Online citations, reference lists, and bibliographies.
Please confirm you are human
(Sign Up for free to never see this)
← Back to Search

Equivalent-Continuum Modeling Of Nano-Structured Materials

M. Gregory, S. Thomas, M. N. Lee, E. W. Kristopher
Published 2001 · Materials Science

Save to my Library
Download PDF
Analyze on Scholarcy
Share
A method has been developed for modeling structure-property relationships of nano-structured materials. This method serves as a link between computational chemistry and solid mechanics by substituting discrete molecular structures with an equivalent-continuum model. It has been shown that this substitution may be accomplished by equating the vibrational potential energy of a nano-structured material with the strain energy of representative truss and continuum models. As an important example with direct application to the development and characterization of single-walled carbon nanotubes, the model has been applied to determine the effective continuum geometry of a graphene sheet. A representative volume element of the equivalent-continuum model has been developed with an effective thickness. This effective thickness has been shown to be similar to, but slightly smaller than, the interatomic spacing of graphite.
This paper references
10.1115/1.3151907
Continuum Modeling for Repetitive Lattice Structures
A. Noor (1988)
10.1002/ZAMM.19800600811
Zienkiewicz, O. C., The Finite Element Method. 3. Edition. London. McGraw‐Hill Book Company (UK) Limited. 1977. XV, 787 S.
J. Altenbach (1980)
10.2514/3.61036
Continuum Models for Beam- and Platelike Lattice Structures
A. Noor (1978)
10.1016/S0040-6090(97)00369-6
Stress Calculations for Carbon Nanotubes
T. Halicioǧlu (1998)
10.1021/JA00124A002
A Second Generation Force Field for the Simulation of Proteins, Nucleic Acids, and Organic Molecules
Wendy D. Cornell (1995)
10.5860/choice.35-0914
Molecular Mechanics Across Chemistry
A. Rappé (1997)
10.1177/002199830003400901
Derivation of Boundary Conditions for Micromechanics Analyses of Plain and Satin Weave Composites
J. Whitcomb (2000)
10.1007/978-1-4612-0555-5_5
Theory of Micropolar Elasticity
A. C. Eringen (1999)
10.1103/PhysRevLett.79.1297
Elastic Properties of Carbon Nanotubes and Nanoropes
J. Lu (1997)
10.1016/S0038-1098(96)00742-9
Elastic properties of single-walled carbon nanotubes in compression
C. F. Cornwell (1997)
10.1021/JA00010A012
MNDO Study of Large Carbon Clusters
D. Bakowies (1991)
10.1038/39282
Bending and buckling of carbon nanotubes under large strain
M. Falvo (1997)
10.1119/1.1645289
Carbon Nanotubes and Related Structures: New Materials for the Twenty-first Century
P. J. Harris (1999)
10.21236/ad0473723
LINEAR THEORY OF MICROPOLAR ELASTICITY
A. C. Eringen (1965)
Handbook of carbon, graphite, diamond, and fullerenes : properties, processing, and applications
H. Pierson (1993)
10.1007/BF01436769
Structural rigidity and low frequency vibrational modes of long carbon tubules
G. Overney (1993)
10.1007/3-540-39947-X_12
Mechanical Properties of Carbon Nanotubes
B. Yakobson (2001)
10.1016/S0038-1098(00)00070-3
Elastic properties of crystals of single-walled carbon nanotubes
V. Popov (2000)
THEORY OF PLATES AND SHELLS
S. Timoshenko (1959)
10.1016/0020-7683(94)90086-8
Equivalent continuum models of large platelike lattice structures
Lee Usik (1994)
10.1061/(ASCE)0893-1321(1989)2:4(220)
Continuum Models of Space Station Structures
J. Dow (1989)
10.1007/S003390050890
Elastic properties of single-wall nanotubes
E. Hernández (1999)
10.1016/S0038-1098(98)00626-7
On the use of continuum mechanics to estimate the properties of nanotubes
S. Govindjee (1999)
10.1063/1.372973
Effect of van der Waals forces on axial buckling of a double-walled carbon nanotube
C. Q. Ru (2000)
10.2514/6.1981-624
ON THE DERIVATION OF EQUIVALENT SIMPLE MODELS FOR BEAM- AND PLATE-LIKE STRUCTURES IN DYNAMIC ANALYSIS
C. Sun (1981)
10.1016/S0009-2614(98)01105-1
The effect of structural distortions on the electronic structure of carbon nanotubes
A. Rochefort (1998)
10.1103/PhysRevLett.80.4502
Elastic Properties of C and B x C y N z Composite Nanotubes
E. Hernández (1998)
10.1115/1.3423754
Theory of elasticity
S. P. Timoshenko (1934)
10.1103/PHYSREVB.58.14013
Young's modulus of single-walled nanotubes
A. Krishnan (1998)
10.1021/AR00150A005
.pi.-Electrons in three dimensiona
R. Haddon (1988)
10.1016/b978-0-7506-7828-5.x5000-8
The finite element method in engineering
S. S. Rao (1982)
10.1103/PHYSREVB.50.18360
Electronic properties of tubule forms of hexagonal BC3.
