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Supersonic impact resilience of nanoarchitected carbon


Architected materials with nanoscale features have enabled extreme combinations of properties by exploiting the ultralightweight structural design space together with size-induced mechanical enhancement at small scales. Apart from linear waves in metamaterials, this principle has been restricted to quasi-static properties or to low-speed phenomena, leaving nanoarchitected materials under extreme dynamic conditions largely unexplored. Here, using supersonic microparticle impact experiments, we demonstrate extreme impact energy dissipation in three-dimensional nanoarchitected carbon materials that exhibit mass-normalized energy dissipation superior to that of traditional impact-resistant materials such as steel, aluminium, polymethyl methacrylate and Kevlar. In-situ ultrahigh-speed imaging and post-mortem confocal microscopy reveal consistent mechanisms such as compaction cratering and microparticle capture that enable this superior response. By analogy to planetary impact, we introduce predictive tools for crater formation in these materials using dimensional analysis. These results substantially uncover the dynamic regime over which nanoarchitecture enables the design of ultralightweight, impact-resistant materials that could open the way to design principles for lightweight armour, protective coatings and blast-resistant shields for sensitive electronics.

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Fig. 1: Material fabrication and microparticle impact experiments.
Fig. 2: Impact processes and resulting damage.
Fig. 3: Impact energetics and comparison to ballistic materials.
Fig. 4: Impact scaling laws for damage prediction.

Data availability

The data supporting the findings of this study are available within this article and its Supplementary Information.


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C.M.P. and D.M.K. acknowledge financial support from Office of Naval Research Award N00014-16-1-2431. J.R.G. acknowledges support from the Vannevar Bush Faculty Fellowship. D.V., Y.S. and K.A.N. acknowledge support by the US Army Research Office through the Institute for Soldier Nanotechnologies (ISN), under Cooperative Agreement Number W911NF-18-2-0048. The authors thank W. J. Schill for valuable discussions.

Author information

Authors and Affiliations



C.M.P., D.V., K.A.N., D.M.K. and J.R.G. designed the study and interpreted the results. C.M.P. and B.W.E. fabricated the samples and conducted nanomechanical experiments. D.V. and Y.S. performed the impact experiments. C.M.P. and B.W.E. analysed all data. C.M.P., K.A.N. and J.R.G. supervised the project. C.M.P., D.M.K. and J.R.G. wrote the manuscript with input from all authors.

Corresponding authors

Correspondence to Carlos M. Portela or Julia R. Greer.

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Competing interests

The authors declare no competing interests.

Additional information

Peer review informationNature Materials thanks the anonymous reviewers for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Pre-pyrolysis sample configuration.

a, Polymeric IP-Dip tetrakaidecahedron sample with overall dimensions of 300 × 300 × 150μm3. b, Diagram of spring elastic foundation decoupling unit cells from the Si substrate, and c, detailed view of a single helical spring with its characteristic parameters (see Methods for values). Scale bar, 100 μm.

Extended Data Fig. 2 Crater morphology evolution.

Crater evolution as a function of relative density \(\overline{\rho }\) and impact velocity v0. Full penetration of the \(\overline{\rho }\approx 14 \%\) sample was observed for the impact at 749 m/s, and deep particle embedding was observed in the \(\overline{\rho }\approx 23 \%\) sample at 757 m/s. White scale bar 40 μm, inset diameters 18 μm.

Extended Data Fig. 3 Material compaction and failure in craters.

a, FIB cross-section at the edge of the crater (and captured projectile) of a \(\overline{\rho }\approx 23 \%\) sample after impact at v0= 516 m/s. b, FIB cross-section at the middle of the crater for the sample in a, showing compacted unit cells below the captured projectile. c,d, Crater of a \(\overline{\rho }\approx 14 \%\) sample after impact at v0= 749 m/s exhibiting full-sample penetration and particle rebound at vr= 296 m/s. Some compacted unit cells are observed to remain within the crater. e-g, Crater of a \(\overline{\rho }\approx 23 \%\) sample after impact at v0= 255 m/s and particle rebound at vr= 48 m/s, showing brittle failure of individual carbon struts. Scale bars in a-c, 10 μm; d,e, 5 μm; and g, 500 nm.

Extended Data Fig. 4 SiO2-Si impact experiments.

Impact of 14 μm-diameter SiO2 spheres onto a Si substrate. a, Impact and rebound speeds of 514 m/s and 339 m/s, respectively, and b, impact speed of 646 m/s causing particle shatter. c, Micrograph of initial SiO2 particle, and d, fragment of a shattered particle. Scale bar in a,b, 30 μm; c,d, 4 μm.

Extended Data Fig. 5 SiO2-Si impact energetics.

a, Normalized rebound (Wr/W0) and inelastic (Wi/W0) energies, as functions of the impact energy (W0), exhibiting a nonlinear increase in dissipation with increasing impact energy and a transition to a particle shatter regime between 650-700 m/s. Particle shatter was categorized as a normalized inelastic energy of 1. b, Inelastic energy as a function of average particle consolidation Jp, that is, the resulting fraction of the original volume after impact, estimated using the model proposed by Schill et al.31. The transition to the shatter regime is estimated to occur for an average Jp of 0.91-0.93. These values serve as a lower bound for the actual consolidation in the particles since consolidation is most likely localized in some regions of the particle rather than being constant throughout the entirety of the volume. c, Estimated consolidation pressure as a function of Jp, obtained from the model by Schill et al.31. Error bars correspond to the standard error in measurements.

