A review on modeling of graphene and associated nanostructures reinforced concrete

Abstract

Concrete is the most popular construction material in infrastructure projects due to its numerous natural advantages. Nevertheless, concrete constructions frequently suffer from low tensile strength and poor durability performance which are always urgent tasks to be solved. The concrete reinforced by various nanomaterials, especially graphene and its associated nanostructures (GANS), shows excellent chemical and physical properties for engineering applications. The influence of GANS on cement composites is a multiscale behavior from the nanoscale to the macroscale, which requires a number of efforts to reveal via numerical and experimental approaches. To meet this need, this study provides a comprehensive overview of the numerical modeling for GANS reinforced concrete in various scales. The background and importance of the topic are addressed in this study, along with the review of its methodologies, findings, and applications. Moreover, the study critically summarizes the performance of GANS reinforced concrete, including its mechanical behavior, transport phenomena, and failure mechanism. Additionally, the primary challenges and future prospects in the research field are also discussed. By presenting an extensive overview, this review offers valuable insights for researchers and practitioners interested in numerical simulation to advance concrete science and engineering.

Full text

Review Article
Qiang Yue, Qiao Wang*, Timon Rabczuk, Wei Zhou, Xiaolin Chang, and Xiaoying Zhuang*
A review on modeling of graphene and associated
nanostructures reinforced concrete
https://doi.org/10.1515/ntrev-2024-0033
received February 5, 2024; accepted April 30, 2024
Abstract: Concrete is the most popular construction mate-
rial in infrastructure projects due to its numerous natural
advantages. Nevertheless, concrete constructions frequently
suffer from low tensile strength and poor durability perfor-
mance which are always urgent tasks to be solved. The
concrete reinforced by various nanomaterials, especially
graphene and its associated nanostructures (GANS), shows
excellent chemical and physical properties for engineering
applications. The influence of GANS on cement composites is
a multiscale behavior from the nanoscale to the macroscale,
which requires a number of efforts to reveal via numerical
and experimental approaches. To meet this need, this study
provides a comprehensive overview of the numerical mod-
eling for GANS reinforced concrete in various scales. The
background and importance of the topic are addressed in
this study, along with the review of its methodologies, find-
ings, and applications. Moreover, the study critically sum-
marizes the performance of GANS reinforced concrete,
including its mechanical behavior, transport phenomena,
and failure mechanism. Additionally, the primary chal-
lenges and future prospects in the research field are also
discussed. By presenting an extensive overview, this review
offers valuable insights for researchers and practitioners
interested in numerical simulation to advance concrete
science and engineering.
Keywords: graphene, cement composites, concrete, numer-
ical modeling, multiscale behavior
1 Introduction
Due to its numerous advantages, such as low-cost manu-
facture, easy shapeability, strong bonding power, and high
compressive strength, concrete has become one of the most
widely used building materials in civil and hydraulic engi-
neering in the whole world [1]. However, the drawbacks of
conventional concrete, including its weak corrosion resis-
tance, poor tensile strength, and intrinsic brittleness, remain
main issues to be overcome in engineering structures. For
the purpose of improving the performance of cement com-
posites, numerous attempts have been made to introduce
various materials and techniques into the concrete, such as
chemical admixtures, supplementary cementitious mate-
rials, surface coating materials, and fibers. It has been
proven that advanced nanotechnology makes it possible to
control the nano-sized defects (pores smaller than 20 nm in
size) before micro-sized crack propagation. Consequently,
nanomaterials like nano-titanium, nano-clay, nano-silica,
and dioxide were studied as additions to concrete in many
works [2,3]. Over the past years, graphene and its associated
nanostructures (GANS) have become the new stars of carbon-
based nanomaterials that can be incorporated into concrete
owing to their extraordinary physical characteristics, e.g.,the
specificsurfacearea(2,630m
2
g
−1
), tensile strength (130 GPa),
Young’s modulus (1.1 TPa), electronic mobility (2 ×10
5
cm
2
V
−1
s
−1
),
and thermal conductivity (∼5,000 W m
−1
K
−1
)[4–7].
Graphene [8], which can be presented in a variety of
shapes, is a single-layer carbon sheet with a two-dimen-
sional honeycomb lattice nanostructure, as illustrated in
Figure 1. In order to meet different requirements, graphene
can be obtained in several chemical forms, including gra-
phene nano platelets (GNP) [9], graphene oxide (GO) [10],
Qiang Yue: State Key Laboratory of Water Resources Engineering and
Management, Wuhan University, Wuhan, Hubei 430072, China; Institute
of Water Engineering Sciences, Wuhan University, Wuhan, 430072, China;
Institute of Structural Mechanics, Bauhaus University Weimar, Weimar,
99423, Germany; Institute of Photonics, Department of Mathematics and
Physics, Leibniz University Hannover, Hannover, 30167, Germany

* Corresponding author: Qiao Wang, State Key Laboratory of Water
Resources Engineering and Management, Wuhan University, Wuhan,
Hubei 430072, China; Institute of Water Engineering Sciences, Wuhan
University, Wuhan, 430072, China, e-mail: qiaowang@whu.edu.cn
Timon Rabczuk: Institute of Structural Mechanics, Bauhaus University
Weimar, Weimar, 99423, Germany
Wei Zhou, Xiaolin Chang: State Key Laboratory of Water Resources
Engineering and Management, Wuhan University, Wuhan, Hubei 430072,
China; Institute of Water Engineering Sciences, Wuhan University,
Wuhan, 430072, China
* Corresponding author: Xiaoying Zhuang, Institute of Photonics,
Department of Mathematics and Physics, Leibniz University Hannover,
Hannover, 30167, Germany, e-mail: zhuang@iop.uni-hannover.de
Nanotechnology Reviews 2024; 13: 20240033
Open Access. © 2024 the author(s), published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 International License.

graphene flakes [11], and reduced graphene oxide (rGO) [12].
Further, GANS can also be recognized as various materials
according to their geometries and stacking modes, such as
carbon nanotubes (CNT) [13], carbon nanofibers (CNF) [14],
carbon nanocoil (CNC) [15], carbon black [16], carbon nano-
cone [17], graphene nanoribbons [18], graphene nanoislands
[19], graphane [20], graphyne [21], and pristine graphene
itself. Among the materials, several types of GANS like
GNP, GO, and CNT are commonly used in cementitious com-
posites to enhance their physical performance [22,23].
Practically, as one of the most often employed nanos-
tructures in graphene reinforced concrete, GNP is a sheet-
like material that can be readily produced from graphite or
graphite oxide. It has a thickness of 3–100 nm and consists
of several layers of graphene. Hence, GNP is a significant
reinforcing material because of its morphological structure.
GO is a layered material oxidized from graphite, with var-
ious oxygen-containing hydrophilic functional groups inter-
spersed on the edges and basal surfaces of graphene. It has
been proven that GO can effectively enhance the durability
as well as mechanical performance of cement composites
[25]. The main distinction between GNPs and GO for con-
crete depends on their electrical properties and dispersi-
bility potential. In comparison to GNPs, GO is easier to dis-
perse in water because of the oxygen groups on its sheet.
However, the oxygen groups also make GO become an elec-
trical insulator and lose advanced capabilities such as self-
sensing. CNT, which is thought to be a good alternative to
traditional reinforced fibers, is another popular research
field in cement composites. It can be considered a cylinder
obtained through rolling two-dimensional graphene layers.
Besides, CNT can be classified into three types according to
the number of walls, i.e., single-walled CNT (SWCNT) [26],
double-walled CNT [27], and multi-walled CNT [28]. Dano-
glidis et al. [29] found that the employment of CNTs
significantly improves the mechanical performance of
cement-based composites.
Researchers have noticed that many properties of con-
crete can be improved by incorporating graphene sheets
into the composite. Pan et al. [30] concluded that adding
0.03% GO by cement weight to the cement paste can,
respectively, increase the flexure, tensile, and compressive
strengths of cement by 60.7, 78.6, and 38.9%. Jing et al. [31]
found that when loading 0.2 and 0.4% graphene by weight
of cement, the flowability of cement mortar can be dimin-
ished by 17.4 and 39%, respectively. According to the work of
Wang et al. [32], evenly dispersed graphene can decrease the
cement’s stress under external loading and thus improve the
strength properties of the cement composite. However,
excessive graphene can lead to a degradation of physical
properties due to the defects on the interface of different
materials. Qureshi and Panesar [33] indicated that concrete’s
flexural and compressive strengths are best improved at
0.02 wt% graphene, whereas a larger concentration of gra-
phene steadily degrades the performance of cement paste.
The heterogeneity of composite materials manifests itself
at different scales, especially for cement-based materials with
complex components [34,35]. To study the mechanical perfor-
mance of GANS reinforced concrete, one can divide its
internal structure into four levels, as depicted in Figure 2.
According to the spatial scale, the four levels correspond to
the macroscale (>10
−1
m), mesoscale (10
−3
–10
−1
m), microscale
(10
−6
–10
−4
m), and nanoscale (<10
−6
m), respectively. At the
nanoscale, the molecular structure of the calcium silicate
hydrate (CSH) matrix and its connections with GANS can be
considered. As one of the main hydration products at early
Figure 1: Graphene is a 2D basic material which can be reshaped to
carbon materials of all other dimensionalities, including 0D buckyballs,
1D nanotubes, and 3D graphite [24].
Figure 2: Four levels of the spatial scale for ultra-high-performance
concrete.
2Qiang Yue et al.

