Abstract

Capture of a prey by spider orb webs is a dynamic process with energy dissipation. The dynamic response of spider orb webs under prey impact requires a multi-scale modeling by considering the material microstructures and the assembly of spider silks in the macro-scale. To better understand the prey capture process, this paper addresses a multi-scale approach to uncover the underlying energy dissipation mechanisms. Simulation results show that the microstructures of spider dragline silk play a significant role on energy absorption during prey capture. The alteration of the microstructures, material internal friction, and plastic deformation lead to energy dissipation, which is called material damping. In addition to the material damping in the micro-scale modeling, the energy dissipation due to drag force on the prey is also taken into consideration in the macro-scale modeling. The results indicate that aerodynamic drag, i.e., aero-damping, plays a significant role when the prey size is larger than a critical size.

References

References
1.
Witt
,
P. N.
, and
Reed
,
C. F.
,
1965
, “
Spider-web Building
,”
Science
,
149
(
3689
), pp.
1190
1197
. 10.1126/science.149.3689.1190
2.
Vollrath
,
F.
,
1992
, “
Spider Webs and Silks
,”
Sci. Am.
,
266
(
3
), pp.
70
77
. 10.1038/scientificamerican0392-70
3.
Gosline
,
J.
,
Guerette
,
P.
,
Ortlepp
,
C.
, and
Savage
,
K.
,
1999
, “
The Mechanical Design of Spider Silks: From Fibroin Sequence to Mechanical Function
,”
J. Exp. Biol.
,
202
(
23
), pp.
3295
3303
.
4.
Xu
,
M.
, and
Lewis
,
R. V.
,
1990
, “
Structure of a Protein Superfiber: Spider Dragline Silk
,”
Proc. Natl. Acad. Sci. U. S. A.
,
87
(
18
), pp.
7120
7124
. 10.1073/pnas.87.18.7120
5.
Vollrath
,
F.
, and
Porter
,
D.
,
2006
, “
Spider Silk as Archetypal Protein Elastomer
,”
Soft Matter
,
2
(
5
), pp.
377
385
. 10.1039/b600098n
6.
Craig
,
C. L.
,
1987
, “
The Ecological and Evolutionary Interdependence Between Web Architecture and Web Silk Spun by Orb Web Weaving Spiders
,”
Biol. J. Linn. Soc.
,
30
(
2
), pp.
135
162
. 10.1111/j.1095-8312.1987.tb00294.x
7.
Das
,
R.
,
Kumar
,
A.
,
Patel
,
A.
,
Vijay
,
S.
,
Saurabh
,
S.
, and
Kumar
,
N.
,
2017
, “
Biomechanical Characterization of Spider Webs
,”
J. Mech. Behav. Biomed. Mater.
,
67
, pp.
101
109
. 10.1016/j.jmbbm.2016.12.008
8.
De Tommasi
,
D.
,
Puglisi
,
G.
, and
Saccomandi
,
G.
,
2010
, “
Damage, Self-Healing, and Hysteresis in Spider Silks
,”
Biophys. J.
,
98
(
9
), pp.
1941
1948
. 10.1016/j.bpj.2010.01.021
9.
Sensenig
,
A. T.
,
Lorentz
,
K. A.
,
Kelly
,
S. P.
, and
Blackledge
,
T. A.
,
2012
, “
Spider Orb Webs Rely on Radial Threads to Absorb Prey Kinetic Energy
,”
J. R. Soc. Interface
,
9
(
73
), pp.
1880
1891
. 10.1098/rsif.2011.0851
10.
Aoyanagi
,
Y.
, and
Okumura
,
K.
,
2010
, “
Simple Model for the Mechanics of Spider Webs
,”
Phys. Rev. Lett.
,
104
(
3
), p.
038102
. 10.1103/PhysRevLett.104.038102
11.
Alam
,
M.
, and
Jenkins
,
C.
,
2005
, “
Damage Tolerance in Naturally Compliant Structures
,”
Int. J. Damage Mech.
,
14
(
4
), pp.
365
384
. 10.1177/1056789505054313
12.
Lin
,
L. H.
,
Edmonds
,
D. T.
, and
Vollrath
,
F.
,
1995
, “
Structural Engineering of an Orb-Spider’s Web
,”
Nature
,
373
(
6510
), p.
146
148
. 10.1038/373146a0
13.
Zaera
,
R.
,
Soler
,
A.
, and
Teus
,
J.
,
2014
, “
Uncovering Changes in Spider Orb-Web Topology Owing to Aerodynamic Effects
,”
J. R. Soc. Interface
,
11
(
98
), p.
20140484
. 10.1098/rsif.2014.0484
14.
Yu
,
H.
,
Yang
,
J.
, and
Sun
,
Y.
,
2015
, “
Energy Absorption of Spider Orb Webs During Prey Capture: A Mechanical Analysis
,”
J. Bionic Eng.
,
12
(
3
), pp.
453
463
. 10.1016/S1672-6529(14)60136-0
15.
Japyassu
,
H. F.
, and
Laland
,
K. N.
,
2017
, “
Extended Spider Cognition
,”
Anim. Cognit.
