Nature has a proven track record of advanced materials with outstanding mechanical properties, which has been the focus of recent research. A well-known trade-off between ultimate strength and toughness is one of the main challenges in materials design. Progress has been made by mimicking tough biological fibers by applying the concepts of (1) sacrificial bond and (2) hidden length, providing a so-called “safety-belt” for biological materials. Prior studies indicate a relatively common behavior across scales, from nano- to macro-, suggesting the potential of a generalized theoretical mechanistic framework. Here, we undertake molecular dynamics (MD) based simulation to investigate the mechanical properties of model nanoscale fibers. We explore representative models of serial looped or coiled fibers with different parameters—specifically number of loops, loop radii, cross-link strength, and fiber stiffness—to objectively compare strength, extensibility, and fiber toughness gain. Observing consistent saw-tooth like behavior, and adapting worm-like chain (WLC) mechanics (i.e., pseudo-entropic elasticity), a theoretical scaling relation which can describe the fiber toughness gain as a function of the structural factors is developed and validated by simulation. The theoretical model fits well with the simulation results, indicating that engineering the mechanical response based on controlled structure is possible. The work lays the foundation for the design of uniaxial metamaterials with tunable and predictable tensile behavior and superior toughness.

References

References
1.
Becker
,
N.
,
Oroudjev
,
E.
,
Mutz
,
S.
,
Cleveland
,
J. P.
,
Hansma
,
P. K.
,
Hayashi
,
C. Y.
,
Makarov
,
D. E.
, and
Hansma
,
H. G.
,
2003
, “
Molecular Nanosprings in Spider Capture-Silk Threads
,”
Nat. Mater.
,
2
(
4
), pp.
278
283
.
2.
Zhao
,
X.
,
2014
, “
Multi-Scale Multi-Mechanism Design of Tough Hydrogels: Building Dissipation Into Stretchy Networks
,”
Soft Matter
,
10
(
5
), pp.
672
687
.
3.
Vasdravellis
,
G.
,
Karavasilis
,
T. L.
, and
Uy
,
B.
,
2014
, “
Design Rules, Experimental Evaluation, and Fracture Models for High-Strength and Stainless-Steel Hourglass Shape Energy Dissipation Devices
,”
J. Struct. Eng.
,
140
(
11
), p.
04014087
.
4.
Habibi
,
A.
,
Chan
,
R. W. K.
, and
Albermani
,
F.
,
2013
, “
Energy-Based Design Method for Seismic Retrofitting With Passive Energy Dissipation Systems
,”
Eng. Struct.
,
46
(
Suppl. C
), pp.
77
86
.
5.
Eatherton
,
M. R.
,
Ma
,
X.
,
Krawinkler
,
H.
,
Mar
,
D.
,
Billington
,
S.
,
Hajjar
,
J. F.
, and
Deierlein
,
G. G.
,
2014
, “
Design Concepts for Controlled Rocking of Self-Centering Steel-Braced Frames
,”
J. Struct. Eng.
,
140
(
11
), p.
04014082
.
6.
Rudykh
,
S.
,
Ortiz
,
C.
, and
Boyce
,
M. C.
,
2015
, “
Flexibility and Protection by Design: Imbricated Hybrid Microstructures of Bio-Inspired Armor
,”
Soft Matter
,
11
(
13
), pp.
2547
2554
.
7.
Wu
,
Y.
,
Shah
,
D. U.
,
Liu
,
C.
,
Yu
,
Z.
,
Liu
,
J.
,
Ren
,
X.
,
Rowland
,
M. J.
,
Abell
,
C.
,
Ramage
,
M. H.
, and
Scherman
,
O. A.
,
2017
, “
Bioinspired Supramolecular Fibers Drawn From a Multiphase Self-Assembled Hydrogel
,”
Proc. Natl. Acad. Sci.
,
114
(
31
), pp.
8163
8168
.
8.
Chang
,
H.
,
Luo
,
J.
,
Gulgunje
,
P. V.
, and
Kumar
,
S.
,
2017
, “
Structural and Functional Fibers
,”
Annu. Rev. Mater. Res.
,
47
(
1
), pp.
331
359
.
9.
Koeppel
,
A.
, and
Holland
,
C.
,
2017
, “
Progress and Trends in Artificial Silk Spinning: A Systematic Review
,”
ACS Biomater. Sci. Eng.
,
3
(
3
), pp.
226
237
.
10.
Isabelle
,
S.
, and
Markus
,
J. B.
,
2016
, “
Nanomechanics of Silk: The Fundamentals of a Strong, Tough and Versatile Material
,”
Nanotechnology
,
27
(
30
), p.
302001
.
11.
Bratzel
,
G. H.
,
Cranford
,
S. W.
,
Espinosa
,
H.
, and
Buehler
,
M. J.
,
2010
, “
Bioinspired Noncovalently Crosslinked ‘Fuzzy' Carbon Nanotube Bundles With Superior Toughness and Strength
,”
J. Mater. Chem.
,
20
(
46
), pp.