ages, CSH significantly affects the mechanical behaviors of
concrete. Further, the CSH matrix, together with the large
portlandite crystals, aluminates, unhydrated cement pro-
ducts, and other cement compositions, forms the cement
paste at the microscale. As for the mesoscale, concrete can
be regarded as a three-phase composite material that is made
up of aggregates, a cement paste matrix, and an interfacial
transition zone connecting them. The highest level refers to
continuous homogeneous materials. More precisely, the
mechanical response of concrete is studied without consid-
ering the distribution of internal components, and the equiva-
lent parameters obtained from homogenization approaches
are used at the macroscale.
In this review, a thorough study on the numerical
simulation of GANS reinforced concrete is performed. In
Section 2, the modeling methods and their performance for
GANS reinforced concrete in nano and micro scales are
discussed. Then, the numerical aspects of GANS in cemen-
titious composites from the meso and macro perspectives
are presented in Section 3. Section 4 is devoted to the multi-
scale modeling strategies for GANS reinforced concrete.
Finally, the concluding remarks and future prospects are
given in Section 5.
2 Nanoscale and microscale
performance of graphene
reinforced concrete
2.1 Numerical models for CSH and GANS
The numerical analysis on atomic and molecular scales is
typically based on the empirical force field methods or the
quantum mechanics approaches. The quantum mechanics
simulation methods, which can describe the electron motion
accurately, are a type of techniques for modeling quantum
mechanics using computer technology. Molecular mechanics
(MD) is a rapidly developing theory based on empirical force
fields as well as the Born-Oppenheimer approximation. The
effects of electrons are neglected in the MD, and the function
of nuclear coordinates is applied to express the energy of the
system.ItmakestheMDmoreapplicableforthemodelingof
larger systems, such as Monte Carlo [36], molecular statics
[37], molecular dynamics [38], and so on.
As an analytical method at the nanometer scale, MD is
the most important and frequently adopted theory due to
its accuracy and flexibility. It combines computer tech-
nology, physics, chemistry, and mathematics to analyze
the motion of molecular systems using Newtonian classical
mechanics. In the past 20 years, MD simulation of CSH has
been continuously improved to help study the structures,
evolution, as well as other characteristics of hydrated
cement matrix at the level of molecules [39]. The selection
of the force field, which is built for representing the atom
interactions, lies at the heart of MD simulation. For dec-
ades, hundreds of empirical force fields, which were vali-
dated with experimental data, have been developed for
different research fields. Among them, some force fields
are commonly applied to model cementitious composites,
such as the consistent valence force field (CVFF), interface
force field (IFF), COMPASS, CSH-FF, and so on. More details
about the force fields can be found in Table 1.
2.2 Microscale mechanical properties and
performance of GANS reinforced cement
GANS, whose sizes range from nanometers to micrometers,
can dramatically impact the chemical and physical proper-
ties of hydrated cement composites, including chemical
reactivity, heat conduction, strength, shrinkage, and creep
[63–68]. In recent years, extensive works have been made
to study the interactions between GANS and cement paste
in cement hydrates, for example, molecular binding modes
and hydration reaction rate [69,70]. The selected MD simu-
lation investigations on the structures and performance of
GANS-cement systems are summarized in Table 2. Based on
the molecular modeling, Fan et al. [71] studied the shear
strength of Go/cement interface. The result showed that the
shear strength was 647.58 ±91.18 MPa for the interface of
GO cement, while 6–35 MPa for Portland cement. Wan
and Zhang [72] compared the mechanical performance of
ordinary Portland cement (OPC) and GO reinforced ultra-
high performance concrete (UHPC), and explained the dif-
ferences from the aspects of the structure, energies, and
material properties of the CSH/GO interface. There are
more hydroxyls and calcium dispersed in the interlayer
for the CSH generated in UHPC, resulting in a larger inter-
layer spacing and more water absorption. The sites for the
interfacial chemical bonds are occupied by hydroxyls and
water, so that the Ca–O bonds and H-bond network at
the CSH/GO interface are weakened. However, the water
and hydroxyls play the role of bridges to connect GO sheet
and CSH gel, as shown in Figure 3. Besides, the CSH/GO
interface has a stronger tensile strength and larger interfa-
cial interaction energy when there is more interlayer cal-
cium for UHPC. Hou et al. [73] modeled the bonding proper-
ties of GO interfaced epoxy-concrete composite based on
A review on modeling of GANS reinforced concrete 3

molecular dynamics. The damage processes of epoxy-CSH
and epoxy-GO-CSH systems under tension are compared in
Figures 4 and 5. Obviously, the contact area on the interface
of epoxy-GO-CSH system was considerably larger than that
on epoxy-CSH system when they were under the same
loading stage. It was concluded that the GO-modification
of the epoxy/CSH interface can significantly increase its ten-
sile resistance. The enhancement of bonding performance at
epoxy-GO interfaces is due to the numerous hydrogen bonds
that formed between GO’s polar oxygen-containing func-
tional groups and the epoxy molecules. When Go was coated
on the polyethylene (PE) fiber, Lu et al. [74] observed a
reduction in the translational motion of the atoms across
the PE/CSH interface, which made the entire composite
system more stable. The bonding energy at the CSH/GO as
well as PE/GO interfaces is much higher compared to that at
the weak CSH/epoxy interface, as illustrated in Figure 6. The
topological structure and physical properties of the nanos-
cale additions, such as the connectivity and size distribution
of pores in GANS, are also aspects that need to be considered
in composite materials. The stochastic behaviors and effective
material properties of functionally graded porous nanoscale
plates are investigated by Tran et al. [75]. It was found that
when the porosity density increases, the critical buckling
loads decrease. For more details on this aspect, please refer
to previous studies [76–78].
The transport properties, including ion diffusion and
water permeability, can also be affected when cement is
incorporated with GANS [79]. The influence of GNPs as well
as graphene oxide nanoplatelets (GONPs) on the freeze-
and-thaw properties of concrete was researched by Tong
et al. [80] at the atomistic level. In their study, CSH-FF and
ReaxFF were utilized to model the interatomic reactions
of CSH gels. For the GONPs, the hydroxyl groups were
described by using the harmonic bond potentials of O–H
and C–O bonds, harmonic angular potentials of C–O–H
and C–C–O angles, and harmonic dihedral potentials of
C–C–O–H and C–C–C–O dihedral angles. Moreover, the
OPLS-AA [81] force field for dialkyl ether was adopted to
represent the epoxy groups. During the freeze/thaw cycles,
the cyclic loads caused by pore water pressure in GNPs and
GONPs reinforced concrete were 15.2 and 12 GPa higher
than that in pure CSH gels, respectively. The graphene
reinforced atomistic structures can increase the risk of
nano-pore failure and worsen the freeze-and-thaw perfor-
mance of concrete, especially for GNPs reinforced CSH gels.
Zhao et al. [25] used molecular dynamics modeling and
chloride diffusion tests to systematically study the trans-
port behavior of GO reinforced cement. It was observed
that the migration of chloride ions solution dramatically
reduced when GO was introduced in the CSH pore. Due to
the GO adsorbed on the inner surface of the CSH pore, the
Table 1: Popular force fields for cementitious systems
Force field Basic features Ref.
UFF It is a full atomic force field that can be used for all elements in the periodic table [40–42]
COMPASS As a superior generalized ab initio force field, it is commonly applied in the modeling of liquids, polymers, and crystals [43–45]
ClayFF It is a force field designed for aqueous solution interfaces and hydrated multi-component mineral systems (mainly for
clay-related phases). By treating most of the bonded interactions in the crystals as pseudo-ionic, the highly complex
systems with millions of atoms are allowed for molecular simulations
[46,47]
CSH-FF As a modified version of ClayFF, the force field is specially designed for CSH. Compared with other force fields such as
ClayFF, it is more efficient for large systems due to the lower computational cost
[48–50]
IFF It yields the consistency of inorganic and organic thermodynamics and is used in the simulation of the inorganic-
organic interface. It is applicable for all kinds of elements and does not depend on quantum mechanical calculations of
atomic charges
[51–53]
CVFF It is a generalized valence force field that has been parameterized for water, various functional groups, and some
inorganic materials, including silica
[25,54,55]
Cement-FF All cementitious materials can be modeled with this force field. Potentials developed for similar atomic species systems
are combined and adjusted in the model
[56]
Dreiding This is a strictly diagonal force field possessing cosine-Fourier expansion torsion and harmonic valence terms. It can be
used for a variety of structures
[40]
PCFF The force field is originally created for organic and polymeric materials. Similar to COMPASS, it was parametrized for a
number of functional groups
[52,57]
ReaxFF It is a methodology between empirical force fields and quantum mechanics. In the modeling of chemical reactions and
transition states, the force field employs bond order rather than fixed connections for chemical bonds
[58–60]
GB It is originally established to express interactions between ellipsoidal particles and can be applied for controlling the
interaction between the building blocks of disk-like CSH gel
[61,62]
4Qiang Yue et al.

Table 2: Summary of MD analyses on GANS reinforced concrete
Matrix GNS type Force field Influence on Highlights Year Ref.
CSH GNPs; GONPs ReaxFF; CSH-FF
OPLS-AA
Freeze-and-thaw
performance
The freeze-and-thaw performance of cement is compromised by the pure GNPs, whereas it
can be improved by the GONPs
2016 [80]
CSH CNT Tersoff[82] Mechanical properties The addition of 2.351 Å CNT to the tobermorite with a diameter of 11 Å simultaneously
improves its bulk modulus, shear modulus, and Young’s modulus
2017 [83]
CSH GO COMPASS Shear strength The shear strength is 647.58 ± 91.18 MPa for CSH-GO interface, while 6–35 MPa for Portland
cement at the macroscale
2017 [71]
CSH GO ReaxFF Reactivity and interfacial
bonding
In contrast to sulfate groups, carboxyl and hydroxyl groups can keep strong stability and
prevent dissociation under the cement hydrate environment, making them ideal functional
groups for reinforcing the GO/CSH composite
2018 [84]
PE-CSH GO ClayFF; CVFF Shear strength Comparing PE-GO-CSH to PE-CSH, the maximum pulling force for PE is enhanced by 41.67%;
By enhancing the CSH-GO and PE-GO interfaces, which have higher interface binding
energies than PE-CSH, GO can improve the strength of the weak PE-CSH interface
2020 [74]
CSH with NaCl
solution
GO ClayFF; CVFF Durability Because of the incorporation of GO sheets, the rate of ion and water migration in CSH is
significantly lowered; The chloride ingress in cement can be restrained by the “immobilizing
effect”and “caging effect”of GO sheets
2020 [25]
CSH CNT CSH-FF Mechanical properties CSH gains 100% more strength, 21% more elastic modulus, 70% more shear modulus, and
17% more bulk modulus after the addition of CNT (1.8%)
2020 [85]
CSH CNT COMPASSII [42] Interaction The binding ability of CNTs is not significantly affected by the number of walls; The strength
of the interface is primarily determined by the type and amount of functional groups, as
well as the relative orientation of the polar groups of CNT
2020 [86]
Epoxy-CSH GO ClayFF; CVFF Tensile strength The epoxy-GO-CSH interface has a much stronger tensile resistance than the epoxy-CSH
interface because of the hydrogen bonds established between the epoxy molecules and the
polar oxygen-containing functional groups of GO
2021 [73]
Concrete matrix CNT Lennard-Jones [87] Poisson’s ratio, Young’s
modulus
The mechanical properties of concrete samples with three different types of CNTs are
compared and calculated
2021 [88]
A review on modeling of GANS reinforced concrete 5

