Atomistic Finite Element Method Research Articles

Identification of microbes using single-layer graphene-based nano biosensors.

Graphene based nano sensors have huge potential in an era of sensor technology. The objective of this study is to create a sensor by investigating the vibration responses of cantilever and bridged boundary conditioned single layer graphene sheets (SLGS) with various attached microorganisms on the tip and at the centre of the sheet. The Parvoviridae, Flaviviridae, and Polyomaviridae biological substances have been comprehensively investigated here. For the Parvoviridae, Polyomaviridae, and Flaviviridae categories of targeted microbes, the sizes are 21nm, 40nm, and 45nm, respectively. The Parvoviridae family has a maximum frequency of 1.87x107 Hz with a cantilever condition and a mass of 4.2441 Zg, and for a bridged condition, it demonstrates a maximum frequency of 1.23x108 Hz with the same mass on armchair SLG (5 5). The data analysis shows that 3.0041 Zg mass of the Mimivirus has the lowest frequency. It demonstrates explicitly that the rate of frequency decreases as the value of mass increases. When compared to chiral SLG, the armchair single layer graphene sheet performs better. The research indicates that the dynamic properties are significantly influenced by the mass of various biological organisms. The application of this sensor will enable the detection of microorganisms or viruses that can be connected to SLG. In this research, the application of Single Layer Graphene (SLG) as a virus sensing device is explored. Atomistic finite element method (AFEM) has been used to carry out the dynamic analysis of SLG. Molecular dynamic analysis and simulations have been performed to see how SLG behaves when employed as sensors for biological entities and when they are exposed to bridged and cantilever boundary conditions. The frequency analysis was performed using ANSYS APDL software. SLG of various chirality has been utilised in the investigation. By altering the applied mass of a biological object, the difference in frequency observed. The idea behind mass detection employing nano biosensors is built on the concept that the stiffness of a biomolecule changes as its mass changes, making the resonant frequency extremely sensitive to that change. A shift in the resonance frequency results from a change in the associated mass on the graphene sheet. The main challenge in mass detection is estimating the variation in resonant frequency driven by the mass of the connected molecule. The SLG-based biosensor has a specific application in the early identification of diseases. The biosensor investigated in this article is novel, whereas the biosensors that are presently on the market operate using the ionization method. The simulations result shows SLG based biosensor's sensitivity considerably faster than an existing one.

Nanoresonator vibrational behaviour analysis of single- and double-layer graphene with atomic vacancy and pinhole defects

Nanosensors and actuators are frequently made of graphene. Any defect in the graphene's manufacturing has an impact on its sensing performance and on its dynamic behaviour. Using a molecular dynamics technique, the influence of pinhole defects and atomic defects on the performance parameters of single-layer graphene sheets (SLGSs) and double-layer graphene sheets (DLGSs) with various boundary conditions and lengths is explored. In contrast to the perfect nanostructure of a graphene sheet, defects are described as holes formed by atomic vacancies. As the number of defects increases, the simulation results show that the presence of defects has the greatest impact on the resonance frequency of SLGSs and DLGSs. The influence of pinhole defect (PD) and atomic vacancy defect (AVD) on armchair, zigzag, and chiral SLGSs and DLGSs was investigated in this article using molecular dynamics simulation. The influence of both types of defects is largest when it is adjacent to the fixed support for all three different types of graphene sheets, i.e. armchair, zigzag, and chiral. The structure of the graphene sheet has been created using ANSYS APDL software. In the structure of the graphene sheet, atomic and pinhole defects have been generated. SLG and DLG sheets are modelled using a space frame structure that is identical to a three-dimensional beam. Dynamic analysis of single-layer and double-layer graphene sheets performed with different lengths using the atomistic finite element method. The interlayer separation in the form of Van der Waals interaction is modelled using characteristic spring element (Combin14). The upper and lower sheets of DLGSs are described as elastic beams connected by a spring element. With atomic vacancy defect for the bridged boundary condition, the highest frequency of 2.86 × 108 Hz was found for zigzag DLG (20 0) and with same boundary condition for pinhole defect 2.79 × 108 Hz frequency achieved. In a single-layer graphene sheet with an atomic vacancy and cantilever boundary condition, the maximum efficiency was 4.13 × 103 Hz for SLG (20 0), while in a pinhole defect, it produced 2.73 × 107 Hz. Moreover, the elastic parameters of beam components are calculated using the mechanical properties of covalent bonds between carbon atoms in the hexagonal lattice. The model has been tested against previous research. The focus of this research is to develop a mechanism for determining how defects affect graphene frequency band in application as nano resonators.