,
20
(
3
), pp.
375
395
. 10.1007/s10071-017-1069-7
16.
Hergenröder
,
R.
, and
Barth
,
F. G.
,
1983
, “
Vibratory Signals and Spider Behavior: How do the Sensory Inputs From the Eight Legs Interact in Orientation?
,”
J. Comp. Physiol.
,
152
(
3
), pp.
361
371
. 10.1007/BF00606241
17.
Mortimer
,
B.
,
Soler
,
A.
,
Siviour
,
C.
, and
Vollrath
,
F.
,
2018
, “
Remote Monitoring of Vibrational Information in Spider Webs
,”
Sci. Nat.
,
105
(
5–6
), p.
37
. 10.1007/s00114-018-1561-1
18.
Landolfa
,
M.
, and
Barth
,
F.
,
1996
, “
Vibrations in the Orb Web of the Spider Nephila clavipes: Cues for Discrimination and Orientation
,”
J. Comp. Physiol. A
,
179
(
4
), pp.
493
508
. 10.1007/BF00192316
19.
Mortimer
,
B.
,
2017
, “
Biotremology: Do Physical Constraints Limit the Propagation of Vibrational Information?
,”
Anim. Behav.
,
130
, pp.
165
174
. 10.1016/j.anbehav.2017.06.015
20.
Barth
,
F. G.
,
1998
, “The Vibrational Sense of Spiders,”
Comparative Hearing: Insects
,
R. R.
Hoy
,
A. N.
Popper
, and
R. R.
Fay
, eds.,
Springer
,
New York
, pp.
228
278
.
21.
Aguirre
,
L. E.
,
de Oliveira
,
A.
,
Seč
,
D.
,
Čopar
,
S.
,
Almeida
,
P. L.
,
Ravnik
,
M.
,
Godinho
,
M. H.
, and
Žumer
,
S.
,
2016
, “
Sensing Surface Morphology of Biofibers by Decorating Spider Silk and Cellulosic Filaments With Nematic Microdroplets
,”
Proc. Natl. Acad. Sci. U. S. A.
,
113
(
5
), pp.
1174
1179
. 10.1073/pnas.1518739113
22.
Yang
,
Q.
, and
Li
,
G.
,
2014
, “
Spider-Silk-Like Shape Memory Polymer Fiber for Vibration Damping
,”
Smart Mater. Struct.
,
23
(
10
), p.
105032
. 10.1088/0964-1726/23/10/105032
23.
Soler
,
A.
, and
Zaera
,
R.
,
2016
, “
The Secondary Frame in Spider Orb Webs: The Detail That Makes the Difference
,”
Sci. Rep.
,
6
(
1
), p.
31265
. 10.1038/srep31265
24.
Alam
,
M.
,
Wahab
,
M.
, and
Jenkins
,
C.
,
2007
, “
Mechanics in Naturally Compliant Structures
,”
Mech. Mater.
,
39
(
2
), pp.
145
160
. 10.1016/j.mechmat.2006.04.005
25.
Ko
,
F. K.
, and
Jovicic
,
J.
,
2004
, “
Modeling of Mechanical Properties and Structural Design of Spider Web
,”
Biomacromolecules
,
5
(
3
), pp.
780
785
. 10.1021/bm0345099
26.
Tietsch
,
V.
,
Alencastre
,
J.
,
Witte
,
H.
, and
Torres
,
F.
,
2016
, “
Exploring the Shock Response of Spider Webs
,”
J. Mech. Behav. Biomed. Mater.
,
56
, pp.
1
5
. 10.1016/j.jmbbm.2015.11.007
27.
Van Beek
,
J. D.
,
Hess
,
S.
,
Vollrath
,
F.
, and
Meier
,
B.
,
2002
, “
The Molecular Structure of Spider Dragline Silk: Folding and Orientation of the Protein Backbone
,”
Proc. Natl. Acad. Sci. U. S. A.
,
99
(
16
), pp.
10266
10271
. 10.1073/pnas.152162299
28.
Bueche
,
F.
,
1960
, “
Molecular Basis for the Mullins Effect
,”
J. Appl. Polym. Sci.
,
4
(
10
), pp.
107
114
. 10.1002/app.1960.070041017
29.
Du
,
N.
,
Yang
,
Z.
,
Liu
,
X. Y.
,
Li
,
Y.
, and
Xu
,
H. Y.
,
2011
, “
Structural Origin of the Strain-Hardening of Spider Silk
,”
Adv. Funct. Mater.
,
21
(
4
), pp.
772
778
. 10.1002/adfm.201001397
30.
Harmer
,
A. M.
,
Blackledge
,
T. A.
,
Madin
,
J. S.
, and
Herberstein
,
M. E.
,
2010
, “
High-performance Spider Webs: Integrating Biomechanics, Ecology and Behaviour
,”
J. R. Soc. Interface
,
8
(
57
), pp.
457
471
. 10.1098/rsif.2010.0454
31.
Keten
,
S.
,
Xu
,
Z.
,
Ihle
,
B.