transportation of water can be hindered. As plotted in
Figure 7, the solution species transportation in GO/CSH com-
posite material is inhibited at the gel pore’s entry point,
while the pure CSH gel does not possess this capability.
Due to the excellent performance of GANS reinforced
concrete, these type of materials have been widely applied
in the fields of self-sensing, electromagnetic shielding, anti-
corrosive coating, and so on [89–91]. It should be high-
lighted that the self-sensing and electromagnetic materials
are themselves structural materials so that the overall
structural performance would not be compromised by
the traditional sensors. Moreover, it also shows great
potential in the construction engineering which requires
ultrahigh strength and durability of materials [92–94].
Figure 3: MD model for CSH gel and CSH/GO interface [72].
Figure 4: The performance of CSH-epoxy system at different loading stages: (a) load–displacement curve, (b) center of mass (COM) vs displacement
curve for epoxy molecules, (c) CSH-epoxy contact area, and (d) simulation snapshots [73].
6Qiang Yue et al.

3 Mesoscale and macroscale
performance of graphene
reinforced concrete
3.1 Numerical methods for large-scale
concrete
Although the microscale performance of GANS incorpo-
rated concrete has been studied by many researchers, it
is quite necessary to develop the simulation at macro and
mesoscales in practical engineering. During the decades,
the mechanical behavior of concrete has been modeled
by applying a series of numerical methods, for instance,
the finite element method (FEM) [12,95,96], meshless method
(MM) [97], discrete element method (DEM) [98], finite differ-
ence method (FDM) [99], peridynamics [100], differential quad-
rature method (DQM) [101], incremental harmonic balanced
method [102], and boundary element method [103]. However,
most of the published literature on modeling GANS reinforced
concrete are based on the finite element simulation as a result
of its wide applicability.
3.2 Mesoscale and macroscale simulation on
GANS reinforced concrete
3.2.1 Research on getting material properties
The selection of precise material properties is crucial in the
modeling of concrete [104]. There are two strategies com-
monly used to get the macroscale properties of concrete.
The first method is measuring the results obtained from
experiments [105], whereas another method is performing
the equivalence using numerical simulation [106]. Anasto-
poulos et al. [107] compared two strategies, i.e., the represen-
tative volume element (RVE) based homogenization method,
and the multi-step homogenization method, to calculate the
elastic properties of graphene-concrete composites, as
depicted in Figure 8. In the method of multi-step homogeniza-
tion, one can break the multi-phase composite into “grains,”
Figure 5: The performance of CSH-GO-epoxy system at different loading stages: (a) Load–displacement curve, (b) COM vs displacement curve for
epoxy molecules, (c) CSH-epoxy contact area, and (d) simulation snapshots [73].
Figure 6: Adhesion energy of CSH/PE and CSH/GO/PE interfaces [74].
A review on modeling of GANS reinforced concrete 7

with each grain composed of the matrix and one inclusion
family. The same orientation, aspect ratio, and material prop-
erties are adopted for the inclusions of each family. Then, the
Mori–Tanaka model and the Voigt formulation are applied in
the homogenization process of the local grains and overall
composite, respectively. For the RVE-based homogenization,
the inclusions with random shapes and orientations are dis-
tributed in the element. The effective elastic properties of the
composite can be obtained by modeling the RVE under tensile
or shear loadings.
The electromagnetic parameters (complex permeability
and complex permittivity) of GANS-based composites were
studied by Santhosi et al. [108] using FEM. Compared to the
conventional material, an improvement in microwave absorp-
tion was observed in composite concrete blocks. Le et al. [109]
developed a mathematical model to estimate the damage
extent in graphene reinforced concrete based on the mea-
sured fractional change in electrical resistance. This model
was well verified by the physical experiments on the GNP-
infused mortar.
3.2.2 Performance of GANS reinforced concrete
The cracking process of fiber-reinforced concrete embedded
with graphene nanoplates was investigated by Pranno et al.
[110,111]. It was noted that an increase in the absorbed
energy by 20% and the first yielding load by 11% could be
achievedfor concrete when the volume fraction of graphene
in concrete reached 0.1%, as shown in Figure 9. Besides,
Figure 7: Translation of ions and water in the pore of (a) pure CSH gel, (b) CSH gel with incorporation of GO sheets (the white, gray, red, yellow, purple,
and pale green balls represent hydrogen, carbon, oxygen, silicon, sodium, and chlorine atoms, respectively) [25].
Figure 8: Homogenization methods of graphene-concrete composites [107]. (a) Representative volume element and (b) multi-step homogenization
method reprentation.
8Qiang Yue et al.

Saeed [12] used FEM to model the influence of rGO on the
damage in concrete which was induced by heat of hydra-
tion. By applying the mechanical properties measured from
experiments, the temperature change and cracking index of
rGO reinforced concrete was successfully reproduced. It was
found that, when substituting 1.2% rGO for OPC, the cracking
index of concrete could be reduced by decreasing the
thermal gradient of the specimens.
In order to study the impact resistance of GO-modified
rubberized engineered cementitious composite (GOCRECC),
Abdulkadir et al. [112] discussed the influence of GO and
crumb rubber (CR) on the initial and final impact energies
of concrete. Based on the experimental data and response
surface methodology (RSM), response-predictive models and
optimization were proposed to get the impact resistance of
similar materials. Similarly, Adamu et al. [113] employed
RSM to examine how GNP and plastic waste (PW) affect
the performance of concrete with high-volume flyash
(HVFA). The established model, which is in great agreement
with experimental data, indicates that the optimal mix can
be obtained by substituting 6.07% of cement with HVFA,
15.3% of coarse aggregate with PW, and adding GNP at
0.22%. Krystek et al. [114] verified the mechanical perfor-
mance of graphene-based concrete via FE modeling based
on the properties measured in laboratory tests. Acar et al.
[115] focused on the influence of monolayer prepreg (MP)
composites or graphene-reinforced monolayer prepreg (GMP)
composites on the mechanical strengths of concrete beams. In
accordance with the findings, credible solutions can be pro-
videdbyMPandGMPcompositesforstrengtheningconcrete
structures. The buckling behavior of concrete columns armed
with SWCNTs was investigated by Ali and Reza [116] based on
DQM. Furthermore, the nonlinear buckling load grew gradu-
allywiththeincreaseinvolumepercentofSWCNTs.Numer-
ical results showed that the structure became stiffer when the
concrete was reinforced by SWCNTs. The long-term perfor-
mance of concrete, which is incorporated with carbon fiber
reinforced polymer (CFRP) strips, was studied by Michele and
Angelo [117]. The reinforcing strips were made of a polymer
matrix incorporated with the long straight CNFs and CNTs,
and their mechanical properties were assessed using a three-
phase constitutive model. Additionally, two distinct creep
functions were adopted to characterize the mechanical fea-
tures of CFRP and concrete in the framework of linear vis-
coelasticity. More details about the mesoscale and macroscale
modeling of GANS reinforced concrete can be found in
Table 3.
4 Multiscale methodologies of
GANS reinforced concrete
4.1 Multiscale models combining GANS with
matrix
In order to precisely describe the physics of GANS based mate-
rials at various length scales, some researchers [125–128] pro-
posed a series of coupling methods by combining MM/MD with
FEM. Wei and Kysar [129] developed a multiscale method
based on FEM to build the connections between macroscopic
graphene membrane deformations with C–Cinteratomicbeha-
viors. Then, many works [130–135] used the theory to model
Figure 9: Comparison of cracking process of ultra-high-performance fiber-reinforced concrete (UHPFRC) with and without GNP: (a) load–deflection
curves and (b) damage states [111].
A review on modeling of GANS reinforced concrete 9

Table 3: Summary of mesoscale and macroscale analyses on GANS reinforced concrete
Matrix GNS type Method Influence on Highlights Year Ref.
Cement CNT FEM Constitutive behavior To best enhance the structural ductility and strength of CNT reinforced
concrete, the optimal combinations for interfacial and mechanical properties
of CNT are searched
2009 [118]
Cement CNT FEM Mechanical properties It is found that the enhancement of CNT reinforced cement becomes stronger
and then weaker with the continuous increase in the percentage of CNT
2012 [119]
Concrete SWCNTs DQM Buckling behavior An original model for the concrete column with SWCNT is proposed, in which
the Timoshenko and Euler-Bernoulli beam models are employed
2016 [116]
Cement CNTs FEM Fracture energy The CNT-cement composite’s size-independent fracture energy is determined
using numerical analyses
2017 [120]
Cement GO Boundary nucleation-
growth model (BNG)
Nucleation-growth during
hydration
BNG [120] is used to mathematically describe the role of GO when it is
regarded as a nucleation-growth site
2017 [121]
Concrete GMP FEM Flexural strength and
tensile strength
When MP was substituted with GMP in concrete, the results showed an
improvement in the tensile strength of about 7% and the flexural strength
of 1–3.7%
2017 [115]
UHPFRC Fiber DFEM Failure modes A discrete-continuum coupled finite element modeling method is developed to
study the crushing, spalling, mortar cracking as well as fiber breakage
behaviors of fiber reinforced concrete
2018 [122]
Concrete CNT FEM Conductive properties To simulate the CNT reinforced composites at an arbitrary strain state, a mixed
micromechanics-FEM approach is presented
2018 [95]
Concrete CFRP FEM Creep behavior The influence of the number and thickness of CFRP strips, as well as the CNT
mass fraction, are researched for the long-term behavior of concrete
2020 [117]
CRECC GO RSM Impact resistance The predictive models for initial and ultimate impact energy of GOCRECC are
proposed. It is indicated that optimal amounts of GO and CR by cement weight
added in the composite are 0.0347% and 5%, respectively
2021 [112]
HVFA concrete GNP RSM Mechanical properties For the strengths of HVFA concrete, the adverse effects of fly ash and PW can
be significantly mitigated by adding GNP in the concrete
2021 [113]
Functionally graded
composite beams
GO MM Bending behavior A multiquadric radial basis function-based meshless collocation method is
applied to assess the mechanical responses of GO powder reinforced
functionally graded composite beams
2021 [97]
Mortar rGO FEM Cracking index The mechanical properties obtained from experiments are adopted to
research how rGO affects the damage process of concrete due to temperature
stress
2022 [12]
Concrete Graphene flake FEM Microwave absorption Compared with conventional concrete blocks, the concrete reinforced by
graphene-based hybrid nanocomposites has a stronger capability in terms of
microwave absorption
2022 [108]
UHPFRC GNP DIM Fracture The cohesive elements with a nonlinear traction-separation law are applied to
model the initiation and evolution of the fracture. The enhancement on the
force responses of UHPFRC, which results from the addition of graphene
nanoparticles, can be successfully predicted by the model
2022 [123]
Concrete CNTs FDM Electrical properties The electrical conductivity of concrete, which is reinforced by randomly
dispersed carbon fibers, can be determined by the model
2023 [124]
10 Qiang Yue et al.

