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Progress in FEM modeling on mechanical and electromechanical properties of carbon nanotube cement-based composites

  • Tao Xuejun , Luo Jianlin EMAIL logo , Zhang Jigang , Zhu Min , Zhang Liqing and Gao Yibo
Published/Copyright: April 26, 2023
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Nanotechnology Reviews
From the journal Nanotechnology Reviews Volume 12 Issue 1

Abstract

Carbon nanotubes (CNTs) reinforced cementitious composite (CNRC) with excellent electrical and self-sensing properties, which enables it to serve as an intrinsic sensor for structural health monitoring (SHM). However, the requirements of modern industry for accurate calculation and performance design of engineering materials are not met by traditional experimental studies alone. The finite element method (FEM) has the advantages of simplicity of operation, accuracy, and cost-effectiveness, and it has been widely used in the property verification and prediction of various composite materials. In this article, the constitutive model, FEM modeling method, and simulation process of CNRC along with existing model types, innate relations, and model parameters are reviewed, and the corresponding mechanical, electrical, and electromechanical coupling properties of CNRC under different parameters are systematically analyzed by FEM method. By combining different uncertainty parameters and model types, the advantages and disadvantages of FEM for mechanical, electromechanical coupling, and SHM applications of CNRC modeling are explored. The results are in good agreement with those in the existing CNRC experiment, which effectively proves the reliability of the FEM method in CNRC research. This work is important to develop a sound theoretical model verification and performance prediction for early applications in SHM of CNRC.

Keywords: FEM modeling; CNT cement-based composite; performance simulation; SHM

1 Introduction

Modern infrastructure requires cement-based materials (CM) to be more mechanically tough and durable. Improvements in the performance of brittle CM are often achieved through the incorporation of ductile fibers, admixtures, or functional components [1]. However, the effect of micro-scale fibers on CM nanoscale defects is restricted, and at the same time, nanomaterials have many excellent properties that differ from those of conventional materials [2]. In recent years, nanomaterials have been used to improve some of the mechanical limitations of CM [3], including hardness, mechanical toughness, and durability, which have even been used to develop functional properties, such as electrical conductivity [4], thermal conductivity [5], electromagnetic wave absorption [6], and damping properties [7], which are used for specific applications. Commonly used nanomaterial includes cellulose [8], graphene [9], nanosilica [10], titanium dioxide [11], and carbon nanotubes (CNT) [12]. Among them, CNTs are favored by oversea scholars for their superior mechanical toughness [13], electrical [14], and thermal conductivity [15], as well as for their significant enhancements of durability to CM [16].

It is low cost-effective to incorporate CNTs into a large-quantity concrete structure to improve the overall performance of concrete due to the high price of CNTs. Allowing for the natural compatibility and durability of CNTs reinforced cementitious composite (CNRC) with concrete, self-sensing CNRCs can well be intrinsic sensors integrated with concrete elements applied in structure health monitoring (SHM) [17]. However, the nature of the variation in the mechanical and electrical signals of the sensors for the complicate structure as a whole is complex [18]. It is inefficient to test the performances of the sensors in the concrete by experimental methods alone, which is also a tremendous consumption of materials. In addition, the mechanical and self-sensing electrical performances of CNRC sensors measured with experimental methods are insufficient to enable the establishment of a complete theoretical system for CNRC sensors in SHM.

Computer simulations and modeling of material with appropriate experiment validation can provide access to a range of information that is difficult to obtain in traditional experiments, which saves significant costs and shortens research time [19]. Actually, within the engineering field, the finite element method (FEM) combines empirical formulas with a high degree of overlap with engineering design with a variety of special tools that are widely simulated in load-bearing and damage processes in materials to solve practical engineering problems [20]. Therefore, there are significant prospects for using FEM software to implement outline optimization design and coupling performance analysis of CNRC sensor materials, which provides effective material model analysis, parameters correction, and performance optimization [21].

Scholars from various countries have used FEM for the self-sensing property prediction of composite materials for SHM. Sivasuriyan et al. [22] argued that establishing a numerical model of SHM can be helpful in determining the structural response through various algorithms, to affirm the usefulness of FEM for SHM. Ghadhban et al. [23] proposed to use FEM to evaluate the change in resistance of a smart CM in detecting weight in perceived motion and apply it to traffic detection. Chalioris et al. [24] describe the utilization and validity of a customized portable low-cost SHM system that has been implemented as a PZT-based electromechanical conductivity (EMA) method for the detection and assessment of damage in bent reinforced concrete (RC) beams. Zacchei et al. [25] collected several data through SHM as well as the building information model of the real bridge and calibrated the bridge model by FEM. Based on that condition, monitoring techniques can be used for various industrial applications, especially for structural fault detection, El-Kafrawy [26] proposed a technique actually representing a non-destructive procedure with an immense benefit for SHM.

In recent years, the research studies on the use of FEM software to study CNRC have been increasing [27], but it is still necessary to fill this gap and to adequately understand the process of FEM modeling and performance analysis of CNRC. This article reviews model parameters, model types, and intrinsic constitutive relationships of CNRC from domestic to overseas, discusses the mechanical modeling methods, and analyzes their advantages and disadvantages in combination with uncertainty parameters. The testing methods and the degree of fit of the CNRC electromechanical coupling model to the existing conductivity theory are discussed to further verify the validity of the electromechanical coupling performance of CNRC in order to consider the feasibility and application of FEM in SHM. The limitations of FEM in modeling and directions for further research in the future are discussed with respect to the existing advances in CNRC models, which is important for establishing a reasonable theoretical constitutive validation and performance prediction for the early applications of CNRC.

2 FEM modeling of the CNRC

Based on the representation of the CNRC microstructure, the FEM is used to analyze the quantitative relationship between material properties and uncertain parameters by creating representative volume elements (RVE) to simulate the mechanical or electrical behavior of the cell under certain mechanical loads and boundary conditions [28]. This section introduces the establishment of RVE to explore the direction of the study of CNRC by models of different scales and also provides the selection of various literature for CNRC unit types and model parameters (as shown in Tables 1 and 2), considering the effects of different intrinsic structure relationships on the model, which provides a reference for the subsequent FEM study of CNRC.

Table 1

The simulation unit types of CNT and cement matrix selected for CNRC in varied literatures

Ref. Unit type
CNT Cement matrix
[35] SOLID65 SOLID45
[45] SOLID65
[46] SOLID65
[43] PLANE82 LINK1
[44] PLANE42
[47,48] SOLID232
Table 2

The simulation model parameters selected for CNRC in varied literatures

Ref. Young’s modulus (MPa) Wall thickness of CNT (nm) Poisson’s ratio
CNT Cement matrix CNT Cement matrix
[35] 1 × 106 3.1 × 104 0.34 None None
[45] 5.234 × 105 3.773 × 104 0.1 0.165 0.22
[46] 1.026 × 106 3 × 104 0.34 0.165 0.2
[43] 5.5 × 106 2.89 × 104 0.066 0.19 0.2
[36] 1 × 106 3 × 104 None 0.35 0.2

2.1 RVE

In order to accurately characterize the behavior of a bulk object, it is desirable that the microscale properties of the object also be considered in the modeling. A representative volume element (RVE) is generally used to model the structure and properties at the microscale [29,30]. The Mori–Tanaka theory proposes that the average stress in a composite matrix is uniformly distributed throughout the material [31], which provides a theoretical basis for the use of RVE in numerical simulations [32]. Suitable size for RVE can significantly improve the accuracy of FEM calculations. RVE is selected in the composite material, which cannot be too small; it needs to cover the complete physical properties of the composite material; RVE cannot be too large, and the size should be smaller than the one of the reinforcing phases so that the reinforcing phase should contain enough micro-elements and the stress and strain of the micro-elements can be advantageously equivalent to those of the reinforcing phase.

2.2 Model categories

At present, the establishment of the CNRC model can be roughly divided into the following three models according to the division of research scale: (1) CNT model based on nanoscale; (2) based on the micro-scale CNT and cement matrix interface bonding model; (3) overall CNRC model based on macro-scale.

The nano-scale model uses FEM to study the relevant characteristics of CNT (such as Young’s modulus, tensile strength) at the nanoscale [33], and then, the simulation results are substituted into the CNRC model (Figure 1(a)). Due to the difference in order of magnitude between CNT and cement-based RVE model, the CNRC model is established by using a multi-scale analysis strategy, which can transmit information at different scales and avoid the influence of errors caused by model grid and material-related parameters on experimental results when using experimental data or other manuscript data. Eftekhari et al. [34] used a multi-scale method to study the fracture properties of CNRC. First, the influence of CNT chirality on the fracture properties of CNT was discussed, and the calculated CNT fracture parameters were reflected in the CNRC model.

Figure 1 Typical multi-scale model of CNRC: (a) nanoscale model of the CNT [33]; (b) microscale XFEM model of CNRC [33]; (c) microscale model of fiber pulling-out from CNRC [35]; (d) macroscale mechanical model of CNRC [36]; and (e) macroscale electrical field model of CNRC [37].
Figure 1

Typical multi-scale model of CNRC: (a) nanoscale model of the CNT [33]; (b) microscale XFEM model of CNRC [33]; (c) microscale model of fiber pulling-out from CNRC [35]; (d) macroscale mechanical model of CNRC [36]; and (e) macroscale electrical field model of CNRC [37].

