Hysteresis due to stick-slip energy dissipation in carbon nanotube (CNT) nanocomposites is experimentally observed, measured, and identified through a one-dimensional (1D) phenomenological model obtained via reduction of a three-dimensional (3D) mesoscale model. The proposed model is shown to describe the nanocomposite hysteretic response, which features the transition from the purely elastic to the post-stick-slip behavior characterized by the interfacial frictional sliding motion between the polymer chains and the CNTs. Parametric analyses shed light onto the physical meaning of each model parameter and the influence on the material response. The model parameters are determined by fitting the experimentally acquired force–displacement curves of CNT/polymer nanocomposites using a differential evolution algorithm. Nanocomposite beam-like samples made of a high performance engineering polymer and high-aspect-ratio CNTs are fabricated and tested in a bending mode at increasing deflection amplitudes. The entire time histories of the restoring force are fitted by the model through a unique set of parameters. The parameter identification is carried out for nanocomposites with various CNT weight fractions, so as to highlight the model capability to identify a wide variety of nanocomposite hysteretic behaviors through a fine tuning of its constitutive parameters. By exploiting the proposed model, a nanostructured material design and its optimization are made possible toward the exploitation of these promising materials for engineering applications.

References

References
1.
Gibson
,
R. F.
,
2010
, “
A Review of Recent Research on Mechanics of Multifunctional Composite Materials and Structures
,”
Compos. Struct.
,
92
(
12
), pp.
2793
2810
.
2.
Gibson
,
R. F.
,
Ayorinde
,
E. O.
, and
Wen
,
Y.-F.
,
2007
, “
Vibrations of Carbon Nanotubes and Their Composites: A Review
,”
Compos. Sci. Technol.
,
67
(
1
), pp.
1
28
.
3.
Ci
,
L.
,
Suhr
,
J.
,
Pushparaj
,
V.
,
Zhang
,
X.
, and
Ajayan
,
P. M.
,
2008
, “
Continuous Carbon Nanotube Reinforced Composites
,”
Nano Lett.
,
8
(
9
), pp.
2762
2766
.
4.
Sun
,
L.
,
Gibson
,
R. F.
,
Gordaninejad
,
F.
, and
Suhr
,
J.
,
2009
, “
Energy Absorption Capability of Nanocomposites: A Review
,”
Compos. Sci. Technol.
,
69
(
14
), pp.
2392
2409
.
5.
Savvas
,
D. N.
,
Papadopoulos
,
V.
, and
Papadrakakis
,
M.
,
2012
, “
The Effect of Interfacial Shear Strength on Damping Behavior of Carbon Nanotube Reinforced Composites
,”
Int. J. Solids Struct.
,
49
(
26
), pp.
3823
3837
.
6.
Rafiee
,
R.
, and
Ghorbanhosseini
,
A.
,
2017
, “
Stochastic Multi-Scale Modeling of Randomly Grown CNTs on Carbon Fiber
,”
Mech. Mater.
,
106
, pp.
1
7
.
7.
Liu
,
A.
,
Wang
,
K. W.
, and
Bakis
,
C. E.
,
2010
, “
Multiscale Damping Model for Polymeric Composites Containing Carbon Nanotube Ropes
,”
J. Compos. Mater.
,
44
(
19
), pp.
2301
2323
.
8.
Huang
,
Y.
, and
Tangpong
,
X. W.
,
2010
, “
A Distributed Friction Model for Energy Dissipation in Carbon Nanotube-Based Composites
,”
Commun. Nonlinear Sci. Numer. Simul.
,
15
(
12
), pp.
4171
4180
.
9.
Dwaikat
,
M. M. S.
,
Spitas
,
C.
, and
Spitas
,
V.
,
2011
, “
A Model for Elastic Hysteresis of Unidirectional Fibrous Nano Composites Incorporating Stick-Slip
,”
Mater. Sci. Eng. A
,
530
, pp.
349
356
.
10.
Bhattacharya
,
S.
,
Alva
,
A.
, and
Raja
,
S.
,
2014
, “
Modeling and Characterization of Multiwall Carbon Nanotube Reinforced Polymer Composites for Damping Applications
,”
Int. J. Comput. Methods Eng. Sci. Mech.
,
15
(
3
), pp.
258
264
.
11.
Formica
,
G.
,
Talò
,
M.
, and
Lacarbonara
,
W.