the multiscale behaviors of GANS based composite structures.
However, it is still difficult to capture the nanoscale character-
istics of all components (matrix, fiber, filler, interphase) of
composites. For this reason, some literature [130,136–138] sim-
plified the composite materials as a multiscale system, in which
some components such as matrix as well as fibers were con-
sidered at the macro-scale level while the other constituents
were modeled at the nanoscale level. Among the works, most
of the simulations adopted strategies that involve representing
GANS as a lattice frame structure. In the structure, GANS are
discretized with one-dimensional truss elements, while the
matrix is represented by the continuous three-dimensional
solid elements. This method can also be called the unit cell
method or RVE method [139], which is also introduced in Sec-
tion 3.1. In the RVE, as shown in Figure 10, the GANS and the
matrix can be connected using van der Waals interaction
forces [138]. When the deflection exceeds a certain threshold,
the interface bonds (truss elements) that connect GANS and the
matrix can be removed. Apart from the spring element, var-
ious other types of elements have been developed to model
carbon nanostructures and C–C bonds in GANS, which are
applicable to different problems [128]. The elements for repre-
senting carbon nanostructures are summarized in Table 4.
Although the atomistic simulation and the beam finite
elements can accurately characterize the structure of GANS,
they are very time-consuming in the multiscale modeling. To
solve this problem, a continuum mechanics surrogate model
was proposed by Papadopoulos et al. [140] for the simulation
of graphene. To reproduce the shell-type structural behavior
of graphene platelets, the work presented an equivalent
shell element as the substitute of the detailed molecular
dynamics models for graphene. This shell finite element
model of graphene is proven to be capable of effectively
representing both its membrane and plate behaviors. As
plotted in Figure 11, the features of the graphene particles,
including the random wrinkling behavior, and the delami-
nation and debonding phenomena, can be well simulated.
Apart from the mentioned elements, various other types of
elements have been developed to represent C–Cbondsand
Figure 10: Multiscale model of graphene reinforced composites: Carbon
atoms, covalent bonds, L–J potential, and the polymer matrix are
represented by nodes, Timoshenko beams, truss elements, and 3D solid
elements, respectively [138].
Table 4: Elements for representing C–C bonds and carbon nanostructures in GANS
Element
type
Highlights Structure Ref.
CC-beams It is a type of element that can model the C–C bonds’
tension, bending, and torsion behaviors. It also has the
benefits of simple implementation and high efficiency
Six beam elements are used to depict the hexagonal
lattice of graphene
[141,142]
CC-springs The geometrical properties of spring elements depend
on the natural characteristics of C–C bonds. It is more
suitable for modeling the nonlinear behavior of carbon
nanostructures
The hexagonal is composed of 12 spring elements,
wherein 6 elements simulate translations and the
remaining 6 elements simulate angular variations
[143,144]
CC-TRF The C–C bonds are modeled with truss, rod, and frame
elements in the method
A hexagonal cell of graphene is also represented by
12 elements, where 6 elements are used for
representing stretching while the remaining 6
elements are used to depict in-plane bending
[145]
2D-Elem Two-dimensional elements such as plane strain, plane
stress, and plate elements are adopted
—[146,147]
Shell-Ele Shell-type elements are applied to express the graphene-
based nanostructures
—[140,148–150]
3D-Ele The nanostructure of GANS is represented by three-
dimensional solid elements, for example, hexahedral and
tetrahedral elements
—[151–153]
Axisym-Elem Axisymmetric elements are used in the model —[154,155]
Spec-Elem Special-purpose elements are introduced to meet specific
requirements
—[156,157]
A review on modeling of GANS reinforced concrete 11

carbon nanostructures in GANS, which are applicable for
different problems [128].
4.2 Multiscale models with multilevel
equivalence
The properties of concrete at a higher scale depend on
those of the components at a lower scale. Hence, many
researches were devoted to revealing the mechanical response
mechanisms of concrete from the nanoscale to the macroscale.
As shown in Figure 12, Eftekhari and Mohammadi [158]
explained the dynamic behaviors of CNT reinforced con-
crete from different scale perspectives, i.e., nanoscale,
microscale, mesoscale, and macroscale. On the nanoscale,
themolecularstructureofCNTwascarefullymodeled
using the MD approach. Then, the mean values of the
results obtained from nanoscale simulations were applied
to the microscale modeling of CNT reinforced cement.
Then, the microscale FE simulation was carried out based
on a particle kinetics chemical hydration theory. When
the properties of cement are determined, the mesoscale
analysis of concrete can be implemented. Finally, based
on the equivalent properties calculated from the numer-
ical results at the mesoscale, the global mechanical beha-
vior at the macroscale can be studied via FEM. This multi-
scale modeling strategy was also adopted by many other
works [159–165] to investigate the influence of the added
graphene-based nanomaterials on concrete. Moreover,
the fracture behavior of the CNT reinforced concrete at
the mesoscale was studied by Eftekhari et al. [13] with the
aid of MD and RVE simulations. It was observed that a
remarkable delay occurred in the initiation and propaga-
tion of mixed-mode fractures.
Similarly, Papadopoulos and Impraimakis [166] evalu-
ated the nonlinear constitutive relationship of CNTs rein-
forced concrete using hierarchical RVEs, which were in
accordance with the material’s microstructural topology.
As can be seen in Figure 13, several RVEs with different
sizes were constructed in the hierarchical multiscale mod-
eling strategy. The lowest nanoscale RVE1, which is initially
resolved, only contains CNTs and the cement paste. The
computational homogenization on the lower RVE can result
in an equivalent “enhanced”cement paste, which is utilized
in the higher RVE. Moreover, the aggregates of different
dimensions (from 0.125 to 32 mm) can be considered in
the corresponding RVEs. Based on the information passed
through scales, both elastic and inelastic analyses of con-
crete can be performed on all scales.
Wang et al. [167] developed a multiscale modeling
method involving the length-scale integration, and further
verified its ability to obtain the effective properties by
Figure 11: Tensile stress distributions on a single-layer graphene sheet: wrinkled (left) and straight (right) [140].
Figure 12: The multiscale simulation for the fracture of a CNT-reinforced
concrete [158].
12 Qiang Yue et al.

upscaling. Based on this upscaling process, the properties
of cement mortar can be estimated using Mori–Tanaka
and self-consistent approaches [168]. Then, the meshless
technique can be applied to estimate the material para-
meters of CNT reinforced cementitious composites at the
macroscale.
4.3 Machine learning
With the development of machine learning, the technique
began to be applied to the prediction of multiscale beha-
viors of concrete [169–172]. Lyngdoh and Das [173] com-
bined machine learning (forward neural network) with a
validated FEM-based multiscale modeling framework to
estimate the strain-sensing performance of self-sensing
concrete which is reinforced by nano-engineered mate-
rials. This model, as illustrated in Figure 14, showed excel-
lent efficiency in the prediction of the electromechanical
response. Lu et al. [174] also outlined a data-driven
computational homogenization method that can be used
in the simulation for the electrical responses of graphene-
reinforced composites. The related works based on other
machine learning techniques, such as deep convolutional
neural network, fully convolutional network, and support
vector machine, can be found in the previous literature
[175–177].
5 Conclusion
In the present work, an extensive overview of the numer-
ical modeling techniques and strategies for GANS rein-
forced concrete is presented. The numerical works consid-
ering the geometry characteristics, material properties,
constitutive models, internal components of GANS rein-
forced concrete are discussed at different spatial scales.
The following conclusions can be drawn based on the
review:
Figure 13: Hierarchical RVEs for cementitious composites with (a) RVE1 CNTs (RVE1), (b) aggregates smaller than 2 mm (RVE2), (c) aggregates smaller
than 8 mm (RVE3), and (d) aggregates smaller than 32 mm (RVE4) [166].
Figure 14: A technique combining multiscale numerical modeling with machine learning [173].
A review on modeling of GANS reinforced concrete 13

