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REVIEW 5 major objections 6 minor 83 references

Harnessing Eversion Buckling for Ideal Omnidirectional Energy Absorption

T0 review · 5 major / 6 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read This paper establishes that everting a toroidal shell creates a geometry-controlled pitchfork bifurcation, giving direction-insensitive snap-through and near-ideal energy absorption in assemblies.

desk verdict Eversion buckling of toroidal shells is a genuinely new mechanism with solid qualitative support, but the central eta < eta_c design rule is unverified without the missing SI and a fitted threshold. read the letter →

arxiv 2512.19987 v2 pith:5ECDEO7V submitted 2025-12-23 math-ph math.MPphysics.class-ph

Junjie Liu , Aijie Tang , Mingchao Liu , Xiaoding Wei , Qingsheng Yang This is my paper · ORCID
classification math-phmath.MPphysics.class-ph MSC 74G6074K25
keywords eversionbucklingtoroidalshellbistabilityomnidirectionalenergyabsorptionpitchforkbifurcationstressplateautunabledampinggranularmetamaterial
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 tries to establish that eversion of a toroidal shell—turning it inside out—creates a symmetry-breaking instability that can be tuned into direction-insensitive bistability. The central claim is that a single dimensionless parameter, related to the ratio of membrane to bending energy, decides whether the everted shell stays axisymmetric and bistable or collapses into a non-axisymmetric monostable state. The transition is a pitchfork bifurcation, so collapse has no preferred in-plane direction. If correct, designers get a simple rule: thin shells with low slenderness behave as omnidirectional snap-through units, and assemblies of them produce an extended stress plateau with high energy absorption efficiency. The paper matters because it addresses the usual single-axis limitation of bistable energy absorbers.

What carries the argument

Eversion buckling, driven by circumferential membrane compression in an axisymmetric toroidal shell, is the central mechanism. The load-bearing design variable is the dimensionless parameter η = sqrt(U_m/U_b), which combines the shell's relative thickness h/R2 and slenderness R2/R1, with a fitted critical threshold η_c separating bistable from monostable behavior. This parameter collapses the stability phase diagram into a single design rule, and the pitchfork nature of the bifurcation, inherited from the shell's axisymmetry, is what makes the snap-through omnidirectional within the plane.

What would settle it

Fabricate everted toroidal shells with the same computed η but very different combinations of R1, R2, and h, and test whether the bistable/monostable boundary shifts between families; if it does, η is not the controlling parameter. Separately, indent a single bistable shell from many angles around its full 360° circumference and check whether the critical force remains constant—any significant directional variation would falsify the in-plane omnidirectionality claim.

Watch

Extended reading notes

Core claim

The paper reports and names eversion buckling: after a toroidal shell is everted, circumferential membrane compression develops, and whether the axisymmetric everted state remains stable is governed by a single dimensionless parameter η, proportional to the square root of membrane-to-bending energy and combining relative thickness with slenderness. When η exceeds a critical value η_c, the axisymmetric state loses stability in a pitchfork bifurcation and the shell collapses spontaneously into a non-axisymmetric configuration; when η is below η_c, the shell is bistable and snaps only when triggered, with a critical force nearly independent of loading direction and boundary support. Finite elem

Load-bearing premise

The whole design rule rests on the assumption that a single dimensionless parameter η, with a universal fitted threshold η_c, fully determines whether an everted shell is bistable; if imperfections, material nonlinearity, loading rate, or support friction also matter, the bistability boundary and omnidirectionality claim do not transfer to other geometries or conditions.

Editorial extensions

If this is right

  • Designers can select bistable omnidirectional shells simply by keeping η below the critical threshold, i.e., using thin shells with low slenderness, without case-by-case tuning.
  • A single everted shell releases more than twice the kinetic energy of a non-everted counterpart and contracts in volume by up to 61% on a timescale of about 0.2 ms, enabling rapid high-capacity dissipation from a reusable unit.
  • Packed assemblies should exhibit an extended, nearly flat stress plateau with densification strain exceeding 60%, outperforming most foams, lattices, and other bistable metamaterials in specific energy absorption efficiency.
  • The system inherits omnidirectionality from its units, so in-plane impacts from any direction should trigger collapse at nearly the same critical force.
  • Damping is passively load-adaptive: the loss factor rises from 0.0859 to 0.468 as more shells collapse, giving a sixfold tunable range at low density.