Extended Data Fig. 6 SiO2 inelastic energy function.

Inelastic energy from the SiO2-Si impact experiments as a function of the rebound energy, restricted to the range of rebound energies observed in the nanoarchitected carbon impact experiments. A quadratic function of the form \({W}_{i,Si{O}_{2}}={C}_{1}{W}_{r}^{2}+{C}_{2}{W}_{r}+{C}_{3}\), with fit parameters C1 = 5.94 × 106, C2 = − 0.126, and C3 = 1.34 × 10−9, was used to estimate the inelastic energy contribution of the SiO2 projectiles in the nanoarchitected carbon impact experiments. This first-order approximation assumes that comparable SiO2 dissipation occurs during rebound from compacted nanoarchitected carbon compared to the Si substrate. This function was used to isolate the contribution of the nanoarchitected carbon to the inelastic energy in the impact experiments. Error bars correspond to the standard error in measurements.

Extended Data Fig. 7 Energy dissipation via compaction shocks.

a, Diagram of a compaction shock front propagating within a cylindrical crater, caused by impact at velocity v0, where the shock front (moving at velocity \(\dot{s}\)) is shown in red. The particle velocity v, density ρ, and stress σ behind and ahead of the discontinuity are depicted using +/- superscripts, respectively. b, Inelastic energy of the nanoarchitected carbon impact experiments, as a function of the impact energy W0, decomposed as Wi = Wc + Wd. Here, \({W}_{c}={m}_{p}{v}_{0}^{2}/2\) corresponds to a measure of the kinetic energy imparted on the participation mass (that is, the crater-mass kinetic energy), and Wd is the energy attributed to other dissipation mechanisms such as compaction shock propagation. This decomposition is in line with the form presented in Eq. (2). For the same impact energy W0, a higher Wd value is observed in the \(\overline{\rho }\approx 23 \%\) compared to the \(\overline{\rho }\approx 14 \%\) samples. Error bars correspond to the standard error in measurements.

Extended Data Fig. 8 Nanomechanical compression experiments.

Uniaxial in situ compression of \(\overline{\rho }=20\pm 1 \%\) relative density samples, with insets showing a representative sample before and after compression. After an extended elastic strain limit on the order of 10% (consistent with other nanoscale pyrolytic carbon explorations23,28), catastrophic brittle failure was observed upon reaching a collapse stress level. All samples were fabricated on a sacrificial pillar which collapsed at low loads to enable proper sample contact with the substrate. Zero-strain was defined as the beginning of the experiment for consistency. Scale bars, 10 μm.

Extended Data Fig. 9 Specific impact energy comparison.

Comparison of the specific inelastic energy \({W}_{i}^{* }={W}_{i}/{m}_{p}\), that is, the inelastic energy normalized by the participation mass, attained by the nanoarchitected carbon materials compared to other materials with specific impact energies \({W}_{0}^{* }={W}_{0}/{m}_{p}\) in the same experimental regime. The nanoarchitected carbon samples were observed to outperform nanoscale polystyrene22 and Kevlar composites38 by 75% and 72%, respectively, for the same specific impact energy. Error bars correspond to the standard error in measurements.

Supplementary information

Supplementary Information

Supplementary text (sections I and II), video captions 1–5 and Tables 1–3.

Supplementary Video 1

LIPIT experiment of a 14 μm-diameter SiO2 microparticle impacting a nanoarchitected tetrakaidecahedron carbon material (\(\overline{\rho }\approx 23 \%\)) at v0= 44 m/s and elastically rebounding at an angle away from the microscope objective. No damage was observed on the sample after this impact.

Supplementary Video 2

LIPIT experiment of a 14 μm-diameter SiO2 microparticle impacting a nanoarchitected tetrakaidecahedron carbon material (\(\overline{\rho }\approx 23 \%\)) at v0= 238 m/s, causing cratering and particle rebound at vr= 50 m/s.

Supplementary Video 3

LIPIT experiment of a 14 μm-diameter SiO2 microparticle impacting a nanoarchitected tetrakaidecahedron carbon material (\(\overline{\rho }\approx 23 \%\)) at v0= 676 m/s, causing cratering and particle capture.

Supplementary Video 4

LIPIT experiment of a 14 μm-diameter SiO2 microparticle impacting a thick Si substrate at v0= 514 m/s and rebounding at vr= 39 m/s.

Supplementary Video 5

LIPIT experiment of a 14 μm-diameter SiO2 microparticle impacting a thick Si substrate at v0= 646 m/s and subsequent shatter.

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Portela, C.M., Edwards, B.W., Veysset, D. et al. Supersonic impact resilience of nanoarchitected carbon. Nat. Mater. 20, 1491–1497 (2021).

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