There have been a variety of attempts to model the quasi-static and high energy impact dynamics of vertically aligned carbon nanotube (VACNT) pads. However, very little work has focused on identifying the behavior at the midlevel frequencies that may occur in materials handling or vibration suppression applications. Moreover, the existing models are predominantly very complex, and yet provide only a very rough approximation of the bulk behavior. While several of the existing models make attempts at ascribing physical relevance, an adequate first principles approach has yet to be demonstrated. In this work, a close-fitting continuous model of these midfrequency dynamics is developed utilizing a combination of phenomenological- and identification-based methodologies. First, a set of specially fabricated carbon nanotube pads are preconditioned and subjected to various position-controlled compression experiments. The measured position and force responses are used to develop load–displacement curves, from which several characteristic features are identified. Based on these observations, a preliminary version of the proposed model is introduced. This simplified model is then systematically refined in order to demonstrate completely both the modeling approach and parameter identification scheme. The accuracy of the model is demonstrated through a comparison between the modeled and experimental responses including a normalized vector correlation of >0.998 across all sets of sinusoidal experimental data. A brief analysis utilizing a Lyapunov linearization approach follows, as well as a discussion of the advantages and limitations of the final model.

References

References
1.
Maschmann
,
M. R.
,
2015
, “
Integrated Simulation of Active Carbon Nanotube Forest Growth and Mechanical Compression
,”
Carbon
,
86
, pp.
26
37
.
2.
Misra
,
A.
,
Raney
,
J. R.
,
Craig
,
A. E.
, and
Daraio
,
C.
,
2011
, “
Effect of Density Variation and Non-Covalent Functionalization on the Compression Behavoir of Carbon Nanotube Arrays
,”
Nanotechnology
,
22
(
42
), p.
425705
.
3.
Sun
,
C.
,
Liu
,
K.
, and
Hong
,
Y.
,
2013
, “
Dynamic Shell Buckling Behavoir of Multi-Walled Carbon Nanotubes Embedded in an Elastic Medium
,”
Sci. China
,
56
(
3
), pp.
483
490
.
4.
Yang
,
X.
,
Hei
,
P.
, and
Gao
,
H.
,
2011
, “
Modeling Frequency and Temperature Invariant Dissipative Behaviors of Randomly Entangled Carbon Nanotube Networks Under Cyclic Loading
,”
Nano Res.
,
4
(
12
), pp.
1191
1198
.
5.
Raney
,
J. R.
,
Fraternali
,
F.
, and
Daraio
,
C.
,
2013
, “
Rate-Independent Dissipation and Loading Direction Effects in Compressed Carbon Nanotube Arrays
,”
Nanotechnology
,
24
(
25
), p.
255707
.
6.
Thevamaran
,
R.
,
Meshot
,
E. R.
, and
Daraio
,
C.
,
2015
, “
Shock Formation and Rate Effects in Impacted Carbon Nanotube Foams
,”
Carbon
,
84
, pp.
390
398
.
7.
Cao
,
A.
,
Dickrell
,
P. L.
,
Sawyer
,
G. W.
,
Ghasemi-Nejhad
,
M. N.
, and
Ajayan
,
P. M.
,
2005
, “
Super Compressible Foamlike Carbon Nanotube Films
,”
Sci.
,
310
(5752), pp.
1307
1310
.
8.
Zbib
,
A. A.
,
Mesarovic
,
S. D.
,
Lilleodden
,
E. T.
,
McClain
,
D.
,
Jiao
,
J.
, and
Bahr
,
D. F.
,
2008
, “
The Coordinated Buckling of Carbon Nanotube Turfs Under Uniform Compression
,”
Nanotechnology
,
19
(
17
), p.
175704
.
9.
Thevamaran
,
R.
,
Fraternali
,
F.
, and
Daraio
,
C.
,
2014
, “
Multiscale Mass-Spring Model for High-Rate Compression of Vertically Aligned Carbon Nanotube Foams
,”
ASME J. Appl. Mech.
,
81
(
12
), p.
121001
.
10.
Blegsen
,
T.
,
Fraternali
,
F.
,
Raney
,
J. R.
, and
Daraio
,
C.
,
2013
, “
Multiscale Mass-Spring Models of Carbon Nanotube Arrays Accounting for Mullins-Like Behavior and Permanent Deformation
,”
Soc. Ind. Appl. Math.
,
11
(
2
), pp.
545
565
.
11.
Torabi
,
H.
,
Radhakrishnan
,
H.
, and
Mesarovic
,
S. D.
,
2014
, “
Micromechanics of Collective Buckling in CNT Turfs
,”
J. Mech. Phys. Solids
,
72
, pp.
144
160
.
12.
Mesarovic
,
S. D.
,
McCarter
,
C. M.
,
Bahr
,
D. F.
,
Radhakrishnan
,
H.
,
Richards
,
R. F.
,
Richards
,
C. D.
,
McClain
,
D.
, and
Jiao
,
J.
,
2007
, “
Mechanical Behavior of a Carbon Nanotube Turf
,”
Scripta Mater.
,
56
(2), pp.
157
160
.
13.