Effect of Mass on the Dynamic Characteristics of Single- and Double-Layered Graphene-Based Nano Resonators.

Graphene has been widely and extensively used in mass sensing applications. The present study focused on exploring the use of single-layer graphene (SLG) and double-layer graphene (DLG) as sensing devices. The dynamic analysis of SLG and DLG with different boundary conditions (BDs) and length was executed using the atomistic finite element method (AFEM). SLG and DLG sheets were modelled and considered as a space–frame structure similar to a 3D beam. Spring elements (Combin14) were used to identify the interlayer interactions between two graphene layers in the DLG sheet due to the van der Waals forces. Simulations were carried out to visualize the behavior of the SLG and DLG subjected to different BDs and when used as mass sensing devices. The variation in frequency was noted by changing the length and applied mass of the SLGs and DLGs. The quantity of the frequency was found to be highest in the armchair SLG (6, 6) for a 50 nm sheet length and lowest in the chiral SLG (16, 4) for a 20 nm sheet length in the bridged condition. When the mass was 0.1 Zg, the frequency for the zigzag SLG (20, 0) was higher in both cases. The results show that the length of the sheet and the various mass values have a significant impact on the dynamic properties. The present research will contribute to the ultra-high frequency nano-resonance applications.

Predicting tensile properties of monolayer white graphene involving edge effect

Elastic properties of monolayer h-BN nanosheet, also known as white graphene, involving edge effect are systematically studied by the atomic finite element method. By carrying out a uniaxial tensile test along zigzag and armchair directions, respectively, the corresponding stress–strain curves of various types of h-BN nanosheets can be obtained by the first-order derivative of potential with respect to the strain. Consequently, zigzag and armchair Young’s moduli of h-BN nanosheets can be extracted from stress to strain curves in the small strain range which mainly follows a linear relationship. The results demonstrate that zigzag edge can always bear a slightly larger stress than armchair edge. As the size increases, both zigzag and armchair Young’s moduli decrease and get close to each other. This phenomenon indicates an isotropy material of h-BN nanosheets which is also verified by an analytical model. From a systemic study of various h-BN nanosheets, it is found that zigzag edge atoms have a distinctly increasing effect on elastic properties while armchair edge atom show a slight decreasing effect.

Revealing Mechanical Strength of Nanopores Using Atomic Finite Element Techniques

Graphene nanopore has been widely employed in nanofilter or nanopore devices due to its outstanding properties. The understanding of its mechanical properties at nanoscale is crucial for device improvement. In this work, the mechanical properties of graphene nanopore is thus investigated using atomistic finite element method (AFEM). Four graphene models with different pore shapes (circular (CR), horizontal rectangle (RH), and vertical rectangle (RV)) in sub-nm size which could be successfully fabricated experimentally have been studied here. The force normal to a pore surface is applied to mimic the impact force due to a fluid flow. Increasing pore size results in the reduction in its strength. Comparing among different pore shapes with comparable sizes, the order of pore strength is CR>RH>RV>SQ. In addition, we observe that the direction of pore alignment and geometries of pore edge also play a key role in mechanical strength of nanopores.

Revealing the Effects of Pore Size and Geometry on the Mechanical Properties of Graphene Nanopore Using the Atomistic Finite Element Method

Graphene nanopore has been extensively employed in nanoscale sensing devices due to its outstanding properties. The understanding of its mechanical properties at nanoscale is crucial for sensing improvement. In this work, the mechanical properties of graphene nanopore are thus investigated using the atomistic finite element method. Four graphene models with different pore shapes (circle (CR), horizontal rectangle (RH), vertical rectangle (RV) and square (SQ)) in sub-5nm size, which could be successfully fabricated experimentally, have been studied here. The force normal to a pore rim is applied to mimic the impact force due to a fluid flow. As expected, the strength of nanoholed graphene is pore size dependent. Increasing pore size results in the reduction in its strength. Comparing between different pore shapes with comparable sizes, the order of pore strength is $$\hbox {CR}>\hbox {RH}>\hbox {RV}>\hbox {SQ}$$ . In addition, two different corner structures (V-like or zigzag and C-like or armchair corners) are observed, where the V-like structure causes higher tensile stress. Besides, we find that the highest tensile stress is produced at the corner in all cases. This finding suggests the corners as an origin of pore fracture. The results of RH and RV highlight the impact of a direction of pore orientation on mechanical properties. Aligning a long side of a pore along the zigzag direction gains more tensile stress, while aligning on an armchair side causes a deflection. Not only the pore geometry and size, but also the pore orientation is crucial for defining the mechanical properties of nanopores.