Reading between the lines

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

  • Beyond the paper: if η truly controls the stability boundary, the design rule should transfer across materials and length scales, so the same phase diagram should hold for metal or polymer shells of very different absolute sizes—a direct, testable extrapolation.
  • The axisymmetry argument is essentially the in-plane case of a more general idea: spherical or ellipsoidal shells might extend omnidirectionality to the full 3D space, where no direction is preferred.
  • The observed hysteretic memory—the system remembers the maximum displacement it has seen—could be exploited as a passive mechanical state recorder or load-history sensor, not just as a damping feature.
  • Because friction dominates energy dissipation, assembly performance likely depends on surface roughness, packing density, and wear over repeated cycles; these factors are not captured by the η-based single-shell design rule and would need separate characterization.
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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

5 major / 6 minor

Summary. The paper reports a new instability mechanism in everted toroidal shells, termed eversion buckling. The authors argue that, after eversion, the axisymmetric state is bistable below a dimensionless threshold η < η_c and monostable above it, with η ∝ sqrt(U_m/U_b) depending on shell geometry. They present FEA, 3D-printed TPU experiments, energy-landscape arguments, and a drop test to show that bistable shells snap omnidirectionally with large volume contraction, and that assemblies of such shells exhibit an extended stress plateau, high specific energy absorption efficiency, and a sixfold tunable damping range. The central design rule is that one geometric parameter controls bistability across geometries.

Significance. If the scaling law and phase boundary are correct, this is a valuable contribution: it identifies a new mechanism (eversion buckling) with a simple geometric design rule for in-plane omnidirectional bistability, and it demonstrates a macroscale energy-absorbing system with an unusually flat stress plateau. The combination of FEA, experiments, and a drop test is a strength. However, the central quantitative claims depend on a derivation relegated to missing Supporting Information, and the threshold η_c appears to be fitted to the same data used for validation. The paper therefore currently establishes a promising phenomenon but not a verifiable, transferable design rule.

major comments (5)
  1. [Section 2.2 / Supporting Information B] The entire bistability design rule rests on the scaling η ∝ sqrt(U_m/U_b) and the pitchfork-bifurcation picture, but the derivation is only referenced to Supporting Information B, which is not included. No intermediate equations, assumptions, or stability analysis appear in the main text. Please provide the full derivation: how U_m and U_b scale, why no other dimensionless groups enter, and how the energy landscape yields a pitchfork with η_c as a universal threshold.
  2. [Figure 2f / Section 2.2] The phase boundary is drawn at η = η_c, with η_c described only as 'a constant.' If η_c is fitted to the experimental/FEA points that are also used to claim agreement with the scaling, then Figure 2f is not an independent validation. Please report the fitted value of η_c, its uncertainty, and the fitting procedure. More convincingly, test the scaling by predicting the boundary for new geometries, materials, or aspect ratios not used to fit η_c, or derive η_c from the elastic-energy model.
  3. [Section 2.2 / Supporting Information D] The claim that η predicts stability for non-semicircular generating curves is deferred to Supporting Information D, which is missing. Since the main text only demonstrates semicircular profiles, the transferability of the design rule to other generators is asserted, not demonstrated. Move this evidence into the main text or a visible SI and reference it explicitly, or restrict the claim to semicircular generators.
  4. [Section 2.3 / Figure 3c] The quantitative snap-through claims—'more than double' kinetic energy, 61% volumetric contraction, ~0.2 ms collapse time—are presented without a reproducible protocol. Is this FEA-only or measured? What is the 'similar shell without internal stress' and how is its geometry matched? What are the loading and boundary conditions in the kinetic-energy calculation? Without definitions, these numbers cannot be reproduced or compared against the claimed baseline.
  5. [Section 2.4 / 2.5] The benchmark claims (SEAE at least twice that of other multistable structures, sixfold loss-factor tunability, 'order-of-magnitude' damping at lower density) depend on normalization conventions and material parameters specified only in missing Supporting Information sections H and I. Please include the definitions of plateau stress, densification strain, loss factor, and the TPU reference values in the main text or complete SI. Also, the title and abstract use 'omnidirectional' while the demonstrated behavior is in-plane omnidirectional; out-of-plane loading is constrained by glass plates and not tested.
minor comments (6)
  1. [Equation (1), Section 2.2] The formula for η is garbled by typesetting: η ∝ sqrt(U_m/U_b) combined with (h/R2)(R2/R1)^{...}. Define η with a clean, numbered equation so readers can see the exact exponents.
  2. [Figure 2f] State the numerical value of η_c in the main text or caption. A 'constant' with no value is not actionable for designers.
  3. [Figure 3b] Specify the loading directions and boundary conditions tested in the omnidirectionality panel, and include error bars or at least the number of repeats.
  4. [Section 4.3 / Figure 4c] Friction is reported as a dominant dissipation mechanism, but the FEA friction coefficient is fixed at 0.2. A sensitivity study on μ would strengthen this claim, since the assembled-system energy absorption depends on it.
  5. [Section 4.3 / Supporting Information I] The Mooney-Rivlin material parameters are not given in the Methods. Include the values used in the simulations, not only in the SI.
  6. [Abstract / Section 2.5] The paper uses both 'sixfold tunable damping' and 'order-of-magnitude increase' for the same loss-factor data. Clarify which claim is meant, and distinguish the loss-factor increase from the density-normalized damping.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular reduction is established in the available text; the central scaling derivation is deferred to missing Supporting Information, but that is a completeness/verifiability issue, not circularity.

