Double-network-inspired mechanical metamaterials

Bastien F. G. Aymon; Carlos M. Portela; James Utama Surjadi; Molly Carton

arxiv: 2409.01533 · v1 · submitted 2024-09-03 · ❄️ cond-mat.soft · physics.app-ph

Double-network-inspired mechanical metamaterials

James Utama Surjadi , Bastien F. G. Aymon , Molly Carton , Carlos M. Portela This is my paper

Pith reviewed 2026-05-23 21:29 UTC · model grok-4.3

classification ❄️ cond-mat.soft physics.app-ph

keywords mechanical metamaterialsdouble-networktruss structureswoven structuresenergy dissipationfrictional dissipationstretchabilitystiffness

0 comments

The pith

Double-network-inspired metamaterials integrate stiff truss and compliant woven networks to achieve tenfold gains in both stiffness and stretchability.

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

The paper establishes that metamaterials built from interpenetrating stiff truss and compliant woven components, modeled after double-network polymer gels, outperform single-network versions by a factor of ten in stiffness and in stretchability. The gains arise because the two networks entangle and rub, dissipating extra energy through friction. The same structures also show that adding internal defects, normally harmful, can triple energy dissipation by spreading failure across more sites. A reader would care because the work points to a route for lightweight materials that combine high load-bearing capacity with large deformation without the usual trade-offs.

Core claim

By integrating monolithic truss (stiff) and woven (compliant) components into a metamaterial architecture, these DNI metamaterials achieve a tenfold increase in stiffness and stretchability compared to their pure woven and truss counterparts, respectively. Nonlinear computational mechanics models elucidate that enhanced energy dissipation in these DNI metamaterials stems from increased frictional dissipation due to entanglements between the two networks. Through introduction of internal defects, which typically degrade mechanical properties, the structures demonstrate an opposite effect of a threefold increase in energy dissipation via failure delocalization.

What carries the argument

The interpenetrating truss and woven networks whose entanglements enable frictional sliding and energy dissipation.

Load-bearing premise

The performance gains are caused specifically by frictional dissipation from entanglements between the two networks, as the models claim, rather than by some other mechanism.

What would settle it

Direct measurement of contact forces or dissipated energy in the entangled regions that shows the friction contribution is too small to explain the observed tenfold improvements, or experiments where the networks are prevented from entangling yet the gains remain.

Figures

Figures reproduced from arXiv: 2409.01533 by Bastien F. G. Aymon, Carlos M. Portela, James Utama Surjadi, Molly Carton.

**Figure 3.** Figure 3: Stretchability and energy dissipation of DNI unit cells uniaxial tension of DNI unit cells. Stressstretch curves of a, concentric octa nd; cinterpenetrating octahedron; and dinterpenetrating diamond DNI unit c [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

**Figure 4.** Figure 4: Energy dissipation mechanisms from finite element models) of DNI UCs showing representative locations of entanglements as well as en [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗

read the original abstract

Mechanical metamaterials are renowned for their ability to achieve high stiffness and strength at low densities, often at the expense of low ductility and stretchability-a persistent trade-off in materials. In contrast, materials such as double-network hydrogels feature interpenetrating compliant and stiff polymer networks, and exhibit unprecedented combinations of high stiffness and stretchability, resulting in exceptional toughness. Here, we present double-network-inspired (DNI) metamaterials by integrating monolithic truss (stiff) and woven (compliant) components into a metamaterial architecture, which achieve a tenfold increase in stiffness and stretchability compared to their pure woven and truss counterparts, respectively. Nonlinear computational mechanics models elucidate that enhanced energy dissipation in these DNI metamaterials stems from increased frictional dissipation due to entanglements between the two networks. Through introduction of internal defects, which typically degrade mechanical properties, we demonstrate an opposite effect of a threefold increase in energy dissipation for these metamaterials via failure delocalization. This work opens avenues for developing new classes of metamaterials in a high-compliance regime inspired by polymer network topologies.

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.