The microscopic model is mainly used to study the interface problem between fiber and matrix at the microscopic scale. Two common methods are the XFEM model (Figure 1(b)) and the fiber pull-out model (Figure 1(c)). The XFEM model is a fiber–matrix interface connection model based on the horizontal enrichment function, which is generally used to describe the interfacial fracture properties of composite materials [38]. Eftekhari et al. [34] used the XFEM method to simulate the fracture behavior of CNRC with steel bars at the mesoscopic scale. The results confirmed that the XFEM method has an excellent contribution to the study of CNRC fracture performance. Another fiber drawing model is mainly used to study the bond–slip relationship between fiber and matrix. For example, Chan and Andrawes [39] established a CNRC mechanical RVE drawing model to study the effects of different mechanical parameters and interface parameters on the structural properties of the material.

The macroscale model is based on the continuous medium mechanics theory to study the influence of constituent materials through the average properties of composite materials [40], which not only provides a better simulation of the consistency and homogeneity of CNRC but also saves a lot of simulation time (Figure 1(d) and (e)). Unfortunately, the macroscopic model is unable to reflect the inhomogeneity and complexity of CNRC in real situations and the effects of local damage [41]. Attempts are being made to compensate for this shortcoming through multi-scale modeling or further optimization of macroscopic models.

2.3 Model parameters and types

2.3.1 Unit types

In FEM analysis, the choice of cell type directly determines the efficiency of the analysis and the accuracy of the results. The unit types are divided into point units: MASS, line units: LINK, BEAM, COMBIN, and surface units: PLANE, SHELL [42]. The units are divided into point units: MASS, line units: LINK, BEAM, COMBIN and surface units: PLANE, SHELL. When modeling CNRC, the CNRC model is divided into a plane model and a 3D model.

In the plane model, the CNT is simulated by the rod, and the unit type used is LINK1 [43] or BEAM4 [44]. LINK1 is a uniaxial compression unit, but it cannot withstand the bending moment. The CNT not only bears the tension and compression but also can withstand bending and torsion. Therefore, the BEAM4 unit can better simulate the C–C chemical bond in the CNT. To simulate the cement matrix by line, a four-node unit, PLANE42 [44] (which has creep, large deformation, plasticity and large strain capabilities and is generally used to study planar problems), or for higher accuracy, a more nodal unit such as the eight-node unit PLANE82 [43].

In the 3D model, the SOLID65 3D eight-node unit is chosen to simulate the cement matrix, which is not only able to better predict the cracks and fragmentation in the cement matrix [35] It is also more consistent with the fact that the compressive properties of the cement matrix are much greater than the tensile properties [45,46]; SOLID232 is a ten-node tetrahedral conduction cell with voltage freedom of 1 at each node and is commonly used to study the variation of conductivity of CNRC [47,48].

2.3.2 Parameter selection

FEM is based on two basic assumptions when analyzing materials: the small deformation assumption and the linear elasticity assumption. For the setting up of materials for CNRC linear elastic analysis, attention needs to be paid to the uniformity of the unit system of materials and the handling of parameters. The linear elastic analysis contains Young’s modulus, Poisson’s ratio, shear modulus, and bulk modulus, and only two of these parameters need to be determined in order to determine the other two. Here, in addition to the elastic modulus and Poisson’s ratio of CNT, the research on the wall thickness of CNT is also added because the wall thickness of CNT must be considered when modeling, and the relevant CNRC parameters selected in the literature are shown in Table 2. The wall thicknesses chosen for CNT modeling are mainly 0.066 nm [49] and 0.34 nm [50].

The choice of Young’s modulus and Poisson’s ratio for CNT is more varied, although care should be taken to take appropriate values that do not exceed the applicable range of the FEM; otherwise, the experimental results will be biased too much. Although the Young’s modulus of CNT was calculated to be 523.4 GPa and the Poisson’s ratio to be 0.65 by establishing a CNT equivalent continuum model simulation, the Poisson’s ratio obtained in this experiment was too high (greater than 0.5), resulting in an error in the calculation [44]. Tang [43] chose CNT with an elastic modulus of 5.5 TPa and a Poisson’s ratio of 0.17 as the reinforcing phase for the study of CNRC; however, the elastic modulus of CNT obtained in the laboratory currently ranges from 0.92 to 1.05 TPa [51]; the CNT selected for this study does not fit the actual situation. In order to better fit the existing CNT research results, a CNT with a wall thickness of 0.34 nm, an elastic modulus of 1 TPa [42,52], and a Poisson’s ratio of 0.165 [46] would be preferable. The selection of cement matrix parameters is similar to existing studies [47,53]; Wang et al. [52] modeled a cement matrix with Young’s modulus of 30 GPa and Poisson’s ratio of 0.2, which is more appropriate.

2.3.3 Constitutive relationships

2.3.3.1 Stress–strain constitutive relationships

CNRCs are mostly under complex stresses. In order to accurately describe the damage characteristics and mechanical behavior of CNRCs under complex loading, it is essential to select the appropriate constitutive relation of CNRC material for research and design [54]. The commonly used constitutive relationships of CNRC and their expressions are as follows.

1) Chan et al. [35,39] used the finite element program ANSYS for numerical simulation and modeling, to investigate the interfacial bond strength between CNT and CM using the RVE pull-out model and the extent of residual stresses on CM. The results demonstrate that the fiber pull-out model is more realistic for the study of the interfacial strength of the fiber and matrix. Typical constitutive relationships for the RVE pull-out model are shown below (Figure 2):

Figure 2 Typical constitutive relation of RVE pull-out model of CNRC [35].
Figure 2

Typical constitutive relation of RVE pull-out model of CNRC [35].

Before cracking:

(1) σ c = ( E m V m + α E f V f ) ε c = E c ε c ,

After cracking:

(2) σ B ( δ ) = V f ∫ 0 π 2 ∫ 0 ( L f / 2 ) cos θ σ b ( δ ¯ , θ ) f ( z ) f ( θ ) d z d θ ,

where σ c is the stress in the composite; E m and E f are the moduli of elasticity of plain concrete and fibers, respectively; ε c is the strain in the composite; V f is the volume fraction of the fibers; L f is the length of the fibers; θ is the angle of embedding of the fibers; z is the depth of embedding of the fibers. σ b ( δ ̅ , θ ) is the load at fiber pull-out displacement function.

2) Song [45] used the Hongnestand model to analyze the constitutive relationship between CNRC interface strength and crack propagation, and found that crack propagation was more obvious at the interface between fiber and CM. The Hongnestand constitutive relation is shown below:

Ascent stage:

(3) σ c = 2 ε c ε 0 − ε c ε 0 2 σ 0 , ε c < ε 0 ,

Descent stage:

(4) σ c = 1 − 0.15 ε c − ε 0 ε cu − ε 0 σ 0 , ε 0 < ε c < ε cu ,

where σ 0 and ε 0 are the initial stress and strain of the composite, respectively; ε cu is the peak strain of the rising section.

3) Tang [43] used Matlab software to input the compressive stress–strain constitutive relation of concrete found by Guo [55] into the finite software to investigate the effect of CNT dosing and aspect ratio on the strength of CM. The compressive stress–strain intrinsic structure relationship of Guo concrete is shown as follows [56,57]:

Ascent stage:

(5) y = 1.2 x − 0.2 x 6 , x ≤ 1.0

Descent stage:

(6) y = x α ( x − 1 ) 1.7 + x , x ≥ 1.0 ,

where x = ε c / ε , p y = σ c / f t ; α is the parameter of the stress–strain curve in the descending section when uniaxial compressed; f t is the representative value of the uniaxial compressive strength of the concrete; ε p is the uniaxial compressive strength.

4) Wang [44] studied the interface separation between CNT and CM and the fracture of CNT in CM using finite element simulation software based on Wang Z M’s theory of composite mechanics. The tensile stress–strain constitutive relationship of concrete deduced by Wang Z M is as follows [58,59]:

(7) σ c = 1 V ε c ∑ k = 1 n σ x k ε x k V k ,

where σ x k , ε x k , and V k represent the axial stress, strain, and volume of element k, respectively.

5) Wang et al. [52] modeled the variation patterns of clinker phase volume fraction and various hydration products with the degree of hydration. Based on the microstructural evolution of the cement hydration process, the mechanical properties of the cement paste were estimated using both autonomous and Mori–Tanaka34 methods, and the macroscopic mechanical properties of CNRC were predicted using a meshless approach based on a moving least squares approximation. The Mori–Tanake principal constructive relationship is shown below:

(8) σ c ( x ) = L s : ε c ( x ),

where L s is the overall stiffness coefficient tensor of the material.

2.3.3.2 Electrical and electromechanical relationships

Dong et al. [47] effectively combined the GEM equation with the volume equation, from which the constructive relationship between CNT doping and resistivity of CNRC was derived to study the conductivity mechanism of CNCR and analyze its electromechanical coupling properties [48].