Phonon-interference resonance effects by nanoparticles embedded in a matrix

We report an unambiguous phonon resonance effect originating from germanium nanoparticles embedded in silicon matrix. Our approach features the combination of phonon wave-packet method with atomistic dynamics and finite element method rooted in continuum theory. We find that multimodal phonon resonance, caused by destructive interference of coherent lattice waves propagating through and around the nanoparticle, gives rise to sharp and significant transmittance dips, blocking the lower-end frequency range of phonon transport that is hardly diminished by other nanostructures. The resonance is sensitive to the phonon coherent length, where the finiteness of the wave packet width weakens the transmittance dip even when coherent length is longer than the particle diameter. Further strengthening of transmittance dips are possible by arraying multiple nanoparticles that gives rise to the collective vibrational mode. Finally, it is demonstrated that these resonance effects can significantly reduce thermal conductance in the lower-end frequency range.

Simulation of mechanical performance of nanoporous FCC copper under compression with pores mimicking several crystalline arrays

The mechanical performance of porous metal with assembly of pores mimicking typical crystalline structures is studied via atomistic simulation and finite element method. The pore lattices are made with the same orientation as the face-centered cubic (FCC) copper lattice. The compression is applied in the [0 0 1] direction. Under the same initial porosity and identical pore size, pores assembled in diamond array result in a superior stress response under compression. The sample with pores assembled in body-centered cubic array, whose surface-to-volume ratio is close to that of either FCC or hexagonally close-packed (HCP) array, has a yet much higher yield stress. However, the FCC- and HCP-structured nanoporous samples exhibit a greater hardening effect. The Lubarda model for critical stress to trigger dislocation emission is extended to the nanoporous geometry numerically. The magnitude and distribution of shear stress on the slip plane are found crucial to dislocation activities. No strong correlation between dislocation formation and early densification of nanoporous geometry is found. Through comparing the yielding and hardening behavior among differently structured nanoporous samples, new understanding could be established on their mechanical performance. Enhanced structural integrity could better support their diverse applications by design.

THE SIZE EFFECT IN MECHANICS PROPERTIES OF BORON NITRIDE NANOTUBE UNDER TENSION

This work aimed at investigating the mechanicals properties of boron nitride nanotubes (BN-NTs) under uniaxial tension using atomic finite element method with Tersoff potential. The zigzag and armchair nanotubes with different length and diameter are considered for researching effect on mechanicals behavior of BN-NTs. It is found that Young’s modulus of BN-NTs are independent of the tubular length, but slightly increase when the diameter go rise. At the given strain, axial stress in the armchair tubes is higher than that in the zigzag ones.

Piezoelectric effects in boron nitride nanotubes predicted by the atomistic finite element method and molecular mechanics

We calculate the tensile and shear moduli of a series of boron nitride nanotubes and their piezoelectric response to applied loads. We compare in detail results from a simple molecular mechanics (MM) potential, the universal force field, with those from the atomistic finite element method (AFEM) using both Euler–Bernoulli and Timoshenko beam formulations. The MM energy minimisations are much more successful than those using the AFEM, and we analyse the failure of the latter approach both qualitatively and quantitatively.

The Logarithmic finite element method in a multigrid setting

AbstractThe Logarithmic finite element (“LogFE”) method is a novel finite element approach for solving boundary‐value problems proposed in [1]. In contrast to the standard Ritz‐Galerkin formulation, the shape functions are given on the logarithmic space of the deformation function, which is obtained by the exponentiation of the linear combination of the shape functions given by the degrees of freedom.Unlike many existing multigrid formulations, the LogFE method allows for a very smooth interpolation between nodal values on the coarse grid. It can thus avoid problems with regard to locking and convergence that appear in multigrid applications using only linear interpolation, especially for larger corsening factors.We illustrate the use of the LogFE method as a coarse grid algorithm, in conjunction with an atomistic finite element method on the fine grid, for calculating the mechanical response of super carbon nanotubes. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Elastic properties of nanocomposite materials: influence of carbon nanotube imperfections and interface bonding

The paper at hand investigates degradation of elastic properties of a composite material reinforced by carbon nanotubes. Sources of degradation are waviness of a nanotube, vacancies and 5-7-7-5 defects. The manuscript aims to establish the computational procedure based on the atomistic finite element method for estimation of elastic properties by accounting for these defects. An epoxy nanocomposite with typical properties is selected and carefully analysed. Special attention is devoted to proper simulation of van der Waals forces at the matrix-nanotube interface. A series of numerical experiments with different waviness ratios and type of defects is performed and based on these results interpolation of elastic properties is carried out. It is found that proper modelling of van der Waals interactions and waviness has a profound influence on the mechanical behaviour of the nanocomposite, while the other type of defects are of secondary importance.