Desk Editor's Note private letter to a colleague

The paper introduces a truss-plus-woven metamaterial architecture that reports large combined gains in stiffness and stretchability plus a defect-driven rise in dissipation, but the mechanistic attribution rests on unvalidated model assumptions.

read the letter

The main point is a new metamaterial that puts a stiff monolithic truss network together with a compliant woven network in one structure, drawing from double-network polymer ideas. The abstract claims this gives roughly tenfold better stiffness than pure woven versions and tenfold better stretchability than pure truss versions, plus a threefold jump in energy dissipation when internal defects are added. That defect result is the most interesting angle because it runs counter to the usual expectation that flaws reduce performance. The computational models are used to tie the extra dissipation to friction at the places where the two networks entangle. Fabrication is mentioned, so the designs are not purely theoretical. The work does a reasonable job of spelling out the topology choice and showing how the hybrid setup changes load sharing and contact. The counterintuitive defect behavior is worth noting even if the numbers need checking. The soft spot is the lack of any reported validation for the friction parameters or local dissipation measurements in the models. The abstract gives no error bars, no calibration details, and no comparison to alternative explanations such as altered load paths or geometry changes. If the full paper has experiments that pin down the contact behavior or DIC data showing where dissipation occurs, that would close the gap; otherwise the attribution stays model-dependent. This is aimed at people who design architected materials for soft or compliant regimes and who care about hybrid network topologies. A reader already working on woven or truss metamaterials would see the combination as a concrete next step. The paper deserves peer review because the architecture is specific, the defect effect is novel enough to test, and the modeling framework is standard enough that referees can evaluate the claims directly.

Referee Report

2 major / 1 minor

Summary. The manuscript introduces double-network-inspired (DNI) metamaterials that integrate monolithic truss (stiff) and woven (compliant) components into a single architecture. It claims these achieve a tenfold increase in stiffness relative to pure woven structures and a tenfold increase in stretchability relative to pure truss structures, with nonlinear computational mechanics models attributing the enhanced energy dissipation to frictional dissipation arising from entanglements between the two networks. The work further reports that introducing internal defects produces a threefold increase in energy dissipation via failure delocalization, in contrast to typical degradation effects.

Significance. If the central claims are substantiated, the work would provide a concrete demonstration that polymer-network topologies can be translated into mechanical metamaterial designs to simultaneously improve stiffness, stretchability, and toughness in the high-compliance regime. The computational modeling approach and the counterintuitive defect-enhanced dissipation result represent potentially useful contributions to the metamaterials literature.

major comments (2)

[Abstract / Computational Models] Abstract and computational modeling section: the claim that enhanced energy dissipation 'stems from increased frictional dissipation due to entanglements between the two networks' rests on nonlinear FE models, yet the manuscript reports neither experimental calibration of the contact/friction constitutive parameters nor direct local measurements of dissipation (e.g., via DIC strain fields or thermal imaging). Without such validation, alternative mechanisms (altered load paths, contact geometry changes, or model-specific constitutive choices) cannot be excluded, rendering the mechanistic attribution load-bearing but unsupported.
[Abstract / Results] Results on quantitative improvements: the tenfold gains in stiffness and stretchability and the threefold dissipation increase with defects are presented as central findings, but the abstract (and by extension the modeling claims) provides no error bars, sample sizes, or exclusion criteria for the computational or experimental data supporting these factors. This absence directly affects the reliability of the reported performance enhancements.

minor comments (1)

[Abstract] The abstract would be strengthened by a brief statement of the specific boundary conditions, mesh convergence criteria, or friction model employed in the nonlinear computations.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed comments. We address each major comment below and indicate the revisions planned for the resubmitted manuscript.

read point-by-point responses

Referee: [Abstract / Computational Models] Abstract and computational modeling section: the claim that enhanced energy dissipation 'stems from increased frictional dissipation due to entanglements between the two networks' rests on nonlinear FE models, yet the manuscript reports neither experimental calibration of the contact/friction constitutive parameters nor direct local measurements of dissipation (e.g., via DIC strain fields or thermal imaging). Without such validation, alternative mechanisms (altered load paths, contact geometry changes, or model-specific constitutive choices) cannot be excluded, rendering the mechanistic attribution load-bearing but unsupported.