First, the constitutive relationship between ρ eff and CNT content χ is determined by the GEM finite calculation equation of resistivity ρ eff. The equation is as follows:

(9) χ 1 ρ 1 − 1 t − ρ eff − 1 t ρ 1 − 1 t + A ρ eff − 1 t + ( 1 − χ 1 ) ρ 2 − 1 t − ρ eff − 1 t ρ 2 − 1 t + A ρ eff − 1 t ,

(10) A = 1 − χ c χ c ,

where A and t are equation parameters, related to the size of the CNT and its spatial distribution in the CM; ρ 1 is the CNT resistivity, and ρ 2 is the CM resistivity; χ c is the percolation threshold of the composite.

The relationship between the stress σ to which the CNRC is subjected and the CNT doping χ is derived from the volume equation (11)

(11) σ c = E 1 − 2 ν 1 − χ 0 χ 1 ,

where ν is the Poisson’s ratio; χ 0 is the volume content (%) of the CNT when initially added to the CM and χ 1 is the volume content (%) of the CNT in the CM after deformation in the same region of the CNRC.

Combining equation (9) with equation (11), the final electromechanical relationship between CNRC stress and effective resistivity can be obtained.

3 Influence of uncertain parameters on CNRC mechanical model

The optimization of the CNRC model is to make it more realistic and feasible. With this purpose, it is crucial to explore the sensitivity analysis of different models for uncertainty parameters [60]. According to the current status of research on CNRC at home and abroad, the content elastic modulus of CNT, the aspect ratio, the arrangement in the matrix, and the interface treatment with the matrix are chosen as uncertainty parameters in this section. The sensitivity of different CNRC mechanical models to uncertain parameters and the accuracy analysis of the FEM method for CNRC are mainly studied.

3.1 CNT dosage

The results of the current experimental study have proved that the effect of CNT content on CM is divided into three stages. First of all, when the content is excessively inexpensive, the mechanical strengthening effect of CNT on the substrate is almost ineffective [61]. Furthermore, with the increase of CNT content, the strength of CNRC also rises, and when the content reaches a certain value, the enhancement effect of CM reaches the maximum, which we call the CNT content at this time the optimal content. At the moment, the optimal results of FEM are between 0.4 and 0.6% [36,44,58,62] (the relationship between volume content of CNT and Young’s modulus of CNRCis shown in Figure 3), which deviates slightly from the laboratory results of recent years and their own experimental results, but the margin of error is acceptable. Eventually, as the content continues to increase, the CNT will have a weakening effect on CM enhancement due to agglomeration caused by excessive van der Waals forces. However, the limitation of FEM in reflecting the effect of content on CM has led to the inability to simulate the real agglomeration of CNT in the cement base, which is one of the main reasons for the error between the current FEM results of optimal CNT content and the real experimental results [63]. In addition to improving the CM intrinsic properties, CNT incorporation can also enhance the seismic performance of the structure. Li and Sun [64] developed a FEM model of CNRC piers with 0.3% optimum content and investigated the seismic performance of CNRC piers under low circumferential repeated loads. It was shown that the load-carrying capacity and average stiffness of carbon nanotube concrete bridge piers were higher than those of ordinary concrete piers within the same cyclic load, while the ultimate load-carrying capacity was increased by 7.3% and the plastic deformation produced was smaller.

Figure 3 Relationship between volume content of aligned or random-distributed CNT and Young’s modulus of CNRC [36].
Figure 3

Relationship between volume content of aligned or random-distributed CNT and Young’s modulus of CNRC [36].

3.2 Young’s modulus of CNT

For the study of the relationship between Young’s modulus of CNT and CM strength, those two different approaches are proposed. Wang [36] adopted a multiscale approach to first establish a continuum equivalent model of CNT based on the molecular structure mechanics approach to predict the longitudinal and transverse elastic modulus constants of CNT and then established a fine-scale cellular model of CNRC planar stress with the influence of interfacial longitudinal and shear stresses based on the CNT simulation results; the proposed results proved that high modulus CNT is more effective for the strength enhancement of CM. Yet a large stiffness was chosen in the definition of the contact during modeling to prevent the matrix and fibers from penetrating each other, with the result that the final strength obtained differs too much from the existing results, which can be corrected by the reader by correcting the contact coefficient. Using a fiber pullout model to investigate the effect of CNT Young’s modulus enhancement on the matrix, Chan [39] discovered that the strength of CNRC with an elastic modulus of 1.5, 1, and 2 TPa increased by 40, 75, and 100%, respectively, compared to a CNT Young’s modulus of 500 GPa, while the toughness was substantially weakened. This is probably related to the fact that as Young’s modulus of CNT increases, the cement matrix needs to provide a larger and more interfacial area to maintain the needle tip displacement of CNT, and then, the strength of CNRC increases with the fast pull-out velocity effect, for which the stress in the CNRC material decreases and the composite becomes brittle [65].

3.3 Aspect ratio of CNT

The effect pattern of CNT aspect ratio on CM is the same as that of content. In the range of minor strains, the strength of CNRC materials increases with increasing CNT aspect ratio [43] (the strength relationship between CNT length and the strength of CNRC is shown in Figure 4). Tang [46] compared the effect of CNT aspect ratio of 1, 2 and 3 on the CM, and it was in the maximum strength of 31.37 GPa for CNRC at aspect ratio of 3. The result that the aspect ratio has a positive effect on the enhancement effect of CM is unanimously accepted, but there are conflicting opinions on its influence agent. Chan and Andrawes [39] attribute the least effect of CNT aspect ratio on CM compared to other factors (e.g. content, Young’s modulus, and interfacial bonding), whereas Al-Maharma et al. [66] commented that the length of CNT is the most critical factor affecting the fracture properties of CNRC. The reason for this disagreement may be that the XFEM model has a more prominent representation of the CNT length compared to the fiber pull-out model.

Figure 4 Strength–strain relationship of CNRC with varied CNT length [43].
Figure 4

Strength–strain relationship of CNRC with varied CNT length [43].

3.4 Arrangement of CNT

When dealing with the model, the arrangement and distribution of CNT in the matrix are the keys to modeling. First, CNT at different angles has an important effect on the model regarding the arrangement and distribution of fibers, as confirmed by the results of Chwał and Muc [67]. Therefore, consideration of fiber alignment is necessary for the modeling process of CNRC. Wang et al. [52] considered the effects of fiber orientation and random distribution in their study of CNRC (Figure 3); Chwał and Muc [67] also analyzed the effects of carbon nanotube alignment on the elastic properties of composites. In the treatment of fiber placement in the matrix, the use of the Monte Carlo method to generate fibers with random positions is unanimously considered to be the most effective treatment.

3.5 Interface bonding between CNT and CM

Interfacial peeling is an important cause of composite damage. The effective prediction of the nonlinear behavior between CNT and CM interfaces (including the nonlinear motion between interfaces and debonding behavior) with the help of FEM simulation method is the main means to quantify the mechanical properties of interfaces.

3.5.1 Interface theory model

For the study of the interfacial behavior between fibers and matrix, shear-lag and cohesion models are considered to be the two most effective methods used to characterize the stress transfer and damage evolution processes between materials.

The shear hysteresis model was first proposed for application in fiber composites in 1952 [68]. The model treats the interface between the fiber and the matrix as a perfect connection and assumes that the fiber receives only axial action, the matrix receives only shear action, and the elastic modulus of the fiber and the matrix does not change, at which time the relationship between the fiber axial stress and the interface shear stress satisfies the following equation.

(12) σ f z ( z ) = σ 0 α 1 − cosh ( β z ) cosh ( β L ) ,

(13) τ i ( a , z ) = σ 0 a β 2 α sinh ( β z ) cosh ( β L ) ,

where α and β satisfy the following equation:

(14) α = E m E f ,

(15) β = α a 2 ( 1 + ν m ) In ( b / α ) 1 / 2 ,

where E m, E f are the elastic modulus of the matrix and fiber; ν m is the matrix Poisson’s ratio; a, b are the equivalent radii of the fiber and matrix in the monofilament system; σ 0 is the applied load.

The theory has a certain universality for composite materials, but the assumptions on materials and interfaces are too idealized, which is far from the actual conditions of composite materials. The accuracy of the model has been increased by modifying the shear-lag theory, such as Wang et al. [69], who first obtained the shear stress distribution between the fibers and the interface using the shear-lag theory and, on this basis, studied the relationship between the load and the fracture number of the material under non-uniform strength distribution using the Monte Carlo method; Zhang and Xu [70] found, based on the non-linear elastic properties of concrete, the stresses at the fiber ends and the temperature due to temperature changes on the shear stresses and the positive fiber stresses. The shear hysteresis theory of stress transfer in short fiber-reinforced concrete was improved based on the effects of non-linear elastic properties of concrete, the stresses at the fiber ends, and the temperature due to temperature changes on shear stresses and positive fiber stresses.

The fracture mechanics-based cohesion model takes into account the elastic–plastic behavior of the matrix and is widely used to calculate the interfacial damage and fracture processes of materials. Hillerborg [71] first applied the cohesion model to finite element calculations and proposed a virtual cracking model for concrete. The cohesion model can better simulate the crack extension behavior and the interfacial mechanical behavior of composite materials because it introduces the cohesive region and cohesive force, thus avoiding the problem of stress singularity at the crack tip as in the linear elastic fracture mechanics. Since the calculation process is more complicated, it is not introduced too much in this article.