Miyamoto (1994)
10.1063/1.368323
Young’s modulus of single-walled carbon nanotubes
Nan Yao (1998)
10.1088/0957-4484/10/3/304
Three-dimensional manipulation of carbon nanotubes under a scanning electron microscope
M. Yu (1999)
10.2514/3.10389
Global-local approach to solving vibration of large truss structures
C. Sun (1990)
10.1119/1.1934059
Dynamical Theory of Crystal Lattices
M. Born (1954)
10.1887/0750305789
Nanomaterials : synthesis, properties, and applications
A. Edelstein (1996)
10.1126/SCIENCE.277.5334.1971
Nanobeam Mechanics: Elasticity, Strength, and Toughness of Nanorods and Nanotubes
E. W. Wong (1997)
10.1557/JMR.1998.0337
Chemical Attachment of Organic Functional Groups to Single-walled Carbon Nanotube Material
Y. Chen (1998)
10.1016/S0009-2614(00)00764-8
Ab initio study of the elastic properties of single-walled carbon nanotubes and graphene
G. Lier (2000)
10.1021/JA00205A002
Molecular mechanics. The MM3 force field for hydrocarbons. 2. Vibrational frequencies and thermodynamics
Jenn Huei Lii (1989)
10.1080/107594100305366
Thermally Induced Damage Initiation and Growth in Plain and Satin Weave Carbon-Carbon Composites
C. Chapman (2000)
10.1103/PHYSREVLETT.84.1712
Stiffness of single-walled carbon nanotubes under large strain
Ozaki (2000)
10.1021/JA00205A001
Molecular mechanics. The MM3 force field for hydrocarbons. 1
N. L. Allinger (1989)
10.1126/science.261.5128.1545
Chemistry of the Fullerenes: The Manifestation of Strain in a Class of Continuous Aromatic Molecules
R. Haddon (1993)
10.1016/0038-1098(92)90911-R
Energetics of carbon nano-tubes
S. Sawada (1992)
The Finite Element Method In Engineering Science
O. Zienkiewicz (1971)
10.1021/JA00315A051
A NEW FORCE FIELD FOR MOLECULAR MECHANICAL SIMULATION OF NUCLEIC ACIDS AND PROTEINS
S. Weiner (1984)
10.1103/PHYSREVLETT.81.1638
Buckling and Collapse of Embedded Carbon Nanotubes
O. Lourie (1998)
10.1103/PHYSREVLETT.76.2511
Nanomechanics of carbon tubes: Instabilities beyond linear response.
Yakobson (1996)
10.1021/JA00205A003
Molecular mechanics. The MM3 force field for hydrocarbons. 3. The van der Waals' potentials and crystal data for aliphatic and aromatic hydrocarbons
Jenn Huei Lii (1989)
10.1021/JP990882S
Predictions of Enhanced Chemical Reactivity at Regions of Local Conformational Strain on Carbon Nanotubes: Kinky Chemistry
D. Srivastava (1999)
Physics of Graphite
B. Kelly (1981)
10.1103/PHYSREVB.62.9973
Effective bending stiffness of carbon nanotubes
C. Q. Ru (2000)
Dynamical TheoIy r?fCrystal Lattices
M Born (1954)
10.1103/PHYSREVLETT.72.1878
Hybridization effects and metallicity in small radius carbon nanotubes.
Blase (1994)
10.1038/354056a0
Helical microtubules of graphitic carbon
S. Iijima (1991)
10.1038/381678A0
Exceptionally high Young's modulus observed for individual carbon nanotubes
M. Treacy (1996)
10.1126/SCIENCE.287.5453.637
Strength and breaking mechanism of multiwalled carbon nanotubes under tensile load
Yu (2000)
10.1103/PHYSREVB.45.12592
Energetics of nanoscale graphitic tubules.