10465
10474
.
12.
Meng
,
J.
,
Zhang
,
Y.
,
Song
,
K.
, and
Minus
,
M. L.
,
2014
, “
Forming Crystalline Polymer-Nano Interphase Structures for High-Modulus and High-Tensile/Strength Composite Fibers
,”
Macromol. Mater. Eng.
,
299
(
2
), pp.
144
153
.
13.
Emiliano
,
L.
,
Federico
,
B.
,
Francesco
,
B.
,
Matteo
,
B.
,
Simone
,
T.
,
Giovanni
,
G.
,
Andrea
,
C. F.
, and
Nicola Maria
,
P.
,
2017
, “
Spider Silk Reinforced by Graphene or Carbon Nanotubes
,”
2D Mater.
,
4
(
3
), p.
031013
.
14.
Pugno
,
N. M.
,
2014
, “
The ‘Egg of Columbus' for Making the World's Toughest Fibres
,”
Plos One
,
9
(
4
), p.
e93079
.
15.
Cranford
,
S. W.
,
2013
, “
Increasing Silk Fibre Strength Through Heterogeneity of Bundled Fibrils
,”
J. R. Soc. Interface
,
10
(
82
), p.
20130148
.
16.
Elbanna
,
A. E.
, and
Carlson
,
J. M.
,
2013
, “
Dynamics of Polymer Molecules With Sacrificial Bond and Hidden Length Systems: Towards a Physically-Based Mesoscopic Constitutive Law
,”
Plos One
,
8
(
4
), p.
e56118
.
17.
Puglisi
,
G.
,
De Tommasi
,
D.
,
Pantano
,
M. F.
,
Pugno
,
N. M.
, and
Saccomandi
,
G.
,
2017
, “
Micromechanical Model for Protein Materials: From Macromolecules to Macroscopic Fibers
,”
Phys. Rev. E
,
96
(
4
), p.
042407
.
18.
Ackbarow
,
T.
, and
Buehler
,
M. J.
,
2007
, “
Superelasticity, Energy Dissipation and Strain Hardening of Vimentin Coiled-Coil Intermediate Filaments: Atomistic and Continuum Studies
,”
J. Mater. Sci.
,
42
(
21
), pp.
8771
8787
.
19.
Ackbarow
,
T.
,
Sen
,
D.
,
Thaulow
,
C.
, and
Buehler
,
M. J.
,
2009
, “
Alpha-Helical Protein Networks are Self-Protective and Flaw-Tolerant
,”
Plos One
,
4
(
6
), p.
e6015
.
20.
Fantner
,
G. E.
,
Hassenkam
,
T.
,
Kindt
,
J. H.
,
Weaver
,
J. C.
,
Birkedal
,
H.
,
Pechenik
,
L.
,
Cutroni
,
J. A.
,
Cidade
,
G. A. G.
,
Stucky
,
G. D.
,
Morse
,
D. E.
, and
Hansma
,
P. K.
,
2005
, “
Sacrificial Bonds and Hidden Length Dissipate Energy as Mineralized Fibrils Separate During Bone Fracture
,”
Nat. Mater.
,
4
(
8
), pp.
612
616
.
21.
De Tommasi
,
D.
,
Puglisi
,
G.
, and
Saccomandi
,
G.
,
2010
, “
Damage, Self-Healing, and Hysteresis in Spider Silks
,”
Biophys. J.
,
98
(
9
), pp.
1941
1948
.
22.
Oroudjev
,
E.
,
Soares
,
J.
,
Arcidiacono
,
S.
,
Thompson
,
J. B.
,
Fossey
,
S. A.
, and
Hansma
,
H. G.
,
2002
, “
Segmented Nanofibers of Spider Dragline Silk: Atomic Force Microscopy and Single-Molecule Force Spectroscopy
,”
Proc. Natl. Acad. Sci.
,
99
(
Suppl. 2
), pp.
6460
6465
.
23.
Rief
,
M.
,
Gautel
,
M.
,
Oesterhelt
,
F.
,
Fernandez
,
J. M.
, and
Gaub
,
H. E.
,
1997
, “
Reversible Unfolding of Individual Titin Immunoglobulin Domains by AFM
,”
Science
,
276
(
5315
), pp.
1109
1112
.
24.
Zhmurov
,
A.
,
Brown
,
A. E. X.
,
Litvinov
,
R. I.
,
Dima
,
R. I.
,
Weisel
,
J. W.
, and
Barsegov
,
V.
,
2011
, “
Mechanism of Fibrin(Ogen) Forced Unfolding
,”
Structure
,
19
(
11
), pp.
1615
1624
.
25.
Qin
,
Z.
,
Cranford
,
S.
,
Ackbarow
,
T.
, and
Buehler
,
M. J.
,
2009
, “
Robustness-Strength Performance of Hierarchical Alpha-Helical Protein Filaments
,”
Int. J. Appl. Mech.
,
1
(
1
), pp.
85
112
.
26.