Nonlinear dynamics of bi-layered graphene sheet, double-walled carbon nanotube and nanotube bundle

Due to strong van der Waals (vdW) interactions, the graphene sheets and nanotubes stick to each other and form clusters of these corresponding nanostructures, viz. bi-layered graphene sheet (BLGS), double-walled carbon nanotube (DWCNT) and nanotube bundle (NB) or ropes. This research work is concerned with the study of nonlinear dynamics of BLGS, DWCNT and NB due to nonlinear interlayer vdW forces using multiscale atomistic finite element method. The energy between two adjacent carbon atoms is represented by the multibody interatomic Tersoff–Brenner potential, whereas the nonlinear interlayer vdW forces are represented by Lennard-Jones 6–12 potential function. The equivalent nonlinear material model of carbon–carbon bond is used to model it based on its force–deflection relation. Newmark’s algorithm is used to solve the nonlinear matrix equation governing the motion of the BLGS, DWCNT and NB. An impulse and harmonic excitations are used to excite these nanostructures under cantilevered, bridged and clamped boundary conditions. The frequency responses of these nanostructures are computed, and the dominant resonant frequencies are identified. Along with the forced vibration of these structures, the eigenvalue extraction problem of armchair and zigzag NB is also considered. The natural frequencies and corresponding mode shapes are extracted for the different length and boundary conditions of the nanotube bundle.

The Elastic Property of Bulk Silicon Nanomaterials through an Atomic Simulation Method

This paper reports a systematic study on the elastic property of bulk silicon nanomaterials using the atomic finite element method. The Tersoff-Brenner potential is used to describe the interaction between silicon atoms, and the atomic finite element method is constructed in a computational scheme similar to the continuum finite element method. Young’s modulus and Poisson ratio are calculated for[100],[110], and[111] silicon nanowires that are treated as three-dimensional structures. It is found that the nanowire possesses the lowest Young’s modulus along the[100] direction, while the[110] nanowire has the highest value with the same radius. The bending deformation of[100] silicon nanowire is also modeled, and the bending stiffness is calculated.

Atomistic Finite Element Modeling and Analysis of pinholes in Double Walled Carbon Nanotube based mass sensor

This paper deals with studying the mass sensing characteristics of defective Double Walled carbon Nanotubes (DWCNT) using atomistic finite element method. Simulations are performed on chiral, zigzag and armchair nanotubes with cantilever and bridged conditions using molecular structure mechanics approach. Carbon nanotubes are widely used in the design of nano sensors, nanoresonators and actuators. In this manuscript the authors have categorized defects like larger vacancies termed as pinhole into two types i.e. 6 missing atoms (A type) and 24(B Type) missing atoms on the outer wall of DWCNT. DWCNTs are modeled considering the weak van der waals force of attraction between the inner and outer tubes as a spring element (COMBIN14). The simulation results indicate that the resonant frequency of defective DWCNT reduces with the increase in chiral angle. The simulation results indicate fundamental frequency reduces with the increase in the number of pinhole defects in DWCNT. The maximum frequency reduction takes place when the defect is located nearer to the fixed end of DWCNT which signifies that position of the defect is an important parameter to judge the mass sensing characteristics of DWCNTs.

Vibration characteristics of open- and capped-end single-walled carbon nanotubes using multi-scale analysis technique incorporating Tersoff–Brenner potential

This research work addresses questions on the vibration characteristics of single-walled carbon nanotubes (SWCNTs) using multi-scale analysis. Atomistic finite element method (AFEM) is one such multi-scale technique where sequential mode is used to transfer information between two length scales to model and simulate the nanostructures at continuum level. This method is used to investigate the vibration characteristics of SWCNTs. Open- and capped-end armchair and zigzag nanotubes are considered with clamped-free and clamped–clamped boundary conditions. The dependence of vibration characteristic of SWCNTs on their length, diameter and atomic structure is also demonstrated. The body interatomic Tersoff–Brenner (TB) potential is used to represent the energy between two carbon atoms. Based on the TB potential, a new set of force constant parameters is established for carbon nanotubes and presented in this paper. Molecular and structural mechanics analogy is used to find the equivalent geometric and elastic properties of the space frame element to represent the carbon–carbon bond. To validate the vibration results of AFEM incorporating the proposed new set of force constants, molecular dynamics simulation is also carried out on the same structure of carbon nanotube, and it is found that they are in good agreement with each other.