,
2014
, “
Nonlinear Modeling of Carbon Nanotube Composites Dissipation Due to Interfacial Stick–Slip
,”
Int. J. Plasticity
,
53
, pp.
148
163
.
12.
Triantafyllou
,
S. P.
, and
Chatzi
,
E. N.
,
2014
, “
A Hysteretic Multiscale Formulation for Nonlinear Dynamic Analysis of Composite Materials
,”
Comput. Mech.
,
54
(
3
), pp.
763
787
.
13.
Papadopoulos
,
V.
, and
Tavlaki
,
M.
,
2016
, “
The Impact of Interfacial Properties on the Macroscopic Performance of Carbon Nanotube Composites. A FE2-Based Multiscale Study
,”
Compos. Struct.
,
136
, pp.
582
592
.
14.
Spitas
,
V.
,
Spitas
,
C.
, and
Michelis
,
P.
,
2013
, “
Modeling of the Elastic Damping Response of a Carbon Nanotube–Polymer Nanocomposite in the Stress-Strain Domain Using an Elastic Energy Release Approach Based on Stick-Slip
,”
Mech. Adv. Mater. Struct.
,
20
(
10
), pp.
791
800
.
15.
Wang
,
T.-Y.
,
Liu
,
S.-C.
, and
Tsai
,
J.-L.
,
2016
, “
Micromechanical Stick-Slip Model for Characterizing Damping Responses of Single-Walled Carbon Nanotube Nanocomposites
,”
J. Compos. Mater.
,
50
(
1
), pp.
57
73
.
16.
Formica
,
G.
, and
Lacarbonara
,
W.
,
2017
, “
Three-Dimensional Modeling of Interfacial Stick-Slip in Carbon Nanotube Nanocomposites
,”
Int. J. Plasticity
,
88
, pp.
204
217
.
17.
Carboni
,
B.
,
Lacarbonara
,
W.
, and
Auricchio
,
F.
,
2015
, “
Hysteresis of Multiconfiguration Assemblies of NiTiNOL and Steel Strands: Experiments and Phenomenological Identification
,”
J. Eng. Mech.
,
141
(
3
), pp.
1
16
.
18.
Carboni
,
B.
, and
Lacarbonara
,
W.
,
2016
, “
A Nonlinear Vibration Absorber With Pinched Hysteresis: Theory and Experiments
,”
J. Eng. Mech.
,
142
(
5
), p.
04016023
.
19.
Brewick
,
P. T.
,
Masri
,
S. F.
,
Carboni
,
B.
, and
Lacarbonara
,
W.
,
2016
, “
Data-Based Nonlinear Identification and Constitutive Modeling of Hysteresis in NiTiNOL and Steel Strands
,”
J. Eng. Mech.
,
142
(
12
), p.
04016107
.
20.
Brewick
,
P. T.
,
Masri
,
S. F.
,
Carboni
,
B.
, and
Lacarbonara
,
W.
,
2017
, “
Enabling Reduced-Order Data-Driven Nonlinear Identification and Modeling Through Nave Elastic Net Regularization
,”
Int. J. Non-Linear Mech.
,
94
, pp.
46
58
.
21.
Sasikumar
,
K.
,
Manoj
,
N. R.
,
Mukundan
,
T.
, and
Khastgir
,
D.
,
2016
, “
Hysteretic Damping in XNBR—MWNT Nanocomposites at Low and High Compressive Strains
,”
Composites, Part B
,
92
, pp.
74
83
.
22.
Kontou
,
E.
,
2018
, “
Stress–Softening Effect of SBR/Nanocomposites by a Phenomenological Gent–Zener Viscoelastic Model
,”
Meccanica
,
53
(
9
), pp.
2353
2362
.
23.
Poojary
,
U. R.
,
Hegde
,
S.
, and
Gangadharan
,
K. V.
,
2018
, “
Experimental Investigation on the Effect of Carbon Nanotube Additive on the Field-Induced Viscoelastic Properties of Magnetorheological Elastomer
,”
J. Mater.
,
53
(
6
), pp.
4229
4241
.
24.
Misra
,
A.
,
Raney
,
J. R.
,
De Nardo
,
L.
,
Craig
,
A. E.
, and
Daraio
,
C.
,
2011
, “
Synthesis and Characterization of Carbon Nanotube–Polymer Multilayer Structures
,”
ACS Nano
,
5
(
10
), pp.
7713
7721
.
25.