Authors: We agree that the mechanistic attribution to frictional dissipation is inferred from the nonlinear FE models without experimental calibration of friction parameters or direct local measurements such as DIC. In the revised manuscript we will add a new subsection on model assumptions, cite literature values used for the friction coefficient, and include a sensitivity study showing the effect of varying the friction coefficient on the predicted dissipation. We will also revise the abstract language to state that the mechanism is suggested by the simulations rather than directly validated experimentally. As the present work is computational, full experimental validation lies outside its scope. revision: partial
Referee: [Abstract / Results] Results on quantitative improvements: the tenfold gains in stiffness and stretchability and the threefold dissipation increase with defects are presented as central findings, but the abstract (and by extension the modeling claims) provides no error bars, sample sizes, or exclusion criteria for the computational or experimental data supporting these factors. This absence directly affects the reliability of the reported performance enhancements.

Authors: The reported improvement factors are obtained from ensembles of simulations. In the revised manuscript we will report the number of independent realizations performed (typically five to ten per configuration), include representative error bars or ranges in the abstract and main figures, and add explicit details on simulation parameters and any data-exclusion criteria to the methods section. revision: yes

Circularity Check

0 steps flagged

No significant circularity; claims rest on independent experimental and modeling validation

full rationale

The paper presents DNI metamaterials via fabrication of truss-woven architectures, mechanical testing showing tenfold gains, and nonlinear FE models attributing dissipation to entanglements. No mathematical derivations, predictions, or first-principles results are described that reduce by construction to fitted inputs, self-definitions, or self-citation chains. The mechanistic explanation is model-based but not shown to be equivalent to its inputs via the paper's own equations. This is the common case of a self-contained computational/experimental study without load-bearing circular steps.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based solely on the abstract, the central claims rest on standard assumptions of nonlinear computational mechanics and the validity of the double-network analogy; no explicit free parameters, ad-hoc axioms, or invented entities are stated.

axioms (1)

domain assumption Nonlinear finite-element models of truss-woven entanglements accurately predict frictional dissipation without additional calibration beyond standard contact mechanics.
Invoked when attributing enhanced energy dissipation to entanglements between the two networks.

pith-pipeline@v0.9.0 · 5723 in / 1261 out tokens · 16481 ms · 2026-05-23T21:29:05.479260+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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author Bauer, J. et al. title Nanolattices: an emerging class of mechanical metamaterials . journal Advanced Materials volume 29 , pages 1701850 ( year 2017 )

work page 2017

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author Surjadi, J. U. et al. title Mechanical metamaterials and their engineering applications . journal Advanced Engineering Materials volume 21 , pages 1800864 ( year 2019 )

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[3] [3]

author Greer, J. R. & author Deshpande, V. S. title Three-dimensional architected materials and structures: Design, fabrication, and mechanical behavior . journal MRS Bulletin volume 44 , pages 750--757 ( year 2019 )

work page 2019

[4] [4]

, author Meza, L

author Schwaiger, R. , author Meza, L. & author Li, X. title The extreme mechanics of micro-and nanoarchitected materials . journal MRS Bulletin volume 44 , pages 758--765 ( year 2019 )

work page 2019

[5] [5]

author Meza, L. R. , author Das, S. & author Greer, J. R. title Strong, lightweight, and recoverable three-dimensional ceramic nanolattices . journal Science volume 345 , pages 1322--1326 ( year 2014 )

work page 2014

[6] [6]

author Zheng, X. et al. title Ultralight, ultrastiff mechanical metamaterials . journal Science volume 344 , pages 1373--1377 ( year 2014 )

work page 2014

[7] [7]

author Shaikeea, A. J. D. , author Cui, H. , author O’Masta, M. , author Zheng, X. R. & author Deshpande, V. S. title The toughness of mechanical metamaterials . journal Nature materials volume 21 , pages 297--304 ( year 2022 )

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, author Wadley, H

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, author Diamantopoulou, M

author Tancogne-Dejean, T. , author Diamantopoulou, M. , author Gorji, M. B. , author Bonatti, C. & author Mohr, D. title 3d plate-lattices: an emerging class of low-density metamaterial exhibiting optimal isotropic stiffness . journal Advanced Materials volume 30 , pages 1803334 ( year 2018 )

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author Crook, C. et al. title Plate-nanolattices at the theoretical limit of stiffness and strength . journal Nature communications volume 11 , pages 1579 ( year 2020 )

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author Yan, D. et al. title Soft three-dimensional network materials with rational bio-mimetic designs . journal Nature communications volume 11 , pages 1180 ( year 2020 )