1) GANS reinforced concrete is a type of composites with
complex performance at different scales. The addition
of GANS has a significant influence on concrete in many
aspects, including the mechanical behaviors, transport
properties, and failure mechanisms. GANS have the
potential to increase the bulk modulus, shear modulus,
and Young’s modulus of concrete, resulting in the larger
strengths of concrete. Additionally, the durability of
concrete can be improved by GANS by lowering the
ion and water migration in CSH gel. The enhancement
of GANS reinforced composites at the nanoscale and
microscale is significantly greater compared to that at
the macroscale, primarily attributed to defects present
across multiple scales. Generally, the appropriate addi-
tion of GANS can lead to an improvement of the proper-
ties for concrete, while excessive GANS may cause harm
to the cementitious composites.
2) In nanoscale and microscale modeling, the structure of
cementitious composites can be generated using quantum
mechanics and molecular dynamics methods. The interfa-
cial bonding and mechanical performance of GANS rein-
forced cement can be predicted using MD simulation. The
force fields developed for cementitious composites can be
adopted to analyze the microscale behavior of GANS rein-
forced concrete. As for the mesoscale and macroscale mod-
eling, many numerical methods can be used to study the
material’s physical and chemical performance, such as the
FEM, meshfree method, and DEM. The equivalent properties
of RVE obtained from physical experiments and homogeni-
zation strategies can be applied to understand the mechan-
ical response mechanism of concrete at a large scale.
3) In the global simulation of concrete considering the
distribution of GANS, a series of elements, such as the
truss elements and beam elements, can be used as effi-
cient and reliable tools to characterize the chemical
bonds and nanostructures of GANS. Hence, multiscale
modeling can be achieved in the framework of FEM.
Another multiscale modeling strategy is passing the mate-
rial parameters between the RVEs at different levels. It
helps to understand the performance of concrete at all
scales and the relationships between material parameters
at different scales. Moreover, machine learning has become
a popular mode to study the multiscale response of GANS
incorporated concrete. Nevertheless, very limited research
was devoted on the multiscale performance of GANS rein-
forced concrete. More efficient and accurate models need to
be developed to reveal the effects of GANS on the macro-
scaleresponseofconcretestructure.
In conclusion, GANS can drive the enhancement of
cementitious materials and support the development of
construction industry. Moreover, numerical modeling can
help in the design and optimization of GANS reinforced
cementitious materials, by providing a thorough under-
standing of their mechanical, structural, and transport
properties. The introduction of GANS into concrete produc-
tion provides a pathway for a more substantial future and
great opportunities for construction engineering.
Acknowledgements: Financial support by the National
Key R&D Program of China (No. 2022YFC3005505) and the
National Natural Science Foundation of China (Nos
U2040223 and 51979207), is gratefully acknowledged.
Funding information: The National Key R&D Program of
China (No. 2022YFC3005505) and the National Natural Science
Foundation of China (Nos U2040223 and 51979207).
Author contributions: All authors have accepted responsi-
bility for the entire content of this manuscript and approved
its submission.
Conflict of interest: The authors state no conflictofinterest.
Data availability statement: All data generated or analysed
during this study are included in this published article.
References
[1] Chanut N, Stefaniuk D, Weaver JC, Zhu Y, Shao-Horn Y, Masic A,
et al. Carbon–cement supercapacitors as a scalable bulk energy
storage solution. Proc Natl Acad Sci. 2023;120:e2304318120.
[2] Kashif Ur Rehman S, Kumarova S, Ali Memon S, Javed MF,
Jameel M. A review of microscale, rheological, mechanical, ther-
moelectrical and piezoresistive properties of graphene based
cement composite. 2020;10:2076.
[3] Zhong R, Zhang F, Poh LH, Wang S, Le HTN, Zhang M-H. Assessing
the effectiveness of UHPFRC, FRHSC and ECC against high velocity
projectile impact. Cem Concr Compos. 2021;120:104013.
[4] Balandin AA, Ghosh S, Bao W, Calizo I, Teweldebrhan D, Miao F,
et al. Superior thermal conductivity of single-layer graphene.
Nano Lett. 2008;8:902–7.
[5] Lee C, Wei X, Kysar JW, Hone J. Measurement of the elastic
properties and intrinsic strength of monolayer graphene.
Science. 2008;321:385–8.
[6] Bolotin KI, Sikes KJ, Jiang Z, Klima M, Fudenberg G, Hone J, et al.
Ultrahigh electron mobility in suspended graphene. Solid State
Commun. 2008;146:351–5.
[7] Stoller MD, Park S, Zhu Y, An J, RuoffRS. Graphene-based ultra-
capacitors. Nano Lett. 2008;8:3498–502.
[8] Mohan VB, Lau K-t, Hui D, Bhattacharyya D. Graphene-based
materials and their composites: A review on production, appli-
cations and product limitations. Compos Part B: Eng.
2018;142:200–20.
14 Qiang Yue et al.

[9] Young RJ, Liu M, Kinloch IA, Li S, Zhao X, Vallés C, et al. The
mechanics of reinforcement of polymers by graphene nanopla-
telets. Compos Sci Technol. 2018;154:110–6.
[10] Habibnejad Korayem A, Ghoddousi P, Shirzadi Javid AA, Oraie MA,
Ashegh H. Graphene oxide for surface treatment of concrete: A
novel method to protect concrete. Constr Build Mater.
2020;243:118229.
[11] Low CTJ, Walsh FC, Chakrabarti MH, Hashim MA, Hussain MA.
Electrochemical approaches to the production of graphene flakes
and their potential applications. Carbon. 2013;54:1–21.
[12] Saeed M. Three-dimensional finite element modelling for
influence of reduced graphene oxide on cracking index
of mass mortar blocks due to heat of hydration. Aust J Civ Eng.
2023;21:194–206.
[13] Eftekhari M, HatefiArdakani S, Mohammadi S. An XFEM multi-
scale approach for fracture analysis of carbon nanotube rein-
forced concrete. Theor Appl Fract Mech. 2014;72:64–75.
[14] Sanchez F, Zhang L, Ince C. Multi-scale performance and dur-
ability of carbon nanofiber/cement composites. In: Bittnar Z,
Bartos PJM, Němeček J, Šmilauer V, Zeman J, editors.
Nanotechnology in Construction Vol. 3. Berlin, Heidelberg:
Springer Berlin Heidelberg; 2009. p. 345–50.
[15] Chen X, Zhang S, Dikin DA, Ding W, RuoffRS, Pan L et al.
Mechanics of a carbon nanocoil. Nano Lett. 2003;3:1299–304.
[16] Ding Y, Chen Z, Han Z, Zhang Y, Pacheco-Torgal F. Nano-carbon
black and carbon fiber as conductive materials for the diagnosing of
thedamageofconcretebeam.ConstrBuildMater.2013;43:233–41.
[17] Yang N, Zhang G, Li B. Carbon nanocone: A promising thermal
rectifier. Appl Phys Lett. 2008;93:243111.
[18] Celis A, Nair MN, Taleb-Ibrahimi A, Conrad EH, Berger C, de
Heer WA, et al. Graphene nanoribbons: fabrication, properties
and devices. J Phys D: Appl Phys. 2016;49:143001.
[19] Fernández-Rossier J, Palacios JJ. Magnetism in graphene nanois-
lands. Phys Rev Lett. 2007;99:177204.
[20] Sofo JO, Chaudhari AS, Barber GD. Graphane: A two-dimensional
hydrocarbon. Phys Rev B. 2007;75:153401.
[21] Cranford SW, Buehler MJ. Mechanical properties of graphyne.
Carbon. 2011;49:4111–21.
[22] Konsta-Gdoutos MS, Metaxa ZS, Shah SP. Carbon nanotubes
reinforced concrete. Special Publication. 2009;267:11–20.
[23] Chuah S, Pan Z, Sanjayan JG, Wang CM, Duan WH. Nano rein-
forced cement and concrete composites and new perspective
from graphene oxide. Constr Build Mater. 2014;73:113–24.
[24] Geim AK, Novoselov KS. The rise of graphene. Nat Mater.
2007;6:183–91.
[25] Zhao L, Hou D, Wang P, Guo X, Zhang Y, Liu J, et al. Experimental
and molecular dynamics studies on the durability of sustainable
cement-based composites: Reinforced by graphene. Constr Build
Mater. 2020;257:119566.
[26] Makar J. The effect of SWCNT and other nanomaterials on cement
hydration and reinforcement. In: Gopalakrishnan K, Birgisson B,
Taylor P, Attoh-Okine NO, editors. Nanotechnology in Civil
Infrastructure: A Paradigm Shift. Berlin, Heidelberg: Springer
Berlin Heidelberg; 2011. p. 103–30.
[27] Al-Zu’bi M, Fan M, Anguilano L. Advances in bonding agents for
retrofitting concrete structures with fibre reinforced polymer
materials: A review. Constr Build Mater. 2022;330:127115.
[28] Choi H, Kang D, Seo GS, Chung W. Effect of some parameters on
the compressive strength of MWCNT-cement composites. Adv
Mater Sci Eng. 2015;2015:340808.
[29] Danoglidis PA, Konsta-Gdoutos MS, Gdoutos EE, Shah SP.
Strength, energy absorption capability and self-sensing proper-
ties of multifunctional carbon nanotube reinforced mortars.
Constr Build Mater. 2016;120:265–74.
[30] Pan Z, He L, Qiu L, Korayem AH, Li G, Zhu JW, et al. Mechanical
properties and microstructure of a graphene oxide–cement
composite. Cem Concr Compos. 2015;58:140–7.
[31] Jing G, Ye Z, Lu X, Hou P. Effect of graphene nanoplatelets on
hydration behaviour of Portland cement by thermal analysis.
2017;29:63–70.
[32] Wang B, Jiang R, Wu Z. Investigation of the mechanical properties
and microstructure of graphene nanoplatelet-cement composite.
Nanomaterials. 2016;6(11):200.
[33] Qureshi TS, Panesar DK. Nano reinforced cement paste compo-
site with functionalized graphene and pristine graphene nano-
platelets. Compos Part B: Eng. 2020;197:108063.
[34] Sorelli L, Constantinides G, Ulm F-J, Toutlemonde F. The nano-
mechanical signature of ultra high performance concrete by
statistical nanoindentation techniques. Cem Concr Res.
2008;38:1447–56.
[35] Bernard O, Ulm F-J, Lemarchand E. A multiscale
micromechanics-hydration model for the early-age elastic prop-
erties of cement-based materials. Cem Concr Res.
2003;33:1293–1309.
[36] Hou D, Zhang J, Li Z, Zhu Y. Uniaxial tension study of calcium
silicate hydrate (C–S–H): structure, dynamics and mechanical
properties. Mater Struct. 2015;48:3811–24.
[37] Palkovic SD, Yip S, Büyüköztürk O. Constitutive response of cal-
cium-silicate-hydrate layers under combined loading. J Am Ceram
Soc. 2017;100:713–23.
[38] Yu J, Hou D, Ma H, Wang P. Nanomodified cement-based mate-
rials: review (2015–2020) of molecular dynamics studies. J Mater
Civ Eng. 2022;34:03121002.
[39] Cho BH, Chung W, Nam BH. Molecular dynamics simulation of
calcium-silicate-hydrate for nano-engineered cement composites
–a review. 2020;10:2158.
[40] Wu W, Al-Ostaz A, Cheng Alexander HD, Song Chung R.
Computation of elastic properties of portland cement using
molecular dynamics. J Micromech Microeng. 2011;1:84–90.
[41] Tavakoli D, Tarighat A. Molecular dynamics study on the
mechanical properties of Portland cement clinker phases.
Comput Mater Sci. 2016;119:65–73.
[42] Al-Ostaz A, Wu W, Cheng AHD, Song CR. A molecular dynamics
and microporomechanics study on the mechanical properties of
major constituents of hydrated cement. Compos Part B: Eng.
2010;41:543–9.
[43] Du J, Bu Y, Shen Z. Interfacial properties and nanostructural
characteristics of epoxy resin in cement matrix. Constr Build
Mater. 2018;164:103–12.
[44] Hajilar S, Shafei B. Nano-scale investigation of elastic properties
of hydrated cement paste constituents using molecular dynamics
simulations. Comput Mater Sci. 2015;101:216–26.
[45] Shu X, Ran Q, Liu J, Zhao H, Zhang Q, Wang X, et al. Tailoring the
solution conformation of polycarboxylate superplasticizer toward
the improvement of dispersing performance in cement paste.
Constr Build Mater. 2016;116:289–98.
[46] Fu J, Bernard F, Kamali-Bernard S. Assessment of the elastic
properties of amorphous calcium silicates hydrates (I) and (II)
structures by molecular dynamics simulation. Mol Simul.
2018;44:285–99.
A review on modeling of GANS reinforced concrete 15