3.5.2 Interface multiscale model

CNRC interface simulation can be divided into nanoscopic, microscopic, and macroscopic in terms of scale. Macroscopic interface model is a numerical analysis method that divides the solution domain into a grid and uses a weighted residual method in the form of equivalent integrals or a variation method for solving generalized stationary values to establish approximate differential equations to predict structural performance based on the assumption of approximate functions in the partition [72]. This model is computationally efficient but does not reflect local damage. Microscopic and nanoscopic interface models are based on the atomic or molecular level to locally study the microscopic or nanoscopic structure of the interface and the interactions between them, and then calculate the properties of the interface, and the main methods are molecular dynamics methods and Monte Carlo methods. This model can reflect the local damage process of the material, but it is difficult to simulate the boundary conditions of the material. In addition, there is a lack of theoretical basis for the intrinsic parameters of the macroscopic model. Therefore, the top-down multiscale approach of predicting parameters from microscopic or nanoscopic models for the interfacial properties of the model and then bringing the predicted parameters into the macroscopic model is widely used in interfacial studies [73,74]. The representation of interfacial strength is mainly divided into two categories. One is bond strength, and the literature studies [46] and [45] first used molecular dynamics methods at the nanoscopic scale to study CNT bonding to CM. The other category is bond slip, where Chan [35] used the fiber-pulling model to find out the bond–slip relationship between CNT and CM at the microscopic scale and carried the calculated intrinsic structure related to the macroscopic model of CNRC (Figure 5). In fact, although the bond strength model has a simpler calculation process, its essence is to give an ultimate peel-bearing capacity to the composite material, which cannot explain the process of interface peeling. On the contrary, the bond–slip model can reflect the intrinsic relationship of debonding between composites in more detail. Therefore, the bond–slip model has more theoretical significance for the study of interfacial strength.

Figure 5 Constitutive relationship of RVE pull-out model of CNRC under varied shear strength [35].
Figure 5

Constitutive relationship of RVE pull-out model of CNRC under varied shear strength [35].

4 FEM Analysis of electrical properties and electromechanical coupling properties of CNRC

A conventional cement-based material is almost insulating, which makes it difficult to attempt their direct use for structural failure and damage monitoring. In recent years, conductive carbon nanotubes have been used to modify the electrical conductivity and electromechanical sensing properties of CNRC oversea [75]. This has resulted in the evolution of intrinsic electromechanical sensors with higher sensitivity and superior performance for SHM applications. By summarizing the current status of FEM research on the electrical and electromechanical coupling properties of CNRC, the section analyzes the advantages and disadvantages of FEM for analyzing the electrical and electromechanical properties of CNRC, which aims to optimize the parameters and performance of the electromechanical coupling properties of CNRC models to help the SHM applications of CNRC.

4.1 Electromechanical coupling performance

The key to putting CNRC into realistic application in SHM is to be able to make an accurate prediction of its electromechanical coupling performance. The main means is to deduce the relationship between mechanical stress or strain and the overall resistivity of CNRC through theory, verify it using experimental or modeling methods, find the percolation threshold of CNRC, further analyze its sensing mechanism in depth, and realize the prediction of CNRC sensing performance. In fact, the FEM method can only select the specified CNT doping amount for the corresponding calculation, which is not sufficient to obtain the percolation threshold of CNRC and the corresponding electromechanical coupling relationship. Therefore, we need to choose a suitable resistivity theory model to fit the numerical results of the FEM method to get the resistivity calculation equation of CNRC. At present, the commonly used conductivity theories mainly include percolation theory, effective medium theory, and tunneling effect theory [76].

Dong et al. [47] and Niu et al. [48] modeled CNRC using Monte Carlo methods and explored the fit of the model to the GEM equation and Simmons tunneling equation and found that the best fit to the GEM equation was achieved when the CNT doping was 1.5%, while the Simmons tunneling equation was satisfied for all CNT doping between 0.31 and 1.33%. Both studies confirm that the FEM method is feasible for the study of the electromechanical coupling performance of CNRC, but the accuracy of the model is not high. On the one hand, the authors only consider the relationship between compressive stress and resistivity, but the actual stress state is much more than that; on the other hand, the model does not take into account the tunneling effect of the conducting material, which is also related to the performance limitation of ANSYS software for electric field calculation.

In contrast, the hybrid fine-scale mechanics and FEM approach for CNRC proposed by Garcia-Macias et al. [37] not only considers the contribution of electron hopping and conductive networks to the conductivity of CNRC (Figure 6), but also enables the analysis of resistivity changes in arbitrary strain states. The results show that the longitudinal and transverse piezoresistive coefficients of CNRC have some similarities, and the CNRC sensor can be approximately modeled as a volumetric strain sensor with a single piezoresistive coefficient. Embedding the simplified simulations into concrete structural members to explore the practical applications of the sensors could be a future research direction.

Figure 6 (a) Nanoscale RVE outline of straight CNT; (b) microscale the contribution of electron transition; (c) macroscale conductive network mechanism to the overall conductivity of CNTRC [37].
Figure 6

(a) Nanoscale RVE outline of straight CNT; (b) microscale the contribution of electron transition; (c) macroscale conductive network mechanism to the overall conductivity of CNTRC [37].

The aforementioned literature only considered the influence of the intrinsic properties or content of CNT on the electromechanical properties of CNRC; in fact, the porosity of CM itself also greatly affects the formation of conductive pathways in CNRC. Xiao [77] and Wang et al. [78] established a three-dimensional random field model of CNRC based on Mori–Tanake and tunneling effect theory, increased the effect of pore water ions on CNRC resistivity with the change of pore connectivity under strain, proposed a prediction model of piezoresistive effect, and compared it with experimental results (Figure 7). The results show that the connectivity of the CNRC conductive network is found to be better with the increase of CNT doping, but after reaching the percolation threshold, the conductivity of the material decreases due to the ionic effect on the piezoresistance effect becomes smaller.

Figure 7 Numerical simulation and experimental results comparison between piezoresistive behaviors of CNRC [78].
Figure 7

Numerical simulation and experimental results comparison between piezoresistive behaviors of CNRC [78].

The FEM model for the electromechanical properties of CNRC needs to be improved gradually. First, the existing literature simplifies the CNT as a cylinder, and thus, the CNT doping in the model is larger compared to the real case (CNT should be a hollow tubular structure [79]), resulting in a lower percolation threshold. Second, only uniform distribution is still considered for the CNT distribution, resulting in slightly larger overall resistivity results for the CNRC than the experimentally obtained resistivity results. Finally, the dynamic simulation of the conductive network inside the CNRC can be further realized, which is important for the analysis and prediction of the microstructure of the conductive network [80].

4.2 SHM applications

The fundamental purpose of studying the electromechanical coupling performance of CNRC is to enable its application in SHM. The principle is to add CNRC into concrete structures by coating or embedding, etc., and obtain the stress and strain inside the concrete through electrical signals to obtain the internal damage state of the structure. Some scholars have tried to simulate the stress state and strain compatibility of CNRC sensors embedded in concrete structures through FEM, such as Cui et al. [81]. The optimally designed CNRC sensors were embedded in concrete for health monitoring and their stress state was investigated, and it is believed that the simulation results can predict the stress–strain relationship in concrete more accurately, but it still needs to be corrected for the corresponding influencing factors to ensure the accuracy of the model. In fact, there are mean reports on the applications of CNRC sensors in concrete structures for SHM using FEM, and they are worthy to further study.

5 FEM limitations of CNRC and future prospects

In order to improve the accuracy of the calculation and to correspond directly to reality, the limitations of CNRC simulations at the present stage are presented, for which the recommendations are made for future prospects:

  1. Simulating the effect of CNT agglomeration on CNRC. It is well-known that as the number of fibers increases, it is difficult to play a role in CM due to CNT’s own properties, but it is still a great challenge to realistically simulate the agglomeration effect of CNT in CNRC. For solving this problem, the study of Romanov et al. [63] is a wonderful inspiration. They investigated the degree of agglomeration from fully discrete to partially discrete and finally fully agglomerated states for the size and density of CNT agglomerates and developed a double-scaled model capable of realistically simulating the aggregation of CNT in composites.

  2. Simulation of CNRC electromechanical performance in different environments. FEM has significant advantages in studying nonlinear problems under complex conditions (e.g., static, dynamic, different humidity and temperature), and its application to SHM under different harsh conditions has a significant effect on future structural safety improvement [82]. Li [83] used ABAQUS software to study the seismic performance of bridge piers containing CNRC, and the structure showed that the seismic performance of bridge piers containing CNRC was superior compared to plain concrete. Liu et al. [84] proposed a combined FEM and computational fluid dynamics approach to evaluate the fire performance of bridges and concluded that the multi-scale modeling approach was more effective for localized fires.