Robertson (1992)



This paper is referenced by
10.7508/JUFGNSM.2016.01.01
Numerical Investigation of Size and Structure Effect on Tensile Characteristics of Symmetric and Asymmetric CNTs
M. Zakeri (2016)
10.1016/J.SSC.2008.09.050
Elastic properties of single-layered graphene sheet
A. Sakhaee-Pour (2009)
10.1063/1.4820565
Development of analytical vibration solutions for microstructured beam model to calibrate length scale coefficient in nonlocal Timoshenko beams
W. Duan (2013)
10.1088/1742-6596/1603/1/012010
Nonlocal beam model and FEM of free vibration for pristine and defective CNTs
M. Chwał (2020)
10.1016/j.euromechsol.2020.103998
Equivalent mechanical properties of tensegrity truss structures with self-stress included
W. Gilewski (2020)
10.1016/J.COMMATSCI.2010.05.008
Displacement time history analysis and radial wave propagation velocity in pressurized multiwall carbon nanotubes
S. Talebian (2010)
10.1016/J.SSC.2012.06.005
Elastic properties of SWCNTs with curved morphology: Density functional tight binding based treatment
M. Ganji (2012)
10.1007/S00707-009-0246-4
Atomistic-based continuum modeling of the nonlinear behavior of carbon nanotubes
J. Wernik (2010)
10.2514/6.2010-2814
Prediction of Mechanical Properties of EPON 862 (DGEBF)- W (DETDA) using MD Simulations
Francis Komuves (2010)
Homogenized Elastic Properties of Graphene for
Eduard Mareni (2013)
10.1016/J.MSEA.2006.11.158
A molecular-mechanics based finite element model for strength prediction of single wall carbon nanotubes
M. Meo (2007)
10.1016/J.MECHMAT.2013.03.004
Elastic in-plane properties of 2D linearized models of graphene
I. Berinskii (2013)
10.1016/J.ISTRUC.2017.12.005
Effects of Size and Shape on Elastic Constants of Graphene Sheet
N. A. Resketi (2018)
10.1007/S00339-017-0860-2
A density functional theory-based finite element method to study the vibrational characteristics of zigzag phosphorene nanotubes
A. Shahnazari (2017)
10.3934/MATERSCI.2017.3.706
Developments in the evaluation of elastic properties of carbon nanotubes and their heterojunctions by numerical simulation
N. Sakharova (2017)
10.4236/JMMCE.2010.94022
Characterizing and Modeling Mechanical Properties of Nanocomposites-Review and Evaluation
H. Hu (2010)
10.1007/S00707-010-0377-7
Multiscale modeling of the nonlinear response of nano-reinforced polymers
J. Wernik (2011)
10.1080/15376494.2018.1430259
On the buckling properties of concentric carbon/boron-nitride multi-walled nanotubes: A finite element investigation
A. Nikkar (2018)
10.1177/0021998318769467
The effect of physical nonlinearity of the interfacial layer between carbon nanotube and polymer matrix on viscoelastic response of nanocomposite materials under harmonic loading
M. Hashemi (2018)
10.1088/0957-4484/19/18/185703
Scale effect on wave propagation of double-walled carbon nanotubes with initial axial loading.
H. Heireche (2008)
Continuum-based multiscale computational damage modeling of cementitious composites
Sun-Myung Kim (2010)
10.1016/S0065-2156(09)43001-1
A shell theory for carbon nanotubes based on the interatomic potential and atomic structure
J. Wu (2009)
10.1016/J.COMMATSCI.2011.11.029
Numerical simulation for finite deformation of single-walled carbon nanotubes at finite temperature using temperature-related higher order Cauchy-Born rule based quasi-continuum model
X. Wang (2012)
10.1016/J.PROGPOLYMSCI.2007.09.002
Multiscale modeling and simulation of polymer nanocomposites
Qing-hua Zeng (2008)
10.1016/J.PHYSE.2012.07.021
Coupled molecular/continuum mechanical modeling of graphene sheets
Cengiz Baykasoglu (2012)
10.1016/J.COMPOSITESB.2018.01.008
Determination of random material properties of graphene sheets with different types of defects
D. Savvas (2018)
10.1115/1.1490129
Mechanics of carbon nanotubes
D. Qian (2002)
10.1080/14786430701344558
A cohesive law for multi-wall carbon nanotubes
Weibang Lu (2007)
10.1360/CJCP2006.19(4).294.7
Atomic Simulation of Structure and Deformation's Influence on the Mechanical Properties of Single-walled Carbon Nanotubes
Xiang-gui Ni (2006)
Modeling With Application to Carbon Nanotubes
G. Odegard (2002)
10.1007/978-1-4302-0477-0_4
Application : An Overview
F. Hussain (2006)
10.1007/978-1-4419-9834-7_145
Damping Augmentation of Nanocomposites Using Carbon Nanotube/Epoxy
N. Kordani (2011)
See more
Semantic Scholar Logo Some data provided by SemanticScholar