[47] Cygan RT, Liang J-J, Kalinichev AG. Molecular models of hydroxide,
oxyhydroxide, and clay phases and the development of a general
force field. J Phys Chem B. 2004;108:1255–66.
[48] Hou D, Yu J, Wang P. Molecular dynamics modeling of the
structure, dynamics, energetics and mechanical properties of
cement-polymer nanocomposite. Compos Part B: Eng.
2019;162:433–44.
[49] Shahsavari R, Pellenq RJM, Ulm F-J. Empirical force fields for
complex hydrated calcio-silicate layered materials. Phys Chem
Chem Phys. 2011;13:1002–11.
[50] Hou D, Li H, Zhang L, Zhang J. Nano-scale mechanical properties
investigation of C-S-H from hydrated tri-calcium silicate by nano-
indentation and molecular dynamics simulation. Constr Build
Mater. 2018;189:265–75.
[51] Heinz H, Lin T-J, Kishore Mishra R, Emami FS. Thermodynamically
consistent force fields for the assembly of inorganic, organic, and
biological nanostructures: the interface force field. Langmuir.
2013;29:1754–65.
[52] Chaudhari O, Biernacki JJ, Northrup S. Effect of carboxylic and
hydroxycarboxylic acids on cement hydration: experimental and
molecular modeling study. J Mater Sci. 2017;52:13719–35.
[53] Mishra RK, Fernández-Carrasco L, Flatt RJ, Heinz HJDT. A force
field for tricalcium aluminate to characterize surface properties,
initial hydration, and organically modified interfaces in atomic
resolution. 2014;43:10602–16.
[54] Zhou Y, Hou D, Jiang J, She W, Li J. Molecular dynamics study of
solvated aniline and ethylene glycol monomers confined in cal-
cium silicate nanochannels: a case study of tobermorite. Phys
Chem Chem Phys. 2017;19:15145–59.
[55] Zhou Y, Tang L, Liu J, Miao C. Interaction mechanisms between
organic and inorganic phases in calcium silicate hydrates/poly
(vinyl alcohol) composites. Cem Concr Res. 2019;125:105891.
[56] Mishra RK, Mohamed AK, Geissbühler D, Manzano H, Jamil T,
Shahsavari R, et al. Cemff: A force field database for cementitious
materials including validations, applications and opportunities.
Cem Concr Res. 2017;102:68–89.
[57] Sun H. Ab initio calculations and force field development for
computer simulation of polysilanes. Macromolecules.
1995;28:701–12.
[58] van Duin ACT, Dasgupta S, Lorant F, Goddard WA. ReaxFF: A
reactive force field for hydrocarbons. J Phys Chem A.
2001;105:9396–409.
[59] Manzano H, Pellenq RJM, Ulm F-J, Buehler MJ, van Duin ACT.
Hydration of calcium oxide surface predicted by reactive force
field molecular dynamics. Langmuir. 2012;28:4187–97.
[60] Manzano H, Masoero E, Lopez-Arbeloa I, Jennings HM. Shear
deformations in calcium silicate hydrates. Soft Matter.
2013;9:7333–41.
[61] Yu Z, Lau D. Nano- and mesoscale modeling of cement matrix.
Nanoscale Res Lett. 2015;10:173.
[62] Ebrahimi D, Whittle AJ, Pellenq RJM. Mesoscale properties of clay
aggregates from potential of mean force representation of inter-
actions between nanoplatelets. J Chem Phys. 2014;140:154309.
[63] Kalinichev AG, Wang J, Kirkpatrick RJ. Molecular dynamics mod-
eling of the structure, dynamics and energetics of mineral–water
interfaces: Application to cement materials. Cem Concr Res.
2007;37:337–47.
[64] Wang J, Wang Y, Wang R, Li W, Xu Y. Creep behavior of graphene
oxide reinforced cement composites: Experiments, numerical
simulations, and prediction models. Struct Concr.
2023;24:5441–50.
[65] Wang Q, Yue Q, Zhou W, Feng YT, Chang X. Modeling of both
tensional-shear and compressive-shear fractures by a unified
phase-field model. Appl Math Model. 2023;117:162–96.
[66] Wang Q, Yue Q, Huang C, Zhou W, Chang X. An adaptive local
algorithm for solving the phase-field evolution equation in the
phase-field model for fracture. Comput Mater Sci. 2022;214:111747.
[67] Yue Q, Zhou W, Wang Q, Feng YT, Ma G, Chang X. An adaptive
phase-field model based on bilinear elements for tensile-com-
pressive-shear fracture. Comput Math Appl. 2022;105:112–35.
[68] Wang Q, Feng YT, Zhou W, Cheng Y, Ma G. A phase-field model for
mixed-mode fracture based on a unified tensile fracture criterion.
Comput Methods Appl Mech Eng. 2020;370:113270.
[69] Yang H, Cui H, Tang W, Li Z, Han N, Xing F. A critical review on
research progress of graphene/cement based composites.
Compos Part A: Appl Sci Manuf. 2017;102:273–96.
[70] Lin C, Wei W, Hu YH. Catalytic behavior of graphene oxide for
cement hydration process. J Phys Chem Solids. 2016;89:128–33.
[71] Fan D, Lue L, Yang S. Molecular dynamics study of interfacial
stress transfer in graphene-oxide cementitious composites.
Comput Mater Sci. 2017;139:56–64.
[72] Wan H, Zhang Y. Interfacial bonding between graphene oxide
and calcium silicate hydrate gel of ultra-high performance con-
crete. Mater Struct. 2020;53:34.
[73] Hou D, Yang Q, Jin Z, Wang P, Wang M, Wang X, et al. Enhancing
interfacial bonding between epoxy and CSH using graphene
oxide: An atomistic investigation. Appl Surf Sci. 2021;568:150896.
[74] Lu Z, Yu J, Yao J, Hou D. Experimental and molecular modeling of
polyethylene fiber/cement interface strengthened by graphene
oxide. Cem Concr Compos. 2020;112:103676.
[75] Tran V-T, Nguyen T-K, Nguyen-Xuan H, Abdel Wahab M. Vibration
and buckling optimization of functionally graded porous micro-
plates using BCMO-ANN algorithm. Thin-Walled Struct.
2023;182:110267.
[76] Cuong-Le T, Nguyen KD, Hoang-Le M, Sang-To T, Phan-Vu P,
Wahab MA. Nonlocal strain gradient IGA numerical solution for
static bending, free vibration and buckling of sigmoid FG sand-
wich nanoplate. Phys B: Condens Matter. 2022;631:413726.
[77] Thanh CL, Nguyen TN, Vu TH, Khatir S, Abdel Wahab M. A geo-
metrically nonlinear size-dependent hypothesis for porous func-
tionally graded micro-plate. Eng Computers. 2022;38:449–60.
[78] Cuong-Le T, Hoang-Le M, Ferreira AJM, Abdel Wahab M. Small
size-effect isogeometric analysis for linear and nonlinear
responses of porous metal foam microplate. Compos Struct.
2022;285:115189.
[79] Du H, Pang SD. Enhancement of barrier properties of cement
mortar with graphene nanoplatelet. Cem Concr Res.
2015;76:10–9.
[80] Tong T, Fan Z, Liu Q, Wang S, Tan S, Yu Q. Investigation of the
effects of graphene and graphene oxide nanoplatelets on the
micro- and macro-properties of cementitious materials. Constr
Build Mater. 2016;106:102–14.
[81] Jorgensen WL, Tirado-Rives J. The OPLS [optimized potentials for
liquid simulations] potential functions for proteins, energy mini-
mizations for crystals of cyclic peptides and crambin. J Am Chem
Soc. 1988;110:1657–66.
[82] TersoffJ. Empirical interatomic potential for carbon, with appli-
cations to amorphous carbon. Phys Rev Lett. 1988;61:2879–82.
16 Qiang Yue et al.