full rationale

The paper's main derivation chain is: thin-shell energy competition -> dimensionless parameter eta ~ sqrt(U_m/U_b) -> threshold eta_c -> pitchfork phase boundary -> bistable/omnidirectional behavior. The scaling form is stated to be derived in Supporting Information section B, which is not included in the manuscript, so the derivation cannot be checked. That omission is a verification problem, not an identified circular reduction: the manuscript does not show eta being defined in terms of the predicted outcome, nor does it explicitly state that eta_c was fitted to the same experimental/FEA points. If SI B derives eta_c, the phase-diagram validation is independent in form; if eta_c was instead calibrated from Figure 2f, the boundary would be a fit, but that cannot be established from the available text and would be speculation. The omnidirectionality argument is a symmetry argument from axisymmetry, supported by measured and simulated force-direction insensitivity, not by a self-citation chain. Assembly-level plateau stress, friction dissipation, densification strain, and damping tunability are benchmarked against independent FEA and experiments. The self-citations present (e.g., refs. 39 and 47) are contextual background on bistable buckling and are not load-bearing uniqueness or ansatz-importing citations. No step in the visible text reduces to its own input by definition.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The quantitative payload rests on one fitted threshold parameter (eta_c), a chosen friction coefficient, and unreported material coefficients. No new physical entities such as particles, forces, or dimensions are introduced; 'eversion buckling' is a label for a shell instability, not an entity.

free parameters (3)
  • eta_c (critical dimensionless threshold) = not reported in main text
    The boundary between bistable and monostable regimes is drawn as eta = eta_c, with eta_c a constant. Its value is not derived but obtained from matching FEA/experiments, so the 'prediction' of the stability boundary includes one fitted constant (Section 2.2, Figure 2f).
  • Friction coefficient mu in ABAQUS general contact = 0.2
    Global friction coefficient between TPU shells is set to 0.2 in all assembly simulations; the frictional dissipation and damping results (Figure 4c, Figure 5) depend on this chosen value (Methods 4.3).
  • Mooney-Rivlin material parameters = not given in main text
    Hyperelastic coefficients for TPU are needed for all FEAs, but the values are deferred to Supporting Information Section I; without them the simulations cannot be reproduced from the main text (Methods 4.1, 4.3).
assumptions (5)
  • domain assumption Thin-shell energy decomposition U = U_m + U_b governs stability; eta is proportional to sqrt(U_m/U_b)
    Introduced in Section 2.2; the detailed derivation is in Supporting Information Section B, which is not part of the arXiv record, so this is an unverified assumption in the present text.
  • domain assumption The TPU shells are incompressible hyperelastic (Mooney-Rivlin; Poisson's ratio 0.5)
    Material model for all FEAs; Poisson's ratio is stated in Methods 4.1, and full material coefficients are in SI Section I.
  • domain assumption Assembly simulations restrict all shells to zero out-of-plane displacement (2D confinement)
    Methods 4.3 states this constraint; the 2D confinement is essential to the hexagonal packing, frictional dissipation, and 'in-plane omnidirectional' claims.
  • domain assumption The shell is perfectly axisymmetric and perturbations have no preferred azimuthal direction
    Underlies the pitchfork-bifurcation and omnidirectionality argument (Section 2.2, Figure 2g); manufactured parts have finite imperfections, and the sensitivity to imperfections is not quantified.
  • domain assumption The material remains elastic and reversible below the snap threshold
    The reusable-bistability claim assumes no plastic deformation or fatigue in TPU. The paper shows stable hysteresis below a prior maximum but permanent collapse after larger amplitudes (Section 2.5), so the reusable regime is bounded.