Dai
,
Z.
,
Liu
,
L.
,
Qi
,
X.
,
Kuang
,
J.
,
Wei
,
Y.
,
Zhu
,
H.
, and
Zhang
,
Z.
,
2016
, “
Three-Dimensional Sponges With Super Mechanical Stability: Harnessing True Elasticity of Individual Carbon Nanotubes in Macroscopic Architectures
,”
Sci. Rep.
,
6
, p.
18930
.
26.
Zhao
,
J.
,
Wang
,
F.
,
Zhang
,
X.
,
Liang
,
L.
,
Yang
,
X.
,
Li
,
Q.
, and
Zhang
,
X.
,
2017
, “
Vibration Damping of Carbon Nanotube Assembly Materials
,”
Adv. Eng. Mater.
,
20
(
3
), p.
1700647
.
27.
Ajayan
,
P.
,
Suhr
,
J.
, and
Koratkar
,
N.
,
2006
, “
Utilizing Interfaces in Carbon Nanotube Reinforced Polymer Composites for Structural Damping
,”
J. Mater. Sci.
,
41
(
23
), pp.
7824
7829
.
28.
Gardea
,
F.
,
Glaz
,
B.
,
Riddick
,
J.
,
Lagoudas
,
D. C.
, and
Naraghi
,
M.
,
2015
, “
Energy Dissipation Due to Interfacial Slip in Nanocomposites Reinforced With Aligned Carbon Nanotubes
,”
ACS Appl. Mater. Interfaces
,
7
(
18
), pp.
9725
9735
.
29.
Suhr
,
J.
,
Koratkar
,
N.
,
Keblinski
,
P.
, and
Ajayan
,
P.
,
2005
, “
Viscoelasticity in Carbon Nanotube Composites
,”
Nat. Mater.
,
4
(
2
), pp.
134
137
.
30.
Ogasawara
,
T.
,
Tsuda
,
T.
, and
Takeda
,
N.
,
2011
, “
Stress–Strain Behavior of Multi-Walled Carbon Nanotube/PEEK Composites
,”
Compos. Sci. Technol.
,
71
(
2
), pp.
73
78
.
31.
Lacarbonara
,
W.
,
Talò
,
M.
,
Carboni
,
B.
, and
Lanzara
,
G.
,
2018
, “
Tailoring of Hysteresis Across Different Material Scales
,”
Recent Trends in Applied Nonlinear Mechanics and Physics
,
M.
Belhaq
, ed.,
Springer International Publishing
,
Cham
, Switzerland, pp.
73
78
.
32.
Storn
,
R.
, and
Price
,
K.
,
1997
, “
Differential Evolution—A Simple and Efficient Heuristic for Global Optimization Over Continuous Spaces
,”
J. Global Optim.
,
11
(
4
), pp.
341
359
.
33.
Talò
,
M.
,
Krause
,
B.
,
Pionteck
,
J.
,
Lanzara
,
G.
, and
Lacarbonara
,
W.
,
2017
, “
An Updated Micromechanical Model Based on Morphological Characterization of Carbon Nanotube Nanocomposites
,”
Composites, Part B
,
115
(
Suppl. C
), pp.
70
78
.
34.
Lau
,
K.-T.
,
Chipara
,
M.
,
Ling
,
H.-Y.
, and
Hui
,
D.
,
2004
, “
On the Effective Elastic Moduli of Carbon Nanotubes for Nanocomposite Structures
,”
Composites, Part B
,
35
(
2
), pp.
95
101
.
35.
Kasaliwal
,
G.
,
Göldel
,
A.
, and
Pötschke
,
P.
,
2009
, “
Influence of Processing Conditions in Small-Scale Melt Mixing and Compression Molding on the Resistivity and Morphology of Polycarbonate–MWNT Composites
,”
J. Appl. Polym. Sci.
,
112
(
6
), pp.
3494
3509
.
36.
Casciati
,
F.
,
1989
, “
Stochastic Dynamics of Hysteretic Media
,”
Struct. Saf.
,
6
(
2–4
), pp.
259
269
.
37.
Ma
,
F. F.
,
Zhang
,
H. H.
,
Bockstedte
,
A. A.
,
Foliente
,
G. C.
, and
Paevere
,
P. P.
,
2004
, “
Parameter Analysis of the Differential Model of Hysteresis
,”
ASME J. Appl. Mech.
,
71
(
3
), pp.
342
349
.
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