[83] Lushnikova A, Zaoui A. Improving mechanical properties of C-S-H
from inserted carbon nanotubes. J Phys Chem Solids.
2017;105:72–80.
[84] Hou D, Yang T, Tang J, Li S. Reactive force-field molecular
dynamics study on graphene oxide reinforced cement composite:
functional group de-protonation, interfacial bonding and strength-
ening mechanism. Phys Chem Chem Phys. 2018;20:8773–89.
[85] Sindu BS, Sasmal S. Molecular dynamics simulations for evalua-
tion of surfactant compatibility and mechanical characteristics of
carbon nanotubes incorporated cementitious composite. Constr
Build Mater. 2020;253:119190.
[86] Merodio-Perea RG, Páez-Pavón A, Lado-Touriño I. Reinforcing
cement with pristine and functionalized carbon nanotubes:
experimental and simulation studies. Int J Smart Nano Mater.
2020;11:370–86.
[87] Verlet L. Computer “experiments”on classical fluids. I. thermo-
dynamical properties of Lennard-Jones Molecules. Phys Rev.
1967;159:98–103.
[88] Zhao L, Nasution MKM, Hekmatifar M, Sabetvand R,
Kamenskov P, Toghraie D, et al. The improvement of mechanical
properties of conventional concretes using carbon nanoparticles
using molecular dynamics simulation. Sci Rep. 2021;11:20265.
[89] Papanikolaou I, Al-Tabbaa A, Goisis M. An industry survey on the
use of graphene-reinforced concrete for self-sensing applica-
tions. International Conference on Smart Infrastructure and
Construction; 2019. p. 613–22.
[90] Zeng H, Qu S, Tian Y, Hu Y, Li Y. Recent progress on graphene
oxide for next-generation concrete: Characterizations, applica-
tions and challenges. J Build Eng. 2023;69:106192.
[91] Zhang Y, Wang Q, Chen J, Tang J, Zhou H, Zhou W, et al.
Preparation and performance study of active chemicals in
cementitious capillary crystalline waterproofing materials. Case
Stud Constr Mater. 2024;20:e02874.
[92] Zhong R, Ai X, Pan M, Yao Y, Cheng Z, Peng X, et al. Durability of
micro-cracked UHPC subjected to coupled freeze-thaw and
chloride salt attacks. Cem Concr Compos. 2024;148:105471.
[93] Zhong R, Zhang F. Engineering high-performance cementitious
matrices for improved projectile impact resistance with silane,
micro fibrillated cellulose and fine calcined bauxite aggregate.
Cem Concr Compos. 2023;135:104835.
[94] Zhong R, Wille K. Deterioration of residential concrete founda-
tions: The role of pyrrhotite-bearing aggregate. Cem Concr
Compos. 2018;94:53–61.
[95] García-Macías E, Castro-Triguero R, Sáez A, Ubertini F. 3D mixed
micromechanics-FEM modeling of piezoresistive carbon nano-
tube smart concrete. Comput Methods Appl Mech Eng.
2018;340:396–423.
[96] Yue Q, Wang Q, Zhou W, Rabczuk T, Zhuang X, Liu B, et al. An
efficient adaptive length scale insensitive phase-field model for
three-dimensional fracture of solids using trilinear multi-node
elements. Int J Mech Sci. 2023;253:108351.
[97] Fouaidi M, Jamal M, Zaite A, Belouaggadia N. Bending analysis of
functionally graded graphene oxide powder-reinforced compo-
site beams using a meshfree method. Aerosp Sci Technol.
2021;110:106479.
[98] Nitka M, Tejchman J. A three-dimensional meso-scale approach to
concrete fracture based on combined DEM with X-ray μCT
images. Cem Concr Res. 2018;107:11–29.
[99] Ranjbarnia M, Zaheri M, Dias D. Three-dimensional finite differ-
ence analysis of shallow sprayed concrete tunnels crossing a
reverse fault or a normal fault: A parametric study. Front Struct
Civ Eng. 2020;14:998–1011.
[100] Huang X, Kong X, Chen Z, Fang Q. Peridynamics modelling of
dynamic tensile failure in concrete. Int J Impact Eng.
2021;155:103918.
[101] Ghezelbash G, Babaelahi M, Saadatfar M. New analytical solution
and optimization of a thermocline solar energy storage using
differential quadrature method and genetic programming. J
Energy Storage. 2022;52:104806.
[102] Andreaus U, Casini P, Vestroni F. Non-linear dynamics of a cracked
cantilever beam under harmonic excitation. 2007;42:566–75.
[103] Saleh AL, Aliabadi MH. Crack growth analysis in concrete using
boundary element method. Eng Fract Mech. 1995;51:533–45.
[104] Yue Q, Wang Q, Tian W, Rabczuk T, Zhou W, Ma G, et al. A phase-
field lattice model (PFLM) for fracture problem: Theory and
application in composite materials. Compos Struct.
2023;323:117432.
[105] Zaid O, Hashmi SRZ, Aslam F, Abedin ZU, Ullah A. Experimental
study on the properties improvement of hybrid graphene oxide
fiber-reinforced composite concrete. Diam Relat Mater.
2022;124:108883.
[106] Gallyamov ER, Cuba Ramos AI, Corrado M, Rezakhani R,
Molinari JF. Multi-scale modelling of concrete structures affected
by alkali-silica reaction: Coupling the mesoscopic damage evo-
lution and the macroscopic concrete deterioration. Int J Solids
Struct. 2020;207:262–78.
[107] Anastopoulos S, Givannaki F, Papanikos P, Metaxa Z,
Alexopoulos ND. Calculation of a composite material’s modulus
of elasticity: comparison of results using fixed angles orientation
and RVE with those using random orientation tensor and multi-
step homogenization. Procedia Struct Integr. 2020;28:2132–41.
[108] Santhosi BVSRN, Ramji K, Rao NBRM, Nagaraju D, Naidu MK.
Microwave absorption analysis of graphene-based hybrid nano-
composites: experimental, numerical and component level
testing studies. Plast, Rubber Compos. 2023;52:129–44.
[109] Le J-L, Du H, Pang SD. Use of 2D graphene nanoplatelets (Gnp) in
cement composites for structural health evaluation. Compos Part
B: Eng. 2014;67:555–63.
[110] De Maio U, Fantuzzi N, Greco F, Leonetti L, Pranno A. Failure
analysis of ultra high-performance fiber-reinforced concrete
structures enhanced with nanomaterials by using a diffuse
cohesive interface approach. 2020;10:1792.
[111] Pranno A, Greco F, Leonetti L, Lonetti P, Blasi PN, De Maio U.
Cracking analysis in ultra-high-performance fiber-reinforced
concrete with embedded nanoparticles via a diffuse interface
approach. Procedia Struct Integr. 2022;39:688–99.
[112] Abdulkadir I, Mohammed BS, Liew MS, Wahab MMA. Modelling
and optimization of the impact resistance of graphene oxide
modified crumb rubber-ECC using response surface metho-
dology. IOP Conference Series: Materials Science and
Engineering. Vol. 1197; 2021. p. 012043
[113] Adamu M, Trabanpruek P, Jongvivatsakul P, Likitlersuang S,
Iwanami M. Mechanical performance and optimization of high-
volume fly ash concrete containing plastic wastes and graphene
nanoplatelets using response surface methodology. Constr Build
Mater. 2021;308:125085.
[114] Krystek M, Szojda L, Górski M. Numerical modelling of cement-
graphene composites. Proceedings of the 12th fib International
PhD Symposium in Civil Engineering; 2018. Prague, Czech
Republic.
A review on modeling of GANS reinforced concrete 17

