Spider silk is a remarkable example of bio-material with superior mechanical characteristics. Its multilevel structural organization of dragline and viscid silk leads to unusual and tunable properties, extensively studied from a quasi-static point of view. In this study, inspired by the Nephila spider orb web architecture, we propose a design for mechanical metamaterials based on its periodic repetition. We demonstrate that spider-web metamaterial structure plays an important role in the dynamic response and wave attenuation mechanisms. The capability of the resulting structure to inhibit elastic wave propagation in sub-wavelength frequency ranges is assessed, and parametric studies are performed to derive optimal configurations and constituent mechanical properties. The results show promise for the design of innovative lightweight structures for tunable vibration damping and impact protection, or the protection of large scale infrastructure such as suspended bridges.
References
1.
H.
Gao
, B.
Ji
, I. L.
Jaeger
, E.
Arzt
, and P.
Fratzl
, “Materials become insensitive to flaws at nanoscales: Lessons from nature
,” Proc. Natl. Acad. Sci. U.S.A.
100
, 5597
–5600
(2003
).2.
J.
Aizenberg
, J. C.
Weaver
, M. S.
Thanawala
, V. C.
Sundar
, D. E.
Morse
, and P.
Fratzl
, “Skeleton of Euplectella sp.: Structural hierarchy from the nanoscale to the macroscale
,” Science
309
, 275
–278
(2005
).3.
S.
Kamat
, X.
Su
, R.
Ballarini
, and A. H.
Heuer
, “Structural basis for the fracture toughness of the shell of the conch Strombus gigas
,” Nature
405
, 1036
–1040
(2000
).4.
F.
Vollrath
, “Spider webs and silks
,” Sci. Am.
266
, 70
–76
(1992
).5.
J. M.
Gosline
, P. A.
Guerette
, C. S.
Ortlepp
, and K. N.
Savage
, “The mechanical design of spider silks: from fibroin sequence to mechanical function
,” J. Exp. Biol.
202
, 3295
–3303
(1999
).6.
C.
Boutry
and T.
Blackledge
, “Biomechanical variation of silk links spinning plasticity to spider web function
,” Zoology
112
, 451
–460
(2009
).7.
A.
Meyer
, N.
Pugno
, and S. W.
Cranford
, “Compliant threads maximize spider silk connection strength and toughness
,” J. R. Soc., Interface
11
, 20140561
(2014
).8.
S.
Cranford
, A.
Tarakanova
, N.
Pugno
, and M.
Buehler
, “Nonlinear material behaviour of spider silk yields robust webs
,” Nature
482
, 72
–76
(2012
).9.
R.
Zaera
, A.
Soler
, and J.
Teus
, “Uncovering changes in spider orb-web topology owing to aerodynamics effects
,” J. R. Soc., Interface
11
, 20140484
(2014
).10.
Y.
Aoyanagi
and K.
Okumura
, “Simple model for the mechanics of spider webs
,” Phys. Rev. Lett.
104
, 038102
(2010
).11.
M. S.
Alam
, M. A.
Wahab
, and C. H.
Jenkins
, “Mechanics in naturally compliant structures
,” Mech. Mater.
39
, 145
–160
(2007
).12.
F. K.
Ko
and J.
Jovicic
, “Modeling of mechanical properties and structural design of spider web
,” Biomacromolecules
5
, 780
–785
(2004
).13.
M.
Miniaci
, A.
Krushynska
, F.
Bosia
, and N. M.
Pugno
, “Large scale mechanical metamaterials as seismic shields
,” New J. Phys.
(to be published).14.
R.
Martínez-Sala
, J.
Sancho
, J. V.
Sánchez
, V.
Gómez
, J.
Llinares
, and F.
Meseguer
, “Sound attenuation by sculpture
,” Nature
378
, 241
(1995
).15.
D.
Bigoni
, S.
Guenneau
, A. B.
Movchan
, and M.