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Cite this review

Pith. "Pith review of Harnessing Eversion Buckling for Ideal Omnidirectional Energy Absorption." pith.science (2026). https://pith.science/paper/5ECDEO7V

@misc{pith2026251219987,
  author       = {Pith},
  title        = {Pith review of: Harnessing Eversion Buckling for Ideal Omnidirectional Energy Absorption},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5ECDEO7V}},
  note         = {Machine review of arXiv:2512.19987}
}
read the original abstract

Thin shells can undergo large shape changes governed by the competition between bending and membrane energies. Here, we identify an instability mechanism in everted toroidal shells, referred to as eversion buckling. After eversion, the axisymmetric configuration may either remain stable or lose stability through symmetry breaking, depending on geometry. A scaling analysis reveals a dimensionless parameter that characterizes the ratio between membrane and bending energies. This parameter defines a critical threshold separating a bistable regime, where the axisymmetric everted state persists, from a monostable regime, where the shell collapses into a non-axisymmetric configuration. The transition is consistent with a pitchfork-type bifurcation, leading to collapse without a preferred in-plane direction. Finite element simulations and experiments validate the proposed scaling and the associated stability boundary across different shell geometries. In the bistable regime, individual everted shells exhibit rapid snap-through accompanied by large volumetric contraction and show limited sensitivity of the critical response to boundary constraints. Building on this mechanism, assemblies of such shells form granular systems with a stable stress plateau and high energy absorption efficiency. These results provide a mechanics-based framework for designing shell-based systems with robust and direction-insensitive energy absorption.

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Reference graph

Works this paper leans on

83 extracted references

  1. [1]

    Introduction The increasing demand for advanced protective systems across aerospace, automotive, and consumer electronics sectors necessitates the development of materials capable of mitigating shock and impact loads. [1-8] A critical, yet often unmet, requirement for these materials is the ability to perform reliably under unpredictable loading condition...

  2. [2]

    everted shell

    Results and discussion Figure 1a illustrates a typical scenario that impact directionality is undetermined. The profound anisotropy of conventional architected materials is a primary obstacle to their application in such complex impact scenarios ( Figure 1b top). Thi s directional depende nce dictates that optimal performance is achieved only when the imp...

  3. [3]

    By harnessing this instability, we have designed truly in-plane omnidirectional bistable units , 17 overcoming a fundamental limitation of conventional bistable structures

    Summary In summary, we have reported the mechanics o f eversion buckling , a unique pitchfork bifurcation in axisymmetric shells , marked by a breakdown of structural symmetry. By harnessing this instability, we have designed truly in-plane omnidirectional bistable units , 17 overcoming a fundamental limitation of conventional bistable structures. The sna...

  4. [4]

    This material has a Poisson ’s ratio of 0.5 and a density of 1

    Methods 4.1 Fabrication Samples were fabricated using Multi Jet Fusion (MJF) technology on a commercial HP Jet Fusion 5200 printer, with gray TPU (thermoplastic polyurethane, UltraSint TPU-01) as the raw material. This material has a Poisson ’s ratio of 0.5 and a density of 1. 1 g/cm³ . Detailed mechanical properties are provided in Supporting Information...

  5. [5]

    S. H. Siddique, P. J. Hazell, H. Wang, J. P. Escobedo, A. A. Ameri, Additive Manufacturing 2022, 58, 103051

    2022

  6. [6]

    Z. Yin, F. Hannard, F. Barthelat, Science 2019, 364, 1260

    2019

  7. [7]

    X. Feng, S. Ma, S. Fu, J. Wei, J. Liu, F. Yang, H. Yue, Y . Lu, Small 2025, 21, 2411205

    2025

  8. [8]

    J. U. Surjadi, C. M. Portela, Nature Materials 2025, 1

    2025

Show all 83 references
  1. [9]