[115] Acar V, Cakir F, Uysal H, Seydibeyoglu MO, Akbulut H,
Mosalam KM. Strengthening of concrete beams by monolayer
prepreg composites with and without graphene reinforcement.
Constr Build Mater. 2017;151:866–80.
[116] Ali Jafarian A, Reza K. Buckling analysis of embedded concrete
columns armed with carbon nanotubes. Comput Concr.
2016;17:567–78.
[117] Bacciocchi M, Tarantino AM. Modeling and numerical investiga-
tion of the viscoelastic behavior of laminated concrete beams
strengthened by CFRP strips and carbon nanotubes. Constr Build
Mater. 2020;233:117311.
[118] Chan LY, Andrawes B. Characterization of the uncertainties in the
constitutive behavior of carbon nanotube/cement composites. Sci
Technol Adv Mater. 2009;10:045007.
[119] Sasmal S, Sindu BS, Gopinath S, Iyer NR. Numerical simulation of
CNT incorporated cement. International Conference on Civil and
Construction Technology; 2012.
[120] Sindu BS, Sasmal S. Properties of carbon nanotube reinforced
cement composite synthesized using different types of surfac-
tants. Constr Build Mater. 2017;155:389–99.
[121] Ghazizadeh S, Duffour P, Skipper NT, Billing M, Bai Y. An inves-
tigation into the colloidal stability of graphene oxide nano-layers
in alite paste. Cem Concr Res. 2017;99:116–28.
[122] Zhang H, Huang YJ, Yang ZJ, Xu SL, Chen XW. A discrete-conti-
nuum coupled finite element modelling approach for fibre rein-
forced concrete. Cem Concr Res. 2018;106:130–43.
[123] Pranno A, Greco F, Leonetti L, Lonetti P, Blasi PN, De Maio U.
Cracking analysis in ultra-high-performance fiber-reinforced
concrete with embedded nanoparticles via a diffuse interface
approach. 2022;39:688–99.
[124] De Sukrit K, Mukherjee A. A numerical model for electrical
properties of self-sensing concrete with carbon fibers. J Mater Civ
Eng. 2023;35:04023311.
[125] Mortazavi B, Benzerara O, Meyer H, Bardon J, Ahzi S. Combined
molecular dynamics-finite element multiscale modeling of
thermal conduction in graphene epoxy nanocomposites. Carbon.
2013;60:356–65.
[126] Park HS, Liu WK. An introduction and tutorial on multiple-scale ana-
lysis in solids. Comput Methods Appl Mech Eng. 2004;193:1733–72.
[127] Ulz MH. Coupling the finite element method and molecular
dynamics in the framework of the heterogeneous multiscale
method for quasi-static isothermal problems. J Mech Phys Solids.
2015;74:1–18.
[128] Chandra Y, Adhikari S, Saavedra Flores EI, Figiel Ł. Advances in
finite element modelling of graphene and associated nanos-
tructures. Mater Sci Eng: R: Rep. 2020;140:100544.
[129] Wei X, Kysar JW. Experimental validation of multiscale modeling
of indentation of suspended circular graphene membranes. Int J
Solids Struct. 2012;49:3201–9.
[130] Montazeri A, Naghdabadi R. Investigation of the interphase
effects on the mechanical behavior of carbon nanotube polymer
composites by multiscale modeling. J Appl Polym Sci.
2010;117:361–7.
[131] Chandra Y, Scarpa F, Adhikari S, Zhang J, Saavedra Flores EI,
Peng H-X. Pullout strength of graphene and carbon
nanotube/epoxy composites. Compos Part B: Eng.
2016;102:1–8.
[132] Chandra Y, Saavedra Flores EI, Scarpa F, Adhikari S. Buckling of
hybrid nanocomposites with embedded graphene and carbon
nanotubes. Phys E. 2016;83:434–41.
[133] Rafiee R, Eskandariyun A. Estimating Young’s modulus of gra-
phene/polymer composites using stochastic multi-scale mod-
eling. Compos Part B: Eng. 2019;173:106842.
[134] Rafiee R, Eskandariyun A. Predicting Young’s modulus of
agglomerated graphene/polymer using multi-scale modeling.
Compos Struct. 2020;245:112324.
[135] Guo Z, Song L, Chai GB, Li Z, Li Y, Wang Z. Multiscale finite ele-
ment analyses on mechanical properties of graphene-reinforced
composites. Mech Adv Mater Struct. 2019;26:1735–42.
[136] Li C, Chou T-W. Multiscale modeling of compressive behavior of
carbon nanotube/polymer composites. Compos Sci Technol.
2006;66:2409–14.
[137] Chandra Y, Scarpa F, Chowdhury R, Adhikari S, Sienz J. Multiscale
hybrid atomistic-FE approach for the nonlinear tensile behaviour
of graphene nanocomposites. Compos Part A: Appl Sci Manuf.
2013;46:147–53.
[138] Chandra Y, Chowdhury R, Scarpa F, Adhikari S, Sienz J, Arnold C,
et al. Vibration frequency of graphene based composites: A
multiscale approach. Mater Sci Eng, B. 2012;177:303–10.
[139] Thilakarathna PSM, Kristombu Baduge KS, Mendis P, Lee H,
Chandrathilaka ERK, Vimonsatit V. Multiscale modelling frame-
work for elasticity of ultra high strength concrete using nano/
microscale characterization and finite element representative
volume element analysis. Constr Build Mater. 2022;327:126968.
[140] Papadopoulos V, Seventekidis P, Sotiropoulos G. Stochastic mul-
tiscale modeling of graphene reinforced composites. Eng Struct.
2017;145:176–89.
[141] Li C, Chou T-W. A structural mechanics approach for the analysis
of carbon nanotubes. Int J Solids Struct. 2003;40:2487–99.
[142] Li C, Chou TW. Multiscale modeling of carbon nanotube rein-
forced polymer composites. J Nanosci Nanotechnol.
2003;3:423–30.
[143] Giannopoulos GI, Kakavas PA, Anifantis NK. Evaluation of the
effective mechanical properties of single walled carbon nano-
tubes using a spring based finite element approach. Comput
Mater Sci. 2008;41:561–9.
[144] Rafiee R, Eskandariyun A. Comparative study on predicting
Young’s modulus of graphene sheets using nano-scale conti-
nuum mechanics approach. Phys E. 2017;90:42–8.
[145] Scarpa F, Adhikari S, Srikantha Phani A. Effective elastic
mechanical properties of single layer graphene sheets.
Nanotechnology. 2009;20:065709.
[146] Bakshi SR, Patel RR, Agarwal A. Thermal conductivity of carbon
nanotube reinforced aluminum composites: A multi-scale study
using object oriented finite element method. Comput Mater Sci.
2010;50:419–28.
[147] Liu JZ, Zheng Q, Jiang Q. Effect of a rippling mode on resonances
of carbon nanotubes. Phys Rev Lett. 2001;86:4843–6.
[148] Arroyo M, Belytschko T. An atomistic-based finite deformation
membrane for single layer crystalline films. J Mech Phys Solids.
2002;50:1941–77.
[149] Pantano A, Boyce MC, Parks DM. Nonlinear structural mechanics
based modeling of carbon nanotube deformation. Phys Rev Lett.
2003;91:145504.
[150] Hemmasizadeh A, Mahzoon M, Hadi E, Khandan R. A method for
developing the equivalent continuum model of a single layer
graphene sheet. Thin Solid Films. 2008;516:7636–40.
[151] Chen XL, Liu YJ. Square representative volume elements for
evaluating the effective material properties of carbon nanotube-
based composites. Comput Mater Sci. 2004;29:1–11.
18 Qiang Yue et al.

[152] Namilae S, Chandra N. Multiscale model to study the effect of
interfaces in carbon nanotube-based composites. J Eng Mater
Technol. 2005;127:222–32.
[153] Wang X, Wang XY, Xiao J. A non-linear analysis of the bending
modulus of carbon nanotubes with rippling deformations.
Compos Struct. 2005;69:315–21.
[154] Wan H, Delale F, Shen L. Effect of CNT length and CNT-matrix
interphase in carbon nanotube (CNT) reinforced composites.
Mech Res Commun. 2005;32:481–9.
[155] Liu YJ, Chen XL. Evaluations of the effective material properties of
carbon nanotube-based composites using a nanoscale repre-
sentative volume element. Mech Mater. 2003;35:69–81.
[156] Nasdala L, Ernst G. Development of a 4-node finite element for
the computation of nano-structured materials. Comput Mater Sci.
2005;33:443–58.
[157] Nasdala L, Kempe A, Rolfes R. Are finite elements appropriate for
use in molecular dynamic simulations? Compos Sci Technol.
2012;72:989–1000.
[158] Eftekhari M, Mohammadi S. Multiscale dynamic fracture behavior
of the carbon nanotube reinforced concrete under impact
loading. Int J Impact Eng. 2016;87:55–64.
[159] Rupasinghe M, Mendis P, Ngo T, Nguyen TN, SofiM. Compressive
strength prediction of nano-silica incorporated cement systems
based on a multiscale approach. Mater Des. 2017;115:379–92.
[160] Eftekhari M, Mohammadi S, Khanmohammadi M. A hierarchical
nano to macro multiscale analysis of monotonic behavior of
concrete columns made of CNT-reinforced cement composite.
Constr Build Mater. 2018;175:134–43.
[161] Eftekhari M, Karrech A, Elchalakani M, Basarir H. Multi-scale
modeling approach to predict the nonlinear behavior of CNT-
reinforced concrete columns subjected to service loading.
Structures. 2018;14:301–12.
[162] Negi A, Bhardwaj G, Saini JS, Khanna K, Godara RK. Analysis of CNT
reinforced polymer nanocomposite plate in the presence of dis-
continuities using XFEM. Theor Appl Fract Mech. 2019;103:102292.
[163] Eftekhari M, Karrech A, Elchalakani M. Investigation into the
nonlinear time-history analysis of CNT-reinforced concrete
column by a multiscale approach. Int J Civ Eng. 2020;18:49–64.
[164] Liew KM, Pan Z, Zhang L-W. The recent progress of functionally
graded CNT reinforced composites and structures. Sci China:
Phys, Mech Astron. 2019;63:234601.
[165] Ahmadi M, Ansari R, Rouhi S. Response of graphene reinforced
concrete to the external compressive load: A multiscale approach.
Struct Concr. 2018;19:1702–12.
[166] Papadopoulos V, Impraimakis M. Multiscale modeling of
carbon nanotube reinforced concrete. Compos Struct.
2017;182:251–60.
[167] Wang JF, Zhang LW, Liew KM. Multiscale simulation of
mechanical properties and microstructure of CNT-reinforced
cement-based composites. Comput Methods Appl Mech Eng.
2017;319:393–413.
[168] Montinaro N, Pantano A. Parameters influencing the stiffness of
composites reinforced by carbon nanotubes –A numerical–ana-
lytical approach. Compos Struct. 2014;109:246–52.
[169] Bagherzadeh F, Shafighfard T. Ensemble machine learning
approach for evaluating the material characterization of carbon
nanotube-reinforced cementitious composites. Case Stud Constr
Mater. 2022;17:e01537.
[170] Bishara D, Xie Y, Liu WK, Li S. A state-of-the-art review on machine
learning-based multiscale modeling, simulation, homogenization
and design of materials. Arch Computational Methods Eng.
2023;30:191–222.
[171] Unger JF, Könke C. Neural networks as material models within a
multiscale approach. Comput Struct. 2009;87:1177–86.
[172] Rao C, Liu Y. Three-dimensional convolutional neural network
(3D-CNN) for heterogeneous material homogenization. Comput
Mater Sci. 2020;184:109850.
[173] Lyngdoh GA, Das S. Integrating multiscale numerical simulations
with machine learning to predict the strain sensing efficiency of
nano-engineered smart cementitious composites. Mater Des.
2021;209:109995.
[174] Lu X, Giovanis DG, Yvonnet J, Papadopoulos V, Detrez F, Bai J. A
data-driven computational homogenization method based on
neural networks for the nonlinear anisotropic electrical response
of graphene/polymer nanocomposites. Comput Mech.
2019;64:307–21.
[175] Wang W, Chen SJ, Duan W, Sagoe-Crentsil K, Pathirage CSN, Li L,
et al. Revealing microstructural modifications of graphene oxide-
modified cement via deep learning and nanoporosity mapping:
implications for structural materials’performance. ACS Appl
Nano Mater. 2022;5:7092–102.
[176] Tong Z, Guo H, Gao J, Wang Z. A novel method for multi-scale
carbon fiber distribution characterization in cement-based com-
posites. Constr Build Mater. 2019;218:40–52.
[177] Huang JS, Liew JX, Liew KM. Data-driven machine learning
approach for exploring and assessing mechanical properties of
carbon nanotube-reinforced cement composites. Compos Struct.
2021;267:113917.
A review on modeling of GANS reinforced concrete 19