Vibration analysis of single-walled carbon nanocones using multiscale atomistic finite element method incorporating Tersoff–Brenner potential

This research work addresses the free and forced vibration characteristics of single-walled carbon nanocones (SWCNCs) using multiscale atomistic finite element method (AFEM) incorporating Tersoff–Brenner (TB) potential. The multibody interatomic TB potential is used to represent the energy between two carbon atoms. Based on the TB potential, new set of force constant parameters is established for carbon nanocones, and the equivalent geometric and elastic properties of the space frame element to represent carbon–carbon bond are derived which are consistent with the material constitutive relations. The eigenvalues of clamped and cantilevered SWCNCs with different disclination angles are extracted using AFEM, and the effect of these angles on the resonant frequencies is investigated. A computational sine sweep test is carried out on the atomic structure of SWCNCs within the frequency range of 0–10 THz to investigate the steady-state forced vibration response under harmonic excitation. The frequency response of the SWCNCs to the cyclic and impulse load over an applied frequency range is calculated. Based on the forced vibration response spectra, the resonant frequency components of SWCNCs are identified. The results have been validated using molecular dynamics simulation.

Determination of Elastic Properties of Hexagonal Sheets by Atomistic Finite Element Method

Determination of Elastic Properties of Hexagonal Sheets by Atomistic Finite Element Method

Multiscale nonlinear frequency response analysis of single-layered graphene sheet under impulse and harmonic excitation using the atomistic finite element method

The atomistic finite element method (AFEM) is a multiscale technique where a sequential mode is used to transfer information between two length scales to model and simulate nanostructures at the continuum level. This method is used in this paper to investigate the nonlinear frequency response of a single-layered graphene sheet (SLGS) for impulse and harmonic excitation. The multi-body interatomic Tersoff–Brenner (TB) potential is used to represent the energy between two adjacent carbon atoms. Based on the TB potential, the equivalent geometric and elastic properties of carbon–carbon bonds are derived which are consistent with the material constitutive relations. These properties are used further to derive the nonlinear material model (stress–strain curve) of carbon–carbon bonds based on the force–deflection curve using the multi-body interatomic Tersoff–Brenner potential. A square SLGS is considered and its nonlinear vibration characteristics under an impulse and harmonic excitation for bridged, cantilever and clamped boundary conditions are investigated using the derived nonlinear material model (NMM). Before using the proposed nonlinear material model, the derived equivalent geometric and elastic properties of carbon–carbon bond are validated using molecular dynamics simulation results. The geometric (large deformation) and material nonlinearities are included in the nonlinear frequency response analysis. The investigated results of the nonlinear frequency response analysis are compared with those of the linear frequency response analysis, and the effect of the nonlinear behavior of carbon–carbon bonds on the frequency response of SLGS is studied.

Influence of atomic vacancies on the dynamic characteristics of nanoresonators based on double walled carbon nanotube

The dynamic analysis of double walled carbon nanotubes (DWCNTs) with different boundary conditions has been performed using atomistic finite element method. The double walled carbon nanotube is modeled considering it as a space frame structure similar to a three dimensional beam. The elastic properties of beam element are calculated by considering mechanical characteristics of covalent bonds between the carbon atoms in the hexagonal lattice. Spring elements are used to describe the interlayer interactions between the inner and outer tubes caused due to the van der Waals forces. The mass of each beam element is assumed as point mass at nodes coinciding with carbon atoms at inner and outer wall of DWCNT. It has been reported that atomic vacancies are formed during the manufacturing process in DWCNT which tend to migrate leading to a change in the mechanical characteristics of the same. Simulations have been carried out to visualize the behavior of such defective DWCNTs subjected to different boundary conditions and when used as mass sensing devices. The variation of such atomic vacancies in outer wall of Zigzag and Armchair DWCNT is performed along the length and the change in response is noted. Moreover, as CNTs have been used as mass sensors extensively, the present approach is focused to explore the use of zigzag and armchair DWCNT as sensing device with a mono-atomic vacancy in it. The results clearly state that the dynamic characteristics are greatly influenced by defects like vacancies in it. A higher frequency shift is observed when the vacancy is located away from the fixed end for both Armchair as well as zigzag type of CNTs. A higher frequency shift is reported for armchair CNT for a mass of 10−22g which remains constant for 10−21g and then decreases gradually. Comparison with the other experimental and theoretical studies exhibits good association which suggests that defective DWCNTs can further be explored for mass sensing. This investigation is helpful in applications involving ultra high frequency nanoresonators which contain one or the other type of manufacturing defects in it.