    Haipeng, L

    W. Haipeng, L. Shaomin, Z. Qijie, P. Haic hun, L. Xiaolin, S. Zhenyu, S. Peng, Composites Part B: Engineering 2025, 304, 112681

    2025

  2. [10]

    C. W. Isaac, C. Ezekwem, Composite Structures 2021, 257, 113081

    2021

  3. [11]

    K. L. Snapp, B. Verdier, A. E. Gongora, S. Silverman, A. D. Adesiji, E. F. Morgan, T. J. Lawton, E. Whiting, K. A. Brown, Nature Communications 2024, 15, 4290

    2024

  4. [12]

    G. Lu, T. Yu, Energy absorption of structures and materials, Elsevier, 2003

    2003

  5. [13]

    Abrate, Progress in Aerospace Sciences 2016, 81, 1

    S. Abrate, Progress in Aerospace Sciences 2016, 81, 1

    2016

  6. [14]

    M. R. Shorten, Journal of biomechanics 1993, 26, 41

    1993

  7. [15]

    Ren, Z.-z

    S.-y. Ren, Z.-z. Gong, Q. Wu, G.-m. Song, Q.-m. Zhang, P.-l. Zhang, C. Chen, Y . Cao, Defence Technology 2023, 27, 284

    2023

  8. [16]

    Latourte, D

    F. Latourte, D. Grégoire, D. Zenkert, X. Wei, H. D. Espinosa, Journal of the Mechanics and Physics of Solids 2011, 59, 1623

    2011

  9. [17]

    Jiang, Y

    H. Jiang, Y . Ren, Composite Structures 2019, 229, 111375

    2019

  10. [18]

    S.-M. Wen, W. Gao, S. -C. Zhang, J. Pang, C. Cui, H. -L. Gao, Z. Zheng, S. -M. Chen, S. -H. Yu, Science Advances, 11, eadv2169

  11. [19]

    Z. Yue, Z. Fan, C. Ma, X. Wei, W. Li, X. Wang, Q. Zhang, R. Chen, T. J. Lu, Journal of the Mechanics and Physics of Solids 2025, 202, 106190

    2025

  12. [20]

    M. D. Nestorović, N. Triantafyllidis, Journal of the Mechanics and Physics of Solids 2004, 52, 941

    2004

  13. [21]

    in Cellular Solids: Structure and Properties, (Eds: L. J. Gibson, M. F. Ashby), Cambridge University Press, Cambridge 1997

    1997

  14. [22]

    V . S. Deshpande, N. A. Fleck, Journal of the Mechanics and Physics of Solids 2000, 48, 1253

    2000

  15. [23]

    L. J. Gibson, M. F. Ashby, J. Zhang, T. C. Triantafillou, International Journal of Mechanical Sciences 1989, 31, 635

    1989

  16. [24]

    Z. Chen, X. Wei, L. Yang, J. Xiong, Journal of the Mechanics and Physics of Solids 2024, 188, 105672

    2024

  17. [25]

    Rahimidehgolan, W

    F. Rahimidehgolan, W. Altenhof, Composites Part B: Engineering 2023, 253, 110513

    2023

  18. [26]

    Jiao, Progress in Materials Science 2023, 137, 101132

    P. Jiao, Progress in Materials Science 2023, 137, 101132

    2023

  19. [27]

    J. U. Surjadi, L. Wang, S. Qu, B. F. G. Aymon, J. Ding, X. Zhou, R. Fan, H. Yang, Q. Zhao, X. Song, Y . Lu, Science Advances, 11, eadt0589

  20. [28]

    N. Zhu, Y . Xu, X. Wang, X. Xu, Z. Yue, X. Guo, H. Ji, B. Li, Y . Ji, Z. Li, P. Wang, Advanced Functional Materials 2025, n/a, 2424390

    2025

  21. [29]

    Haver, D

    D. Haver, D. Acuña, S. Janbaz, E. Lerner, G. Düring, C. Coulais, Proceedings of the National Academy of Sciences 2024, 121, e2317915121

    2024

  22. [30]

    Peretz, E

    O. Peretz, E. Ben Abu, A. Zigelman, S. Givli, A. D. Gat, Nature Communications 2022, 13, 1810

    2022

  23. [31]

    S. Yan, L. Wu, Y . Wen, J. Sun, J. Zhou, Responsive Materials 2025, e20240035

    2025

  24. [32]

    Y. Chen, L. Jin, Advanced Functional Materials 2021, 31, 2102113

    2021

  25. [33]