  3. Simulation of the inhomogeneity of CNT in CM. The uniformity assumption is widely used in FEM, which is obviously unrealistic. To further consider the inhomogeneous distribution of CNT in CM, the following method can be used for reference. Lu and Leung [85] proposed to calculate the bridging law for each different section, which contributes to simulating the strength dispersion and unsaturated cracking phenomena in fibrous concrete; Elnekhaily and Talreja [86] calculated the degree of inhomogeneity of fibers in the matrix by statistical data and developed a related algorithm; Song et al. [87] used a modified A&A (Andreasen & Andersen) model to design a densely compacted UHPFRC cement matrix, which optimized some key parameters of fiber orientation and distribution; Ghasemi et al. [88] optimized the distribution of short fibers in a continuous media structure made of fiber-reinforced composites by an efficient gradient-based optimization method, which maintained the accuracy of the model while greatly reducing the computational time by increasing the mesh size.

6 Conclusion

Since the CNT greatly improves the mechanical and electrical properties of the CM and gives it a good electromechanical coupling performance, it helps to realize the SHM of CNRC sensors. Yet, the experimental method alone is not sufficient to support the establishment of a theoretical system for the electromechanical coupling performance of CNRC, and FEM can be used as a supplement and extension of the experimental study to obtain some data and conclusions that are difficult to obtain from the experimental study. Therefore, this article investigates and analyzes the CNRC model and performance analysis based on FEM.

  1. The multiscale approach can combine the advantages of different models for CNRC analysis, which can substantially improve the accuracy of CNRC simulation.

  2. The fiber pullout model is currently the optimal method for the study of composite interfaces, reflecting the bond–slip relationship between fiber and matrix debonding of CNRC.

  3. The FEM of the mechanical and electrical properties of CNRC has been gradually developed and optimized, which has a non-negligible role in the improvement of the electromechanical coupling theory of CNRC.

  4. The method of probing the stress–strain distribution of CNRC sensors embedded in concrete using FEM is feasible, and the sensing performance under different environmental conditions can be discussed in the future.

  1. Funding information: This study was financially supported by the National Natural Science Foundation of China (No. 51878364), Projects from China Construction Eighth Division (No. JM20191030, QUT-2022-FW-0192, and QUT-2022-FW-0028), and the National “111” project, and Gaofeng discipline project funded by Shandong Province.

  2. Author contributions: Conceptualization, supervision, and resources: Jianlin Luo, Jigang Zhang, Liqing Zhang; data curation, formal analysis, and methodology: Xuejun Tao and Jianlin Luo; funding acquisition, investigation, and project administration: Jianlin Luo and Min Zhu; validation, visualization, and writing – original draft: Xuejun Tao, and Jianlin Luo; writing – review and editing: Xuejun Tao, Jianlin Luo, Liqing Zhang. All authors have accepted responsibility for the entire content of this manuscript and approved its submission

  3. Conflict of interest: The authors state no conflict of interest.

  4. Data availability statement: Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.

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Received: 2022-10-11
Revised: 2022-12-10
Accepted: 2023-01-13
Published Online: 2023-04-26