, and
Buehler
,
M. J.
,
2010
, “
Nanoconfinement Controls Stiffness, Strength and Mechanical Toughness of β-Sheet Crystals in Silk
,”
Nat. Mater.
,
9
(
4
), p.
359
367
. 10.1038/nmat2704
32.
Keten
,
S.
, and
Buehler
,
M. J.
,
2010
, “
Nanostructure and Molecular Mechanics of Spider Dragline Silk Protein Assemblies
,”
J. R. Soc. Interface
,
7
(
53
), pp.
1709
1721
. 10.1098/rsif.2010.0149
33.
Hayashi
,
C. Y.
,
Shipley
,
N. H.
, and
Lewis
,
R. V.
,
1999
, “
Hypotheses That Correlate the Sequence, Structure, and Mechanical Properties of Spider Silk Proteins
,”
Int. J. Biol. Macromol.
,
24
(
2–3
), pp.
271
275
. 10.1016/S0141-8130(98)00089-0
34.
Marko
,
J. F.
, and
Siggia
,
E. D.
,
1995
, “
Stretching DNA
,”
Macromolecules
,
28
(
26
), pp.
8759
8770
. 10.1021/ma00130a008
35.
Rubinstein
,
M.
, and
Colby
,
R. H.
,
2003
,
Polymer Physics
,
Oxford University Press
,
New York
.
36.
Ogden
,
R. W.
,
Saccomandi
,
G.
, and
Sgura
,
I.
,
2005
, “
On Worm-Like Chain Models Within the Three-Dimensional Continuum Mechanics Framework
,”
Proc. R. Soc. A: Math. Phys. Eng. Sci.
,
462
(
2067
), pp.
749
768
. 10.1098/rspa.2005.1592
37.
Kuhl
,
E.
,
Garikipati
,
K.
,
Arruda
,
E. M.
, and
Grosh
,
K.
,
2005
, “
Remodeling of Biological Tissue: Mechanically Induced Reorientation of a Transversely Isotropic Chain Network
,”
J. Mech. Phys. Solids
,
53
(
7
), pp.
1552
1573
. 10.1016/j.jmps.2005.03.002
38.
Kuhn
,
W.
,
1934
, “
Über die Gestalt Fadenförmiger Moleküle in Lösungen
,”
Kolloid-Zeitschrift
,
68
(
1
), pp.
2
15
. 10.1007/BF01451681
39.
Arruda
,
E. M.
, and
Boyce
,
M. C.
,
1993
, “
A Three-Dimensional Constitutive Model for the Large Stretch Behavior of Rubber Elastic Materials
,”
J. Mech. Phys. Solids
,
41
(
2
), pp.
389
412
. 10.1016/0022-5096(93)90013-6
40.
Termonia
,
Y.
,
1994
, “
Molecular Modeling of Spider Silk Elasticity
,”
Macromolecules
,
27
(
25
), pp.
7378
7381
. 10.1021/ma00103a018
41.
Diani
,
J.
,
Brieu
,
M.
,
Vacherand
,
J.-M.
, and
Rezgui
,
A.
,
2004
, “
Directional Model for Isotropic and Anisotropic Hyperelastic Rubber-Like Materials
,”
Mech. Mater.
,
36
(
4
), pp.
313
321
. 10.1016/S0167-6636(03)00025-5
42.
Guinea
,
G.
,
Pérez-Rigueiro
,
J.
,
Plaza
,
G.
, and
Elices
,
M.
,
2006
, “
Volume Constancy During Stretching of Spider Silk
,”
Biomacromolecules
,
7
(
7
), pp.
2173
2177
. 10.1021/bm060138v
43.
Reese
,
S.
, and
Govindjee
,
S.
,
1998
, “
A Theory of Finite Viscoelasticity and Numerical Aspects
,”
Int. J. Solids Struct.
,
35
(
26–27
), pp.
3455
3482
. 10.1016/S0020-7683(97)00217-5
44.
Bergström
,
J.
, and
Boyce
,
M.
,
1998
, “
Constitutive Modeling of the Large Strain Time-Dependent Behavior of Elastomers
,”
J. Mech. Phys. Solids
,
46
(
5
), pp.
931
954
. 10.1016/S0022-5096(97)00075-6
45.
Marckmann
,
G.
,
Verron
,
E.
,
Gornet
,
L.
,
Chagnon
,
G.
,
Charrier
,
P.
, and
Fort
,
P.
,
2002
, “
A Theory of Network Alteration for the Mullins Effect
,”
J. Mech. Phys. Solids
,
50
(
9
), pp.
2011
2028
. 10.1016/S0022-5096(01)00136-3
46.
Pan
,
Y.
, and
Zhong
,
Z.
,
2017
, “
Modeling the Mullins Effect of Rubber-Like Materials
,”
Int. J. Damage Mech.
,
26
(
6
), pp.
933
948
. 10.1177/1056789516635728
47.
Liu
,
Y.
,
Shao
,
Z.
, and
Vollrath
,
F.
,
2008
, “
Elasticity of Spider Silks
,”
Biomacromolecules
,
9
(
7
), pp.
1782
1786
. 10.1021/bm7014174
48.
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