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author Moestopo, W. P. , author Mateos, A. J. , author Fuller, R. M. , author Greer, J. R. & author Portela, C. M. title Pushing and pulling on ropes: hierarchical woven materials . journal Advanced Science volume 7 , pages 2001271 ( year 2020 )

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work page 2023

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author Gong, J. P. , author Katsuyama, Y. , author Kurokawa, T. & author Osada, Y. title Double-network hydrogels with extremely high mechanical strength . journal Advanced materials volume 15 , pages 1155--1158 ( year 2003 )

work page 2003

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work page 2004

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author Sun, J.-Y. et al. title Highly stretchable and tough hydrogels . journal Nature volume 489 , pages 133--136 ( year 2012 )

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, author Kawakami, R

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work page 2019

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, author Zhang, G

author Kim, J. , author Zhang, G. , author Shi, M. & author Suo, Z. title Fracture, fatigue, and friction of polymers in which entanglements greatly outnumber cross-links . journal Science volume 374 , pages 212--216 ( year 2021 )

work page 2021

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author Huang, M. et al. title Importance of entanglement between first and second components in high-strength double network gels . journal Macromolecules volume 40 , pages 6658--6664 ( year 2007 )

work page 2007

[21] [21]

author Yu, Q. M. , author Tanaka, Y. , author Furukawa, H. , author Kurokawa, T. & author Gong, J. P. title Direct observation of damage zone around crack tips in double-network gels . journal Macromolecules volume 42 , pages 3852--3855 ( year 2009 )

work page 2009

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author Zheng, X. et al. title Multiscale metallic metamaterials . journal Nature materials volume 15 , pages 1100--1106 ( year 2016 )

work page 2016

[23] [23]

& author Pikul, J

author Jiang, Z. & author Pikul, J. H. title Centimetre-scale crack-free self-assembly for ultra-high tensile strength metallic nanolattices . journal Nature materials volume 20 , pages 1512--1518 ( year 2021 )

work page 2021

[24] [24]

author Mateos, A. J. , author Huang, W. , author Zhang, Y.-W. & author Greer, J. R. title Discrete-continuum duality of architected materials: failure, flaws, and fracture . journal Advanced Functional Materials volume 29 , pages 1806772 ( year 2019 )

work page 2019

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author Bauer, J. et al. title Push-to-pull tensile testing of ultra-strong nanoscale ceramic--polymer composites made by additive manufacturing . journal Extreme Mechanics Letters volume 3 , pages 105--112 ( year 2015 )

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, author Wong, W

author Montemayor, L. , author Wong, W. , author Zhang, Y.-W. & author Greer, J. title Insensitivity to flaws leads to damage tolerance in brittle architected meta-materials . journal Scientific reports volume 6 , pages 20570 ( year 2016 )

work page 2016

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author Glaesener, R. et al. title Predicting the influence of geometric imperfections on the mechanical response of 2d and 3d periodic trusses . journal Acta Materialia volume 254 , pages 118918 ( year 2023 )

work page 2023

[28] [28]

, author Chen, H

author Chen, Q. , author Chen, H. , author Zhu, L. & author Zheng, J. title Fundamentals of double network hydrogels . journal Journal of Materials Chemistry B volume 3 , pages 3654--3676 ( year 2015 )

work page 2015

[29] [29]

, author Lu, G

author Hu, Q. , author Lu, G. & author Tse, K. M. title Compressive and tensile behaviours of 3d hybrid auxetic-honeycomb lattice structures . journal International Journal of Mechanical Sciences volume 263 , pages 108767 ( year 2024 )

work page 2024

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work page 1953

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author Zhao, X. title Multi-scale multi-mechanism design of tough hydrogels: building dissipation into stretchy networks . journal Soft matter volume 10 , pages 672--687 ( year 2014 )

work page 2014

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, author Lin, S

author Zhang, T. , author Lin, S. , author Yuk, H. & author Zhao, X. title Predicting fracture energies and crack-tip fields of soft tough materials . journal Extreme Mechanics Letters volume 4 , pages 1--8 ( year 2015 )

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author Zheng, Y. et al. title How chain dynamics affects crack initiation in double-network gels . journal Proceedings of the National Academy of Sciences volume 118 , pages e2111880118 ( year 2021 )

work page 2021

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ENTRY address archive author booktitle chapter edition editor eprint howpublished institution 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 ...

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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...

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