© 2023 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

Articles in the same Issue

  1. Research Articles
  2. Preparation of CdS–Ag2S nanocomposites by ultrasound-assisted UV photolysis treatment and its visible light photocatalysis activity
  3. Significance of nanoparticle radius and inter-particle spacing toward the radiative water-based alumina nanofluid flow over a rotating disk
  4. Aptamer-based detection of serotonin based on the rapid in situ synthesis of colorimetric gold nanoparticles
  5. Investigation of the nucleation and growth behavior of Ti2AlC and Ti3AlC nano-precipitates in TiAl alloys
  6. Dynamic recrystallization behavior and nucleation mechanism of dual-scale SiCp/A356 composites processed by P/M method
  7. High mechanical performance of 3-aminopropyl triethoxy silane/epoxy cured in a sandwich construction of 3D carbon felts foam and woven basalt fibers
  8. Applying solution of spray polyurea elastomer in asphalt binder: Feasibility analysis and DSR study based on the MSCR and LAS tests
  9. Study on the chronic toxicity and carcinogenicity of iron-based bioabsorbable stents
  10. Influence of microalloying with B on the microstructure and properties of brazed joints with Ag–Cu–Zn–Sn filler metal
  11. Thermohydraulic performance of thermal system integrated with twisted turbulator inserts using ternary hybrid nanofluids
  12. Study of mechanical properties of epoxy/graphene and epoxy/halloysite nanocomposites
  13. Effects of CaO addition on the CuW composite containing micro- and nano-sized tungsten particles synthesized via aluminothermic coupling with silicothermic reduction
  14. Cu and Al2O3-based hybrid nanofluid flow through a porous cavity
  15. Design of functional vancomycin-embedded bio-derived extracellular matrix hydrogels for repairing infectious bone defects
  16. Study on nanocrystalline coating prepared by electro-spraying 316L metal wire and its corrosion performance
  17. Axial compression performance of CFST columns reinforced by ultra-high-performance nano-concrete under long-term loading
  18. Tungsten trioxide nanocomposite for conventional soliton and noise-like pulse generation in anomalous dispersion laser cavity
  19. Microstructure and electrical contact behavior of the nano-yttria-modified Cu-Al2O3/30Mo/3SiC composite
  20. Melting rheology in thermally stratified graphene-mineral oil reservoir (third-grade nanofluid) with slip condition
  21. Re-examination of nonlinear vibration and nonlinear bending of porous sandwich cylindrical panels reinforced by graphene platelets
  22. Parametric simulation of hybrid nanofluid flow consisting of cobalt ferrite nanoparticles with second-order slip and variable viscosity over an extending surface
  23. Chitosan-capped silver nanoparticles with potent and selective intrinsic activity against the breast cancer cells
  24. Multi-core/shell SiO2@Al2O3 nanostructures deposited on Ti3AlC2 to enhance high-temperature stability and microwave absorption properties
  25. Solution-processed Bi2S3/BiVO4/TiO2 ternary heterojunction photoanode with enhanced photoelectrochemical performance
  26. Electroporation effect of ZnO nanoarrays under low voltage for water disinfection
  27. NIR-II window absorbing graphene oxide-coated gold nanorods and graphene quantum dot-coupled gold nanorods for photothermal cancer therapy
  28. Nonlinear three-dimensional stability characteristics of geometrically imperfect nanoshells under axial compression and surface residual stress
  29. Investigation of different nanoparticles properties on the thermal conductivity and viscosity of nanofluids by molecular dynamics simulation
  30. Optimized Cu2O-{100} facet for generation of different reactive oxidative species via peroxymonosulfate activation at specific pH values to efficient acetaminophen removal
  31. Brownian and thermal diffusivity impact due to the Maxwell nanofluid (graphene/engine oil) flow with motile microorganisms and Joule heating
  32. Appraising the dielectric properties and the effectiveness of electromagnetic shielding of graphene reinforced silicone rubber nanocomposite
  33. Synthesis of Ag and Cu nanoparticles by plasma discharge in inorganic salt solutions
  34. Low-cost and large-scale preparation of ultrafine TiO2@C hybrids for high-performance degradation of methyl orange and formaldehyde under visible light
  35. Utilization of waste glass with natural pozzolan in the production of self-glazed glass-ceramic materials
  36. Mechanical performance of date palm fiber-reinforced concrete modified with nano-activated carbon
  37. Melting point of dried gold nanoparticles prepared with ultrasonic spray pyrolysis and lyophilisation
  38. Graphene nanofibers: A modern approach towards tailored gypsum composites
  39. Role of localized magnetic field in vortex generation in tri-hybrid nanofluid flow: A numerical approach
  40. Intelligent computing for the double-diffusive peristaltic rheology of magneto couple stress nanomaterials
  41. Bioconvection transport of upper convected Maxwell nanoliquid with gyrotactic microorganism, nonlinear thermal radiation, and chemical reaction
  42. 3D printing of porous Ti6Al4V bone tissue engineering scaffold and surface anodization preparation of nanotubes to enhance its biological property
  43. Bioinspired ferromagnetic CoFe2O4 nanoparticles: Potential pharmaceutical and medical applications
  44. Significance of gyrotactic microorganisms on the MHD tangent hyperbolic nanofluid flow across an elastic slender surface: Numerical analysis
  45. Performance of polycarboxylate superplasticisers in seawater-blended cement: Effect from chemical structure and nano modification
  46. Entropy minimization of GO–Ag/KO cross-hybrid nanofluid over a convectively heated surface
  47. Oxygen plasma assisted room temperature bonding for manufacturing SU-8 polymer micro/nanoscale nozzle
  48. Performance and mechanism of CO2 reduction by DBD-coupled mesoporous SiO2
  49. Polyarylene ether nitrile dielectric films modified by HNTs@PDA hybrids for high-temperature resistant organic electronics field
  50. Exploration of generalized two-phase free convection magnetohydrodynamic flow of dusty tetra-hybrid Casson nanofluid between parallel microplates
  51. Hygrothermal bending analysis of sandwich nanoplates with FG porous core and piezomagnetic faces via nonlocal strain gradient theory
  52. Design and optimization of a TiO2/RGO-supported epoxy multilayer microwave absorber by the modified local best particle swarm optimization algorithm
  53. Mechanical properties and frost resistance of recycled brick aggregate concrete modified by nano-SiO2
  54. Self-template synthesis of hollow flower-like NiCo2O4 nanoparticles as an efficient bifunctional catalyst for oxygen reduction and oxygen evolution in alkaline media
  55. High-performance wearable flexible strain sensors based on an AgNWs/rGO/TPU electrospun nanofiber film for monitoring human activities
  56. High-performance lithium–selenium batteries enabled by nitrogen-doped porous carbon from peanut meal
  57. Investigating effects of Lorentz forces and convective heating on ternary hybrid nanofluid flow over a curved surface using homotopy analysis method
  58. Exploring the potential of biogenic magnesium oxide nanoparticles for cytotoxicity: In vitro and in silico studies on HCT116 and HT29 cells and DPPH radical scavenging
  59. Enhanced visible-light-driven photocatalytic degradation of azo dyes by heteroatom-doped nickel tungstate nanoparticles
  60. A facile method to synthesize nZVI-doped polypyrrole-based carbon nanotube for Ag(i) removal
  61. Improved osseointegration of dental titanium implants by TiO2 nanotube arrays with self-assembled recombinant IGF-1 in type 2 diabetes mellitus rat model
  62. Functionalized SWCNTs@Ag–TiO2 nanocomposites induce ROS-mediated apoptosis and autophagy in liver cancer cells
  63. Triboelectric nanogenerator based on a water droplet spring with a concave spherical surface for harvesting wave energy and detecting pressure
  64. A mathematical approach for modeling the blood flow containing nanoparticles by employing the Buongiorno’s model
  65. Molecular dynamics study on dynamic interlayer friction of graphene and its strain effect
  66. Induction of apoptosis and autophagy via regulation of AKT and JNK mitogen-activated protein kinase pathways in breast cancer cell lines exposed to gold nanoparticles loaded with TNF-α and combined with doxorubicin
  67. Effect of PVA fibers on durability of nano-SiO2-reinforced cement-based composites subjected to wet-thermal and chloride salt-coupled environment
  68. Effect of polyvinyl alcohol fibers on mechanical properties of nano-SiO2-reinforced geopolymer composites under a complex environment
  69. In vitro studies of titanium dioxide nanoparticles modified with glutathione as a potential drug delivery system
  70. Comparative investigations of Ag/H2O nanofluid and Ag-CuO/H2O hybrid nanofluid with Darcy-Forchheimer flow over a curved surface
  71. Study on deformation characteristics of multi-pass continuous drawing of micro copper wire based on crystal plasticity finite element method