    W. Liu, S. Janbaz, D. Dykstra, B. Ennis, C. Coulais, Nature 2024, 1

    2024

  26. [34]

    H. Yang, J. Zhang, J. Wang, J. Hu, Z. Wu, F. Pan, J. Wu, Advanced Functional Materials 2025, 35, 2410217

    2025

  27. [35]

    T. G. Sano, E. Hohnadel, T. Kawata, T. Métivet, F. Bertails-Descoubes, Communications Materials 2023, 4, 21 59

    2023

  28. [36]

    Puglisi, L

    G. Puglisi, L. Truskinovsky, Journal of the Mechanics and Physics of Solids 2000, 48, 1

    2000

  29. [37]

    Y . Cao, M. Derakhshani, Y . Fang, G. Huang, C. Cao, Advanced Functional Materials 2021, 31, 2106231

    2021

  30. [38]

    Y . Chi, Y . Li, Y . Zhao, Y . Hong, Y . Tang, J. Yin, Advanced Materials 2022, 34, 2110384

    2022

  31. [39]

    R. Xu, Y . He, X. Li, M. Lu, Y . Chen, Applied Materials Today 2023, 30, 101714

    2023

  32. [40]

    Y . Liu, Z. Meng, Y . Wang, C. Q. Chen, Journal of the Mechanics and Physics of Solids 2025, 196, 106042

    2025

  33. [41]

    F. O. Falope, M. Pelliciari, L. Lanzoni, A. M. Tarantino, International Journal of Non -Linear Mechanics 2021, 134, 103739

    2021

  34. [42]

    D. Yan, M. Pezzulla, L. Cruveiller, A. Abbasi, P. M. Reis, Nature communications 2021, 12, 2831

    2021

  35. [43]

    J. Liu, M. Teunisse, G. Korovin, I. R. Vermaire, L. Jin, H. Bense, M. van Hecke, Proceedings of the National Academy of Sciences 2024, 121, e2308414121

    2024

  36. [44]

    J. Byun, A. Pal, J. Ko, M. Sitti, Nature Communications 2024, 15, 2933

    2024

  37. [45]

    X. Li, Z. Lu, Z. Yang, C. Yang, Materials & Design 2018, 158, 88

    2018

  38. [46]

    Ahmad, D

    Z. Ahmad, D. P. Thambiratnam, A. C. C. Tan, International Journal of Impact Engineering 2010, 37, 475

    2010

  39. [47]

    Z. Sun, J. Zhang, T. Hua, Y . Ding, Engineering Structures 2025, 340, 120695

    2025

  40. [48]

    Armon, E

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

    2011

  41. [49]

    M. Liu, L. Domino, I. D. de Dinechin, M. Taffetani, D. Vella, Journal of the Mechanics and Physics of Solids 2023, 170, 105116

    2023

  42. [50]

    Taffetani, X

    M. Taffetani, X. Jiang, D. P. Holmes, D. Vella, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 2018, 474, 20170910

    2018

  43. [51]

    M. Liu, M. Gomez, D. Vella, Journal of the Mechanics and Physics of Solids 2021, 151, 104386

    2021

  44. [52]

    G. Wan, Y . Liu, Z. Xu, C. Jin, L. Dong, X. Han, J. X. Zhang, Z. Chen, Extreme Mechanics Letters 2020, 34, 100603

    2020

  45. [53]

    Zhang, S

    L. Zhang, S. Feih, S. Daynes, S. Chang, M. Y . Wang, J. Wei, W. F. Lu, Additive Manufacturing 2018, 23, 505

    2018

  46. [54]

    C. Ling, A. Cernicchi, M. D. Gilchrist, P. Cardiff, Materials & Design 2019, 162, 106

    2019

  47. [55]

    X. Ma, D. Z. Zhang, M. Zhao, J. Jiang, F. Luo, H. Zhou, The International Journal of Advanced Manufacturing Technology 2022, 1

    2022

  48. [56]

    Zheng, C

    Z. Zheng, C. Wang, J. Yu, S. R. Reid, J. J. Harrigan, Journal of the Mechanics and Physics of Solids 2014, 72, 93

    2014

  49. [57]

    T.-J. Lim, B. Smith, D. McDowell, Acta Materialia 2002, 50, 2867

    2002

  50. [58]

