus, W. Huang, K. Chin, Z. Ren, M. K. Jawed, C. Majidi, Advanced Intelligent Systems 2022, 4, 10 2200163

    2022

  2. [10]

    Tao, Y.-C

    Y. Tao, Y.-C. Lee, H. Liu, X. Zhang, J. Cui, C. Mondoa, M. Babaei, J. Santillan, G. Wang, D. Luo, et al., Science Advances 2021, 7, 19 eabf4098

    2021

  3. [11]

    Y. Kim, X. Zhao, Chemical Reviews 2022, 122, 5 5317

    2022

  4. [12]

    X. Yang, Y. Zhou, H. Zhao, W. Huang, Y. Wang, K. J. Hsia, M. Liu, Soft Science 2023, 3, 4 38

    2023

  5. [13]

    Armon, E

    S. Armon, E. Efrati, R. Kupferman, E. Sharon, Science 2011, 333, 6050 1726

    2011

  6. [14]

    Z. Chen, C. Majidi, D. J. Srolovitz, M. Haataja, Applied Physics Letters 2011, 98, 1 011906

    2011

  7. [15]

    J. Li, X. Sun, Z. He, Y. Hou, H. Wu, Y. Zhu, Journal of the Mechanics and Physics of Solids 2025, 196 105999

    2025

  8. [16]

    Timoshenko, J

    S. Timoshenko, J. Opt. Soc. Am. 1925, 11, 3 233

    1925

  9. [17]

    Efrati, E

    E. Efrati, E. Sharon, R. Kupferman, Journal of the Mechanics and Physics of Solids 2009, 57, 4 762

    2009

  10. [18]

    W. M. van Rees, E. Vouga, L. Mahadevan, Proceedings of the National Academy of Sciences 2017, 114, 44 11597

    2017

  11. [19]

    Grinspun, M

    E. Grinspun, M. Desbrun, K. Polthier, P. Schr \"o der, A. Stern, ACM Siggraph Course 2006, 7, 1

    2006

  12. [20]

    D. Tong, A. Choi, J. Joo, A. Borum, M. Khalid Jawed, Journal of Applied Mechanics 2023, 90, 4 041008

    2023

  13. [21]

    D. Tong, A. Borum, M. K. Jawed, IEEE Robotics and Automation Letters 2021, 7, 2 1126

    2021

  14. [22]

    A. Choi, D. Tong, M. K. Jawed, J. Joo, Journal of Applied Mechanics 2021, 88, 5 051010

    2021

  15. [23]

    D. Tong, A. Choi, J. Joo, M. K. Jawed, Extreme Mechanics Letters 2023, 58 101924

    2023

  16. [24]

    A. Choi, D. Tong, D. Terzopoulos, J. Joo, M. K. Jawed, arXiv preprint arXiv:2301.01968 2023

    2023 arXiv

  17. [25]

    D. Tong, A. Choi, L. Qin, W. Huang, J. Joo, M. K. Jawed, The International Journal of Robotics Research 2024, 43, 6 791

    2024

  18. [26]

    Huang, X

    W. Huang, X. Huang, C. Majidi, M. K. Jawed, Nature communications 2020, 11, 1 2233

    2020

  19. [27]

    Huang, M

    W. Huang, M. Liu, K. J. Hsia, Extreme Mechanics Letters 2023, 59 101967

    2023

  20. [28]

    Huang, M

    W. Huang, M. Jawed, Soft matter 2020, 16, 3 604

    2020

  21. [29]

    D. Tong, Z. Hao, M. Liu, W. Huang, IEEE Robotics and Automation Letters 2024

    2024

  22. [30]

    Huang, P

    W. Huang, P. Xu, Z. Liu, Journal of Applied Mechanics 2024, 1--13

    2024

  23. [31]

    A. Choi, R. Jing, A. Sabelhaus, M. K. Jawed, IEEE Robotics and Automation Letters 2024

    2024

  24. [32]

    M. K. Jawed, A. Novelia, O. M. O'Reilly, A primer on the kinematics of discrete elastic rods, Springer, 2018

    2018

  25. [33]

    Bergou, B

    M. Bergou, B. Audoly, E. Vouga, M. Wardetzky, E. Grinspun, ACM Trans. Graph. 2010, 29, 4

    2010

  26. [34]

    Bergou, M

    M. Bergou, M. Wardetzky, S. Robinson, B. Audoly, E. Grinspun, In ACM SIGGRAPH 2008 papers, 1--12. ACM, 2008

    2008

  27. [35]

    Huang, M

    W. Huang, M. K. Jawed, Journal of Applied Mechanics 2019, 86, 8 084501

    2019

  28. [36]

    Audoly, Y

    B. Audoly, Y. Pomeau, In Peyresq Lectures on Nonlinear Phenomena, 1--35. World Scientific, 2000

    2000

  29. [37]

    M. Li, Z. Ferguson, T. Schneider, T. R. Langlois, D. Zorin, D. Panozzo, C. Jiang, D. M. Kaufman, ACM Trans. Graph. 2020, 39, 4 49

    2020

  30. [38]

    M. Li, D. M. Kaufman, C. Jiang, arXiv preprint arXiv:2012.04457 2020

    2012 arXiv

  31. [39]

    Mallick, A

    M. Mallick, A. Kumar, N. Tamboli, A. Kulkarni, P. Sati, V. Devi, S. Chandar, International Journal of Civil Engineering Research 2014, 5, 4 301

    2014

  32. [40]

    Modarres-Sadeghi, M

    Y. Modarres-Sadeghi, M. Pa \" doussis, C. Semler, Journal of Fluids and Structures 2005, 21, 5-7 609

    2005

  33. [41]

    Y. Dong, J. Wang, X. Guo, S. Yang, M. O. Ozen, P. Chen, X. Liu, W. Du, F. Xiao, U. Demirci, et al., Nature Communications 2019, 10, 1 4087

    2019

  34. [42]

    J. Li, Y. Hou, Z. He, H. Wu, Y. Zhu, Nano Letters 2024

    2024

Pith tools

Reviewed August 9, 2026 · model on record in the stance chip above.