  72. Properties of ultra-high-performance self-compacting fiber-reinforced concrete modified with nanomaterials
  73. Prediction of lap shear strength of GNP and TiO2/epoxy nanocomposite adhesives
  74. A novel exploration of how localized magnetic field affects vortex generation of trihybrid nanofluids
  75. Fabrication and physicochemical characterization of copper oxide–pyrrhotite nanocomposites for the cytotoxic effects on HepG2 cells and the mechanism
  76. Thermal radiative flow of cross nanofluid due to a stretched cylinder containing microorganisms
  77. In vitro study of the biphasic calcium phosphate/chitosan hybrid biomaterial scaffold fabricated via solvent casting and evaporation technique for bone regeneration
  78. Insights into the thermal characteristics and dynamics of stagnant blood conveying titanium oxide, alumina, and silver nanoparticles subject to Lorentz force and internal heating over a curved surface
  79. Effects of nano-SiO2 additives on carbon fiber-reinforced fly ash–slag geopolymer composites performance: Workability, mechanical properties, and microstructure
  80. Energy bandgap and thermal characteristics of non-Darcian MHD rotating hybridity nanofluid thin film flow: Nanotechnology application
  81. Green synthesis and characterization of ginger-extract-based oxali-palladium nanoparticles for colorectal cancer: Downregulation of REG4 and apoptosis induction
  82. Abnormal evolution of resistivity and microstructure of annealed Ag nanoparticles/Ag–Mo films
  83. Preparation of water-based dextran-coated Fe3O4 magnetic fluid for magnetic hyperthermia
  84. Statistical investigations and morphological aspects of cross-rheological material suspended in transportation of alumina, silica, titanium, and ethylene glycol via the Galerkin algorithm
  85. Effect of CNT film interleaves on the flexural properties and strength after impact of CFRP composites
  86. Self-assembled nanoscale entities: Preparative process optimization, payload release, and enhanced bioavailability of thymoquinone natural product
  87. Structure–mechanical property relationships of 3D-printed porous polydimethylsiloxane films
  88. Nonlinear thermal radiation and the slip effect on a 3D bioconvection flow of the Casson nanofluid in a rotating frame via a homotopy analysis mechanism
  89. Residual mechanical properties of concrete incorporated with nano supplementary cementitious materials exposed to elevated temperature
  90. Time-independent three-dimensional flow of a water-based hybrid nanofluid past a Riga plate with slips and convective conditions: A homotopic solution
  91. Lightweight and high-strength polyarylene ether nitrile-based composites for efficient electromagnetic interference shielding
  92. Review Articles
  93. Recycling waste sources into nanocomposites of graphene materials: Overview from an energy-focused perspective
  94. Hybrid nanofiller reinforcement in thermoset and biothermoset applications: A review
  95. Current state-of-the-art review of nanotechnology-based therapeutics for viral pandemics: Special attention to COVID-19
  96. Solid lipid nanoparticles for targeted natural and synthetic drugs delivery in high-incidence cancers, and other diseases: Roles of preparation methods, lipid composition, transitional stability, and release profiles in nanocarriers’ development
  97. Critical review on experimental and theoretical studies of elastic properties of wurtzite-structured ZnO nanowires
  98. Polyurea micro-/nano-capsule applications in construction industry: A review
  99. A comprehensive review and clinical guide to molecular and serological diagnostic tests and future development: In vitro diagnostic testing for COVID-19
  100. Recent advances in electrocatalytic oxidation of 5-hydroxymethylfurfural to 2,5-furandicarboxylic acid: Mechanism, catalyst, coupling system
  101. Research progress and prospect of silica-based polymer nanofluids in enhanced oil recovery
  102. Review of the pharmacokinetics of nanodrugs
  103. Engineered nanoflowers, nanotrees, nanostars, nanodendrites, and nanoleaves for biomedical applications
  104. Research progress of biopolymers combined with stem cells in the repair of intrauterine adhesions
  105. Progress in FEM modeling on mechanical and electromechanical properties of carbon nanotube cement-based composites
  106. Antifouling induced by surface wettability of poly(dimethyl siloxane) and its nanocomposites
  107. TiO2 aerogel composite high-efficiency photocatalysts for environmental treatment and hydrogen energy production
  108. Structural properties of alumina surfaces and their roles in the synthesis of environmentally persistent free radicals (EPFRs)
  109. Nanoparticles for the potential treatment of Alzheimer’s disease: A physiopathological approach
  110. Current status of synthesis and consolidation strategies for thermo-resistant nanoalloys and their general applications
  111. Recent research progress on the stimuli-responsive smart membrane: A review
  112. Dispersion of carbon nanotubes in aqueous cementitious materials: A review
  113. Applications of DNA tetrahedron nanostructure in cancer diagnosis and anticancer drugs delivery
  114. Magnetic nanoparticles in 3D-printed scaffolds for biomedical applications
  115. An overview of the synthesis of silicon carbide–boron carbide composite powders
  116. Organolead halide perovskites: Synthetic routes, structural features, and their potential in the development of photovoltaic
  117. Recent advancements in nanotechnology application on wood and bamboo materials: A review
  118. Application of aptamer-functionalized nanomaterials in molecular imaging of tumors
  119. Recent progress on corrosion mechanisms of graphene-reinforced metal matrix composites
  120. Research progress on preparation, modification, and application of phenolic aerogel
  121. Application of nanomaterials in early diagnosis of cancer
  122. Plant mediated-green synthesis of zinc oxide nanoparticles: An insight into biomedical applications
  123. Recent developments in terahertz quantum cascade lasers for practical applications
  124. Recent progress in dielectric/metal/dielectric electrodes for foldable light-emitting devices
  125. Nanocoatings for ballistic applications: A review
  126. A mini-review on MoS2 membrane for water desalination: Recent development and challenges
  127. Recent updates in nanotechnological advances for wound healing: A narrative review
  128. Recent advances in DNA nanomaterials for cancer diagnosis and treatment
  129. Electrochemical micro- and nanobiosensors for in vivo reactive oxygen/nitrogen species measurement in the brain
  130. Advances in organic–inorganic nanocomposites for cancer imaging and therapy
  131. Advancements in aluminum matrix composites reinforced with carbides and graphene: A comprehensive review
  132. Modification effects of nanosilica on asphalt binders: A review
  133. Decellularized extracellular matrix as a promising biomaterial for musculoskeletal tissue regeneration
  134. Review of the sol–gel method in preparing nano TiO2 for advanced oxidation process
  135. Micro/nano manufacturing aircraft surface with anti-icing and deicing performances: An overview
  136. Cell type-targeting nanoparticles in treating central nervous system diseases: Challenges and hopes
  137. An overview of hydrogen production from Al-based materials
  138. A review of application, modification, and prospect of melamine foam
  139. A review of the performance of fibre-reinforced composite laminates with carbon nanotubes
  140. Research on AFM tip-related nanofabrication of two-dimensional materials
  141. Advances in phase change building materials: An overview
  142. Development of graphene and graphene quantum dots toward biomedical engineering applications: A review
  143. Nanoremediation approaches for the mitigation of heavy metal contamination in vegetables: An overview
  144. Photodynamic therapy empowered by nanotechnology for oral and dental science: Progress and perspectives
  145. Biosynthesis of metal nanoparticles: Bioreduction and biomineralization
  146. Current diagnostic and therapeutic approaches for severe acute respiratory syndrome coronavirus-2 (SARS-COV-2) and the role of nanomaterial-based theragnosis in combating the pandemic
  147. Application of two-dimensional black phosphorus material in wound healing
  148. Special Issue on Advanced Nanomaterials and Composites for Energy Conversion and Storage - Part I
  149. Helical fluorinated carbon nanotubes/iron(iii) fluoride hybrid with multilevel transportation channels and rich active sites for lithium/fluorinated carbon primary battery
  150. The progress of cathode materials in aqueous zinc-ion batteries
  151. Special Issue on Advanced Nanomaterials for Carbon Capture, Environment and Utilization for Energy Sustainability - Part I
  152. Effect of polypropylene fiber and nano-silica on the compressive strength and frost resistance of recycled brick aggregate concrete
  153. Mechanochemical design of nanomaterials for catalytic applications with a benign-by-design focus
https://doi.org/10.1515/ntrev-2022-0522
Keywords for this article
FEM modeling; CNT cement-based composite; performance simulation; SHM
Creative Commons
BY 4.0