Boddu
,
V. M.
, and
Brenner
,
M. W.
,
2016
, “
Energy Dissipation in Intercalated Carbon Nanotube Forests With Metal Layers
,”
Appl. Phys. A
,
122
, p.
88
.
14.
Hutchens
,
S. B.
, and
Pathak
,
S.
,
2012
, “
Vertically Aligned Carbon Nanotubes, Collective Mechanical Behavior
,”
Encyclopedia of Nanotechnology
,
B.
Bhushan
, ed.,
Springer
, Dordrecht,
The Netherlands
, pp.
2809
2818
.
15.
Hutchens
,
S. B.
,
Hall
,
L. J.
, and
Greer
,
J. R.
,
2010
, “
In Situ Mechanical Testing Reveals Periodic Buckle Nucleation and Propagation in Carbon Nanotube Bundles
,”
Adv. Funct. Mater.
,
20
(4), pp.
2338
2346
.
16.
Li
,
Y.
,
Kang
,
J.
,
Choi
,
J.
,
Nam
,
J.
, and
Suhr
,
J.
,
2015
, “
Determination of Material Constants of Vertically Aligned Carbon Nanotube Structures in Compressions
,”
Nanotechnology
,
26
(24), p.
245701
.
17.
Thevamaran
,
R.
, and
Daraio
,
C.
,
2014
, “
An Experimental Technique for the Dynamic Characterization of Soft Complex Materials
,”
Exp. Mech.
,
54
(8), pp.
1319
1328
.
18.
Daraio
,
C.
,
Nesterenko
,
V. F.
, and
Jin
,
S.
, “
Highly Nonlinear Contact Interaction and Dynamic Energy Dissipation by Forest of Carbon Nanotubes
,”
Appl. Phys. Lett.
,
85
(
23
), pp.
5724
5726
.
19.
Misra
,
A.
,
Greer
,
J. R.
, and
Daraio
,
C.
,
2009
, “
Strain Rate Effects in the Mechanical Response of Polymer-Anchored Carbon Nanotube Foams
,”
Adv. Mater.
,
21
(3), pp.
334
338
.
20.
Pathak
,
S.
,
Lim
,
E. J.
,
Abadi
,
P.
,
Graham
,
S.
,
Cola
,
B. A.
, and
Greer
,
J. R.
,
2012
, “
Higher Recovery and Better Energy Dissipation at Faster Strain Rates in Carbon Nanotube Bundles: An In-Situ Study
,”
ACS Nano
,
6
(
3
), pp.
2189
2197
.
21.
Raney
,
J. R.
,
Fraternali
,
F.
,
Amendola
,
A.
, and
Daraio
,
C.
,
2011
, “
Modeling and In Situ Identification of Material Parameters for Layered Structures Based on Carbon Nanotube Arrays
,”
Compos. Struct.
,
93
(
11
), pp.
3013
3018
.
22.
Hong
,
S.
,
Lundstrom
,
T.
,
Ghosh
,
R.
,
Abdi
,
H.
,
Hao
,
J.
,
Jung
,
S.
,
Su
,
P.
,
Vaziri
,
A.
,
Jalili
,
N.
, and
Jung
,
Y.
,
2016
, “
Highly Anisotropic Adhesive Film Made From Upside-down, Flat and Uniform Vertically Aligned CNTs
,”
ACS Appl. Mater. Interfaces
,
8
(
49
), pp.
34061
34067
.
23.
Physik Instrumente GmbH, 2016, “P-733.2 • P-733.3 XY(Z) Piezo Nanopositioning Stage
,” Physik Instrumente GmbH, Karlsruhe, Germany, accessed Nov. 17, 2016, https://www.physikinstrumente.com/en/products/xyz-scanners/piezo-flexure-scanners/p-7332-p-7333-xyz-piezo-nanopositioning-stage-201200/
24.
PCB Piezotronics
,
2016
, “
PCB Model 208C01
,” PCB Piezotronics, Depew, NY, accessed Nov. 17, 2016, http://www.pcb.com/Products.aspx?m=208C01
25.
DiStefano
,
J.
, III
,
2014
,
Dynamic Systems Biology Modeling and Simulation
,
Academic Press
,
London
.
26.
Hill
,
A. V.
,
1910
, “
The Possible Effects of the Aggregation of the Molecules of Haemoglobin on Its Dissociation Curves
,”
J. Physiol.
,
40
, pp.
iv
vii
.http://onlinelibrary.wiley.com/doi/10.1113/jphysiol.1910.sp001386/epdf
27.
Goutelle
,
S.
,
Maurin
,
M.
,
Rougier
,
F.
,
Barbaut
,
X.
,
Bourguignon
,
L.
,
Ducher
,
M.
, and
Maire
,
P.
,
2008
, “
The Hill Equation: A Review of Its Capabilities in Pharmocological Modelling
,”
Fundam. Clin. Pharmacol.
,
22
(6), pp.
633
648
.
28.
Khalil
,
H. K.
,
2002
,
Nonlinear Systems
,
3rd ed.
,
Prentice Hall
,
Upper Saddle River, NJ
.
You do not currently have access to this content.