Brun
, “Elastic metamaterials with inertial locally resonant structures: Application to lensing and localization
,” Phys. Rev. B
87
, 174303
(2013
).16.
T.
Zhu
and E.
Ertekin
, “Phonon transport on two-dimensional graphene/boron nitride superlattices
,” Phys. Rev. B
90
, 195209
(2014
).17.
T.
Zhu
and E.
Ertekin
, “Resolving anomalous strain effects on two-dimensional phonon flows: The cases of graphene, boron nitride, and planar superlattices
,” Phys. Rev. B
91
, 205429
(2015
).18.
M.
Fahrat
, S.
Enoch
, S.
Guenneau
, and A. B.
Movchan
, “Broadband cylindrical acoustic cloak for linear surface waves in a fluid
,” Phys. Rev. Lett.
101
, 134501
(2008
).19.
M.
Maldovan
, “Sound and heat revolutions in phononics
,” Nature
503
, 209
–217
(2013
).20.
L.
Brillouin
, Wave Propagation in Periodic Structures
(McGraw-Hill Book Company
, 1946
).21.
Z.
Liu
, X.
Zhang
, Y.
Mao
, Y. Y.
Zhu
, Z.
Yang
, C. T.
Chan
, and P.
Sheng
, “Locally resonant sonic materials
,” Science
289
, 1734
–1736
(2000
).22.
Y.
Pennec
, J. O.
Vasseur
, B.
Djafari-Rouhani
, L.
Dobrzynski
, and P. A.
Deymier
, “Two-dimensional phononic crystals: Examples and applications
,” Surf. Sci. Rep.
65
, 229
–291
(2010
).23.
M. I.
Hussein
, M. J.
Leamy
, and M.
Ruzzene
, “Dynamics of phononic materials and structures: Historical origins, recent progress, and future outlook
,” Appl. Mech. Rev.
66
, 040802
(2014
).24.
A. O.
Krushynska
, V. G.
Kouznetsova
, and M. G. D.
Geers
, “Towards optimal design of locally resonant acoustic metamaterials
,” J. Mech. Phys. Solids
71
, 179
–196
(2014
).25.
M.
Miniaci
, A.
Krushynska
, F.
Bosia
, and N. M.
Pugno
, “Bio-inspired hierarchical dissipative metamaterials
,” e-print arXiv:1606.03596.26.
P.
Wang
, F.
Casadei
, S. H.
Kang
, and K.
Bertoldi
, “Locally resonant band gaps in periodic beam lattices by tuning connectivity
,” Phys. Rev. B
91
, 020103
(2015
).27.
Q. J.
Lim
, P.
Wang
, S. J. A.
Koh
, E. H.
Khoo
, and K.
Bertoldi
, “Wave propagation in fractal-inspired self-similar beam lattices
,” Appl. Phys. Lett.
107
, 221911
(2015
).28.
P. G.
Martinsson
and A. B.
Movchan
, “Vibrations of lattice structures and phononic band gaps
,” Q. J. Mech. Appl. Math.
56
, 45
–64
(2003
).29.
M.
Miniaci
, A.
Marzani
, N.
Testoni
, and L.
De Marchi
, “Complete band gaps in a polyvinyl chloride (PVC) phononic plate with cross-like holes: Numerical design and experimental verification
,” Ultrasonics
56
, 251
–259
(2015
).30.
P.
Wang
, J.
Shim
, and K.
Bertoldi
, “Effects of geometric and material nonlinearities on tunable band gaps and low-frequency directionality of phononic crystals
,” Phys. Rev. B
88
, 014304
(2013
).31.
R.
Sainidou
, N.
Stefanou
, and A.
Modinos
, “Formation of absolute frequency gaps in three-dimensional solid phononic crystals
,” Phys. Rev. B
66
, 212301
(2002
).32.
S.
Timoshenko
, Vibration Problems in Engineering
, 3rd ed. (D. Van Nostrand Company Inc.
, Princeton, NJ
, 1955
).© 2016 Author(s).
2016
Author(s)
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