Articles in the same Issue

  1. Research Articles
  2. Preparation of CdS–Ag2S nanocomposites by ultrasound-assisted UV photolysis treatment and its visible light photocatalysis activity
  3. Significance of nanoparticle radius and inter-particle spacing toward the radiative water-based alumina nanofluid flow over a rotating disk
  4. Aptamer-based detection of serotonin based on the rapid in situ synthesis of colorimetric gold nanoparticles
  5. Investigation of the nucleation and growth behavior of Ti2AlC and Ti3AlC nano-precipitates in TiAl alloys
  6. Dynamic recrystallization behavior and nucleation mechanism of dual-scale SiCp/A356 composites processed by P/M method
  7. High mechanical performance of 3-aminopropyl triethoxy silane/epoxy cured in a sandwich construction of 3D carbon felts foam and woven basalt fibers
  8. Applying solution of spray polyurea elastomer in asphalt binder: Feasibility analysis and DSR study based on the MSCR and LAS tests
  9. Study on the chronic toxicity and carcinogenicity of iron-based bioabsorbable stents
  10. Influence of microalloying with B on the microstructure and properties of brazed joints with Ag–Cu–Zn–Sn filler metal
  11. Thermohydraulic performance of thermal system integrated with twisted turbulator inserts using ternary hybrid nanofluids
  12. Study of mechanical properties of epoxy/graphene and epoxy/halloysite nanocomposites
  13. Effects of CaO addition on the CuW composite containing micro- and nano-sized tungsten particles synthesized via aluminothermic coupling with silicothermic reduction
  14. Cu and Al2O3-based hybrid nanofluid flow through a porous cavity
  15. Design of functional vancomycin-embedded bio-derived extracellular matrix hydrogels for repairing infectious bone defects
  16. Study on nanocrystalline coating prepared by electro-spraying 316L metal wire and its corrosion performance
  17. Axial compression performance of CFST columns reinforced by ultra-high-performance nano-concrete under long-term loading
  18. Tungsten trioxide nanocomposite for conventional soliton and noise-like pulse generation in anomalous dispersion laser cavity
  19. Microstructure and electrical contact behavior of the nano-yttria-modified Cu-Al2O3/30Mo/3SiC composite
  20. Melting rheology in thermally stratified graphene-mineral oil reservoir (third-grade nanofluid) with slip condition
  21. Re-examination of nonlinear vibration and nonlinear bending of porous sandwich cylindrical panels reinforced by graphene platelets
  22. Parametric simulation of hybrid nanofluid flow consisting of cobalt ferrite nanoparticles with second-order slip and variable viscosity over an extending surface
  23. Chitosan-capped silver nanoparticles with potent and selective intrinsic activity against the breast cancer cells
  24. Multi-core/shell SiO2@Al2O3 nanostructures deposited on Ti3AlC2 to enhance high-temperature stability and microwave absorption properties
  25. Solution-processed Bi2S3/BiVO4/TiO2 ternary heterojunction photoanode with enhanced photoelectrochemical performance
  26. Electroporation effect of ZnO nanoarrays under low voltage for water disinfection
  27. NIR-II window absorbing graphene oxide-coated gold nanorods and graphene quantum dot-coupled gold nanorods for photothermal cancer therapy
  28. Nonlinear three-dimensional stability characteristics of geometrically imperfect nanoshells under axial compression and surface residual stress
  29. Investigation of different nanoparticles properties on the thermal conductivity and viscosity of nanofluids by molecular dynamics simulation
  30. Optimized Cu2O-{100} facet for generation of different reactive oxidative species via peroxymonosulfate activation at specific pH values to efficient acetaminophen removal
  31. Brownian and thermal diffusivity impact due to the Maxwell nanofluid (graphene/engine oil) flow with motile microorganisms and Joule heating
  32. Appraising the dielectric properties and the effectiveness of electromagnetic shielding of graphene reinforced silicone rubber nanocomposite
  33. Synthesis of Ag and Cu nanoparticles by plasma discharge in inorganic salt solutions
  34. Low-cost and large-scale preparation of ultrafine TiO2@C hybrids for high-performance degradation of methyl orange and formaldehyde under visible light
  35. Utilization of waste glass with natural pozzolan in the production of self-glazed glass-ceramic materials
  36. Mechanical performance of date palm fiber-reinforced concrete modified with nano-activated carbon
  37. Melting point of dried gold nanoparticles prepared with ultrasonic spray pyrolysis and lyophilisation
  38. Graphene nanofibers: A modern approach towards tailored gypsum composites
  39. Role of localized magnetic field in vortex generation in tri-hybrid nanofluid flow: A numerical approach
  40. Intelligent computing for the double-diffusive peristaltic rheology of magneto couple stress nanomaterials
  41. Bioconvection transport of upper convected Maxwell nanoliquid with gyrotactic microorganism, nonlinear thermal radiation, and chemical reaction
  42. 3D printing of porous Ti6Al4V bone tissue engineering scaffold and surface anodization preparation of nanotubes to enhance its biological property
  43. Bioinspired ferromagnetic CoFe2O4 nanoparticles: Potential pharmaceutical and medical applications
  44. Significance of gyrotactic microorganisms on the MHD tangent hyperbolic nanofluid flow across an elastic slender surface: Numerical analysis
  45. Performance of polycarboxylate superplasticisers in seawater-blended cement: Effect from chemical structure and nano modification
  46. Entropy minimization of GO–Ag/KO cross-hybrid nanofluid over a convectively heated surface
  47. Oxygen plasma assisted room temperature bonding for manufacturing SU-8 polymer micro/nanoscale nozzle
  48. Performance and mechanism of CO2 reduction by DBD-coupled mesoporous SiO2
  49. Polyarylene ether nitrile dielectric films modified by HNTs@PDA hybrids for high-temperature resistant organic electronics field
  50. Exploration of generalized two-phase free convection magnetohydrodynamic flow of dusty tetra-hybrid Casson nanofluid between parallel microplates
  51. Hygrothermal bending analysis of sandwich nanoplates with FG porous core and piezomagnetic faces via nonlocal strain gradient theory
  52. Design and optimization of a TiO2/RGO-supported epoxy multilayer microwave absorber by the modified local best particle swarm optimization algorithm
  53. Mechanical properties and frost resistance of recycled brick aggregate concrete modified by nano-SiO2
  54. Self-template synthesis of hollow flower-like NiCo2O4 nanoparticles as an efficient bifunctional catalyst for oxygen reduction and oxygen evolution in alkaline media
  55. High-performance wearable flexible strain sensors based on an AgNWs/rGO/TPU electrospun nanofiber film for monitoring human activities
  56. High-performance lithium–selenium batteries enabled by nitrogen-doped porous carbon from peanut meal
  57. Investigating effects of Lorentz forces and convective heating on ternary hybrid nanofluid flow over a curved surface using homotopy analysis method
  58. Exploring the potential of biogenic magnesium oxide nanoparticles for cytotoxicity: In vitro and in silico studies on HCT116 and HT29 cells and DPPH radical scavenging
  59. Enhanced visible-light-driven photocatalytic degradation of azo dyes by heteroatom-doped nickel tungstate nanoparticles
  60. A facile method to synthesize nZVI-doped polypyrrole-based carbon nanotube for Ag(i) removal
  61. Improved osseointegration of dental titanium implants by TiO2 nanotube arrays with self-assembled recombinant IGF-1 in type 2 diabetes mellitus rat model
  62. Functionalized SWCNTs@Ag–TiO2 nanocomposites induce ROS-mediated apoptosis and autophagy in liver cancer cells
  63. Triboelectric nanogenerator based on a water droplet spring with a concave spherical surface for harvesting wave energy and detecting pressure
  64. A mathematical approach for modeling the blood flow containing nanoparticles by employing the Buongiorno’s model
  65. Molecular dynamics study on dynamic interlayer friction of graphene and its strain effect
  66. Induction of apoptosis and autophagy via regulation of AKT and JNK mitogen-activated protein kinase pathways in breast cancer cell lines exposed to gold nanoparticles loaded with TNF-α and combined with doxorubicin
  67. Effect of PVA fibers on durability of nano-SiO2-reinforced cement-based composites subjected to wet-thermal and chloride salt-coupled environment
  68. Effect of polyvinyl alcohol fibers on mechanical properties of nano-SiO2-reinforced geopolymer composites under a complex environment
  69. In vitro studies of titanium dioxide nanoparticles modified with glutathione as a potential drug delivery system
  70. Comparative investigations of Ag/H2O nanofluid and Ag-CuO/H2O hybrid nanofluid with Darcy-Forchheimer flow over a curved surface
  71. Study on deformation characteristics of multi-pass continuous drawing of micro copper wire based on crystal plasticity finite element method
  72. Properties of ultra-high-performance self-compacting fiber-reinforced concrete modified with nanomaterials
  73. Prediction of lap shear strength of GNP and TiO2/epoxy nanocomposite adhesives
  74. A novel exploration of how localized magnetic field affects vortex generation of trihybrid nanofluids
  75. Fabrication and physicochemical characterization of copper oxide–pyrrhotite nanocomposites for the cytotoxic effects on HepG2 cells and the mechanism
  76. Thermal radiative flow of cross nanofluid due to a stretched cylinder containing microorganisms
  77. In vitro study of the biphasic calcium phosphate/chitosan hybrid biomaterial scaffold fabricated via solvent casting and evaporation technique for bone regeneration
  78. Insights into the thermal characteristics and dynamics of stagnant blood conveying titanium oxide, alumina, and silver nanoparticles subject to Lorentz force and internal heating over a curved surface
  79. Effects of nano-SiO2 additives on carbon fiber-reinforced fly ash–slag geopolymer composites performance: Workability, mechanical properties, and microstructure
  80. Energy bandgap and thermal characteristics of non-Darcian MHD rotating hybridity nanofluid thin film flow: Nanotechnology application
  81. Green synthesis and characterization of ginger-extract-based oxali-palladium nanoparticles for colorectal cancer: Downregulation of REG4 and apoptosis induction
  82. Abnormal evolution of resistivity and microstructure of annealed Ag nanoparticles/Ag–Mo films
  83. Preparation of water-based dextran-coated Fe3O4 magnetic fluid for magnetic hyperthermia
  84. Statistical investigations and morphological aspects of cross-rheological material suspended in transportation of alumina, silica, titanium, and ethylene glycol via the Galerkin algorithm
  85. Effect of CNT film interleaves on the flexural properties and strength after impact of CFRP composites
  86. Self-assembled nanoscale entities: Preparative process optimization, payload release, and enhanced bioavailability of thymoquinone natural product
  87. Structure–mechanical property relationships of 3D-printed porous polydimethylsiloxane films
  88. Nonlinear thermal radiation and the slip effect on a 3D bioconvection flow of the Casson nanofluid in a rotating frame via a homotopy analysis mechanism
  89. Residual mechanical properties of concrete incorporated with nano supplementary cementitious materials exposed to elevated temperature
  90. Time-independent three-dimensional flow of a water-based hybrid nanofluid past a Riga plate with slips and convective conditions: A homotopic solution
  91. Lightweight and high-strength polyarylene ether nitrile-based composites for efficient electromagnetic interference shielding
  92. Review Articles
  93. Recycling waste sources into nanocomposites of graphene materials: Overview from an energy-focused perspective
  94. Hybrid nanofiller reinforcement in thermoset and biothermoset applications: A review
  95. Current state-of-the-art review of nanotechnology-based therapeutics for viral pandemics: Special attention to COVID-19
  96. Solid lipid nanoparticles for targeted natural and synthetic drugs delivery in high-incidence cancers, and other diseases: Roles of preparation methods, lipid composition, transitional stability, and release profiles in nanocarriers’ development
  97. Critical review on experimental and theoretical studies of elastic properties of wurtzite-structured ZnO nanowires
  98. Polyurea micro-/nano-capsule applications in construction industry: A review
  99. A comprehensive review and clinical guide to molecular and serological diagnostic tests and future development: In vitro diagnostic testing for COVID-19
  100. Recent advances in electrocatalytic oxidation of 5-hydroxymethylfurfural to 2,5-furandicarboxylic acid: Mechanism, catalyst, coupling system
  101. Research progress and prospect of silica-based polymer nanofluids in enhanced oil recovery
  102. Review of the pharmacokinetics of nanodrugs
  103. Engineered nanoflowers, nanotrees, nanostars, nanodendrites, and nanoleaves for biomedical applications
  104. Research progress of biopolymers combined with stem cells in the repair of intrauterine adhesions
  105. Progress in FEM modeling on mechanical and electromechanical properties of carbon nanotube cement-based composites
  106. Antifouling induced by surface wettability of poly(dimethyl siloxane) and its nanocomposites
  107. TiO2 aerogel composite high-efficiency photocatalysts for environmental treatment and hydrogen energy production
  108. Structural properties of alumina surfaces and their roles in the synthesis of environmentally persistent free radicals (EPFRs)
  109. Nanoparticles for the potential treatment of Alzheimer’s disease: A physiopathological approach
  110. Current status of synthesis and consolidation strategies for thermo-resistant nanoalloys and their general applications
  111. Recent research progress on the stimuli-responsive smart membrane: A review
  112. Dispersion of carbon nanotubes in aqueous cementitious materials: A review
  113. Applications of DNA tetrahedron nanostructure in cancer diagnosis and anticancer drugs delivery
  114. Magnetic nanoparticles in 3D-printed scaffolds for biomedical applications
  115. An overview of the synthesis of silicon carbide–boron carbide composite powders
  116. Organolead halide perovskites: Synthetic routes, structural features, and their potential in the development of photovoltaic
  117. Recent advancements in nanotechnology application on wood and bamboo materials: A review
  118. Application of aptamer-functionalized nanomaterials in molecular imaging of tumors
  119. Recent progress on corrosion mechanisms of graphene-reinforced metal matrix composites
  120. Research progress on preparation, modification, and application of phenolic aerogel
  121. Application of nanomaterials in early diagnosis of cancer
  122. Plant mediated-green synthesis of zinc oxide nanoparticles: An insight into biomedical applications
  123. Recent developments in terahertz quantum cascade lasers for practical applications
  124. Recent progress in dielectric/metal/dielectric electrodes for foldable light-emitting devices
  125. Nanocoatings for ballistic applications: A review
  126. A mini-review on MoS2 membrane for water desalination: Recent development and challenges
  127. Recent updates in nanotechnological advances for wound healing: A narrative review
  128. Recent advances in DNA nanomaterials for cancer diagnosis and treatment
  129. Electrochemical micro- and nanobiosensors for in vivo reactive oxygen/nitrogen species measurement in the brain
  130. Advances in organic–inorganic nanocomposites for cancer imaging and therapy
  131. Advancements in aluminum matrix composites reinforced with carbides and graphene: A comprehensive review
  132. Modification effects of nanosilica on asphalt binders: A review
  133. Decellularized extracellular matrix as a promising biomaterial for musculoskeletal tissue regeneration
  134. Review of the sol–gel method in preparing nano TiO2 for advanced oxidation process
  135. Micro/nano manufacturing aircraft surface with anti-icing and deicing performances: An overview
  136. Cell type-targeting nanoparticles in treating central nervous system diseases: Challenges and hopes
  137. An overview of hydrogen production from Al-based materials
  138. A review of application, modification, and prospect of melamine foam
  139. A review of the performance of fibre-reinforced composite laminates with carbon nanotubes
  140. Research on AFM tip-related nanofabrication of two-dimensional materials
  141. Advances in phase change building materials: An overview
  142. Development of graphene and graphene quantum dots toward biomedical engineering applications: A review
  143. Nanoremediation approaches for the mitigation of heavy metal contamination in vegetables: An overview
  144. Photodynamic therapy empowered by nanotechnology for oral and dental science: Progress and perspectives
  145. Biosynthesis of metal nanoparticles: Bioreduction and biomineralization
  146. Current diagnostic and therapeutic approaches for severe acute respiratory syndrome coronavirus-2 (SARS-COV-2) and the role of nanomaterial-based theragnosis in combating the pandemic
  147. Application of two-dimensional black phosphorus material in wound healing
  148. Special Issue on Advanced Nanomaterials and Composites for Energy Conversion and Storage - Part I
  149. Helical fluorinated carbon nanotubes/iron(iii) fluoride hybrid with multilevel transportation channels and rich active sites for lithium/fluorinated carbon primary battery
  150. The progress of cathode materials in aqueous zinc-ion batteries
  151. Special Issue on Advanced Nanomaterials for Carbon Capture, Environment and Utilization for Energy Sustainability - Part I
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