Lieou
,
C. K. C.
,
Elbanna
,
A. E.
, and
Carlson
,
J. M.
,
2013
, “
Sacrificial Bonds and Hidden Length in Biomaterials: A Kinetic Constitutive Description of Strength and Toughness in Bone
,”
Phys. Rev. E
,
88
(
1
), p.
012703
.
27.
Fantner
,
G. E.
,
Oroudjev
,
E.
,
Schitter
,
G.
,
Golde
,
L. S.
,
Thurner
,
P.
,
Finch
,
M. M.
,
Turner
,
P.
,
Gutsmann
,
T.
,
Morse
,
D. E.
,
Hansma
,
H.
, and
Hansma
,
P. K.
,
2006
, “
Sacrificial Bonds and Hidden Length: Unraveling Molecular Mesostructures in Tough Materials
,”
Biophys. J.
,
90
(
4
), pp.
1411
1418
.
28.
Koebley
,
S. R.
,
Vollrath
,
F.
, and
Schniepp
,
H. C.
,
2017
, “
Toughness-Enhancing Metastructure in the Recluse Spider's Looped Ribbon Silk
,”
Mater. Horiz.
,
4
(
3
), pp.
377
382
.
29.
Zhu
,
F.
,
Cheng
,
L.
,
Wang
,
Z. J.
,
Hong
,
W.
,
Wu
,
Z. L.
,
Yin
,
J.
,
Qian
,
J.
, and
Zheng
,
Q.
,
2017
, “
3D-Printed Ultratough Hydrogel Structures With Titin-Like Domains
,”
ACS Appl. Mater. Interfaces
,
9
(
13
), pp.
11363
11367
.
30.
Lipton
,
J. I.
, and
Lipson
,
H.
,
2016
, “
3D Printing Variable Stiffness Foams Using Viscous Thread Instability
,”
Sci. Rep.
,
6
(
1
), p.
29996
.
31.
Zhou
,
X.
,
Guo
,
B.
,
Zhang
,
L.
, and
Hu
,
G.-H.
,
2017
, “
Progress in Bio-Inspired Sacrificial Bonds in Artificial Polymeric Materials
,”
Chem. Soc. Rev.
,
46
(
20
), pp.
6301
6329
.
32.
Passieux
,
R.
,
Guthrie
,
L.
,
Rad
,
S. H.
,
Lévesque
,
M.
,
Therriault
,
D.
, and
Gosselin
,
F. P.
,
2015
, “
Instability-Assisted Direct Writing of Microstructured Fibers Featuring Sacrificial Bonds
,”
Adv. Mater.
,
27
(
24
), pp.
3676
3680
.
33.
Barnes
,
G.
, and
Woodcock
,
R.
,
1958
, “
Liquid Rope-Coil Effect
,”
Am. J. Phys.
,
26
(
4
), pp.
205
209
.
34.
Steven
,
W. C.
, and
Markus
,
J. B.
,
2010
, “
In Silico Assembly and Nanomechanical Characterization of Carbon Nanotube Buckypaper
,”
Nanotechnology
,
21
(
26
), p.
265706
.
35.
Assenza
,
S.
,
Adamcik
,
J.
,
Mezzenga
,
R.
, and
De Los Rios
,
P.
,
2014
, “
Universal Behavior in the Mesoscale Properties of Amyloid Fibrils
,”
Phys. Rev. Lett.
,
113
(
26
), p.
268103
.
36.
Paparcone
,
R.
,
Cranford
,
S. W.
, and
Buehler
,
M. J.
,
2011
, “
Self-Folding and Aggregation of Amyloid Nanofibrils
,”
Nanoscale
,
3
(
4
), pp.
1748
1755
.
37.
Cranford
,
S. W.
,
Tarakanova
,
A.
,
Pugno
,
N. M.
, and
Buehler
,
M. J.
,
2012
, “
Nonlinear Material Behaviour of Spider Silk Yields Robust Webs
,”
Nature
,
482
(
7383
), pp.
72
72–76
.
38.
Meyer
,
A.
,
Pugno
,
N. M.
, and
Cranford
,
S. W.
,
2014
, “
Compliant Threads Maximize Spider Silk Connection Strength and Toughness
,”
J. R. Soc. Interface
,
11
(
98
), p.
20140561
.
39.
Cranford
,
S. W.
,
Han
,
L.
,
Ortiz
,
C.
, and
Buehler
,
M. J.
,
2017
, “
Mutable Polyelectrolyte Tube Arrays: Mesoscale Modeling and Lateral Force Microscopy
,”
Soft Matter
,
13
(
33
), pp.
5543
5557
.
40.
Cranford
,
S. W.
, and
Buehler
,
M. J.
, and
2012
,
Biomateriomics
(Springer Series in Materials Science),
Springer
,
Dordrecht, The Netherlands
, p.
438
.
41.
Humphrey
,
W.
,
Dalke
,
A.
, and
Schulten
,
K.
,
1996
, “
VMD: Visual Molecular Dynamics
,”
J. Mol. Graph.
,
14
(
1
), pp.
33
38
.
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