    Neville, A

    B. Neville, A. Rabiei, Materials & Design 2008, 29, 388

    2008

  51. [59]

    Rabiei, L

    A. Rabiei, L. Vendra, Materials letters 2009, 63, 533

    2009

  52. [60]

    D. Ruan, G. Lu, F. Chen, E. Siores, Composite structures 2002, 57, 331

    2002

  53. [61]

    X. Xia, X. Chen, Z. Zhang, X. Chen, W. Zhao, B. Liao, B. Hur, Materials & Design 2014, 56, 353

    2014

  54. [62]

    X. Xia, H. Feng, X. Zhang, W. Zhao, Materials & Design 2013, 51, 797

    2013

  55. [63]

    J. Marx, A. Rabiei, Advanced Engineering Materials 2017, 19, 1600776

    2017

  56. [64]

    K. F. Peng, Z. J. Zheng, H. Pan, Y . L. Zhang, K. Zhao, J. L. Yu, MECHANICS OF MATERIALS 2022, 167, 104250

    2022

  57. [65]

    T. A. Schaedler, A. J. Jacobsen, A. Torrents, A. E. Sorensen, J. Lian, J. R. Greer, L. Valdevit, W. B. Carter, Science 2011, 334, 962

    2011

  58. [66]

    Zhang, B

    Z. Zhang, B. Song, Y . Yao, L. Zhang, X. Wang, J. Fan, Y . Shi, Advanced Materials Technologies 2022, 7, 2200076

    2022

  59. [67]

    Deng, Q.-K

    F. Deng, Q.-K. Nguyen, P. Zhang, Applied Materials Today 2022, 29, 101671

    2022

  60. [68]

    Xiang, J

    J. Xiang, J. Du, D. Li, F. Scarpa, Journal of Materials Science 2017, 52, 13247. 22

    2017

  61. [69]

    N. S. Ha, G. Lu, X. Xiang, Journal of materials science 2019, 54, 6286

    2019

  62. [70]

    Zhang, S

    W. Zhang, S. Yin, T. Yu, J. Xu, International Journal of Impact Engineering 2019, 125, 163

    2019

  63. [71]

    Tsang, S

    H. Tsang, S. Raza, Composite Structures 2018, 195, 199

    2018

  64. [72]

    Restrepo, N

    D. Restrepo, N. D. Mankame, P. D. Zavattieri, Extreme Mechanics Letters 2015, 4, 52

    2015

  65. [73]

    Frenzel, C

    T. Frenzel, C. Findeisen, M. Kadic, P. Gumbsch, M. Wegener, Advanced materials (Deerfield Beach, Fla.) 2016, 28, 5865

    2016

  66. [74]

    A. P. Garland, K. M. Adstedt, Z. J. Casias, B. C. White, W. M. Mook, B. Kaehr, B. H. Jared, B. T. Lester, N. S. Leathe, E. Schwaller, Extreme Mechanics Letters 2020, 40, 100847

    2020

  67. [75]

    S. Chen, X. Tan, J. Hu, S. Zhu, B. Wang, L. Wang, Y . Jin, L. Wu, Composites Part B: Engineering 2021, 215, 108745

    2021

  68. [76]

    J. Li, Z. Chen, Q. Li, L. Jin, Z. Zhao, Advanced Science 2022, 9, 2105769

    2022

  69. [77]

    S. Chen, B. Wang, S. Zhu, X. Tan, J. Hu, X. Lian, L. Wang, L. Wu, Composites Part A: Applied science and manufacturing 2020, 129, 105697

    2020

  70. [78]

    K. Fu, Z. Zhao, L. Jin, Advanced Functional Materials 2019, 29, 1901258

    2019

  71. [79]

    Shohat, D

    D. Shohat, D. Hexner, Y . Lahini, Proceedings of the National Academy of Sciences 2022, 119, e2200028119

    2022

  72. [80]

    J. D. Paulsen, N. C. Keim, Annual Review of Condensed Matter Physics 2024, 16

    2024

  73. [81]

    M. F. Ashby, D. Cebon, Le Journal de Physique IV 1993, 3, C7

    1993

  74. [82]

    Beards, Structural vibration: analysis and damping, Elsevier, 1996

    C. Beards, Structural vibration: analysis and damping, Elsevier, 1996

    1996

  75. [83]

    S. H. Crandall, Journal of sound and vibration 1970, 11, 3

    1970

Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.