Atomistic-continuum Model Research Articles

Two-dimensional graphyne monolayers as substrate discs of piezoelectric nanogenerators: A hybrid atomistic-continuum model study

The different phases of α-, β-, and γ-graphyne, which are new types of two-dimensional carbon allotropes, hold promise as potential candidates for designing substrate discs in piezoelectric nanogenerators. Accurate modeling of the bending rigidity and stretching properties as well as resonance frequencies of these materials is crucial for engineering applications like nano-resonator and nanogenerator systems. This step is imperative in designing and advancing future applications involving these structures. This study aims to create a hybrid atomistic-continuum model for modeling graphyne monolayers used as substrate discs in nanogenerators. The model integrates the benefits of both atomistic and continuum approaches. Based on the results, α-graphyne is the least mechanically stable, while γ-graphyne is the most stable. However, in terms of vibration frequency, α-graphyne has the highest frequency while γ-graphyne has the lowest. Therefore, β-graphyne, with moderate stability and resonance frequency, is recommended as the ideal choice for the substrate disc in piezoelectric nanogenerators. It can function within the Q-F frequency range (30–140 GHz) and induce deformation in the piezoelectric shim as well as generation voltage.

Vibrational analysis of graphyne-based nanoplates using a hybrid nonlocal strain gradient-atomistic simulation model

By employing a hybrid atomistic-continuum model, we can combine the advantages of atomic and continuum models. In this approach, resonance frequencies are matched to those obtained from the continuum model using the size effect and Young’s modulus as fit parameters. Our proposed method examines how radius affects the elastic modulus, size effect parameters, and resonance frequency values of the graphyne family, taking into account both macro and nano-scale models. The non-local strain gradient model has been calibrated to achieve optimal error. In contrast, the error is highest when the non-local strain gradient effect is not considered in the continuum mechanics model.

Молекулярно-динамическое исследование механизмов абляции золота под воздействием ультракоротких лазерных импульсов с использованием различных потенциалов

Using simulation with a continuum-atomistic model, a study of ablation under the action of an ultrashort laser pulse on a metal (Au) was carried out. Three regimes of ablation were studied: supercritical expansion, phase explosion, and mechanical spallation. The results for two EAM potentials of gold are compared. A graph of the dependence of the amount of removed substance on the fluence of laser radiation for two potentials is constructed, followed by comparison with experimental data.

Atomistic modeling of high-speed laser action on thin gold film: determination of main mechnaisms of ablation

The action of an ultrashort laser pulse on a thin gold film was studied using a single-speed nonequilibrium combined continuum-atomistic model, which was further developed in the work. Three ablation modes were studied: supercritical expansion, phase explosion and mechanical spallation. The simulation results are compared with experimental data. The dependence of the amount of removed substance on the fluence of laser radiation was obtained.

A comparative study of polymer viscosity modifiers: Flow field challenges & alternative trends

In recent years, substantial advancements have been achieved in augmenting the energy efficiency of hydraulic fluids through the integration of polymers. This study employs a multiscale approach, encompassing an analysis of polymer coil size evolution and flow field characteristics, with the aim of investigating the behavior of both dipole and non-dipole polymers within the host solvent. The ultimate goal is to establish a comprehensive understanding of the correlation between atomic properties of additives and the macroscopic properties of the polymer solution.To achieve this, the study employs an atomistic-continuum hybrid model that combines Brownian Dynamics and Lattice Boltzmann techniques within the bead-spring concept framework. Four chains, each comprising 64 particles, are subjected to varying shear rates. The primary focus centers on the examination of alterations in the radius of gyration and the velocity field within the polymer solution. Notably, the inclusion of dipole-dipole interactions exerts a profound influence on the configuration of the polymers. The results illuminate that non-dipole polymers display a more pronounced coupling with bulk flow hydrodynamics, leading to the confinement of particle motion in directions perpendicular to the primary stream. In contrast, dipole polymers experience a slower increase in coil size when compared to their non-dipole counterparts. These findings furnish valuable insights for the enhancement of energy-efficient hydraulic fluids and contribute to a fundamental comprehension of polymer behavior in lubricants, charting the course for the development of advanced hydraulic fluids in the future.

Comprehensive scrutiny of surface mechanical parameters of graphyne-based materials for metal-ions and metal-air batteries applications: A perspective and a hybrid atomistic-continuum model

Graphyne family, as a low-dimensional carbon allotrope, is utilized for metal-ion and –air batteries as the anode and cathode materials due to their unique characteristics. These novel carbon nanomaterials can provide more theoretical storage capacity than graphene, while their specific surface mechanical parameters and vibrational frequencies can influence battery performance. However, there needs to be clear information that can explain the effects of these parameters on battery efficiency. In this respect, the influences of the surface elasticity, residual stress, density, vibrational modes, and frequencies of α, β, and γ-graphyne circular monolayers on anode and cathode materials have been investigated in current research using the hybrid molecular dynamics simulation and modified classical continuum mechanics methods. Concerning metal-ion batteries, the results disclose that the suitability sequence for anode materials can be expressed as γ-graphyne > graphene > β-graphyne > α-graphyne monolayers. In the case of metal-air batteries, the competence sequence for cathode materials is in the order of γ-graphyne > β-graphyne ∼ graphene > α-graphyne monolayers. Therefore, γ-graphyne with suitable storage capacity, low volume expansion, good surface elasticity, low surface residual stress, and appropriate specific surface area is the promising anode and cathode material for metal-ion and -air batteries, respectively.

A proposition: feasibility of classical plate theory on bending monolayer graphene

In this paper, we carry out a comparison study between classical plate theory and ‘bottom to top’ atomistic-continuum multiscale model regarding the prediction of bending of monolayer graphene to state the general feasibility of classical plate theory. We replace the commonly used interlayer spacing value by the newly launched intrinsic material thickness value as the monolayer graphene thickness. Based on this correction, we amend the flexural rigidity and find that classical plate theory gives a much better prediction of the force-bending deflection curve for various graphene obtained by the atomistic-continuum multiscale approach. The onset of weak nonlinearity observed by the atomistic-continuum approach is at a midpoint deflection of ∼0.01 nm, approximately 0.14 w/h ratio, which secondarily confirm the feasibility of our newly proposed intrinsic material thickness value. The effect of boundary constraint, graphene size and loading mode on the bending of graphene is discussed to explain the cause of deviation between the two methods, and finally we confirm the feasibility of classical plate theory on bending monolayer graphene.

Визуализационный анализ результатов континуально-атомистического моделирования кулоновского взрыва в металлах под влиянием ультракороткого (fs, ps) лазерного воздействия

A continuum-atomistic model that describes nonequilibrium thermal, hydrodynamic, and electronic processes in metals that occur under the action of ultrashort (fs, ps) laser radiation has been developed. A detailed study of two mechanisms of ultrashort laser ablation of Cu was carried out: fast - Coulomb, determined by Coulomb forces, and slow - thermal, realized in the unloading wave after the end of the laser pulse. Modeling showed that the excess nonequilibrium pressure of collectivized electrons plays a leading role in the formation of a strong electric field at the metal-vacuum interface. This effect can be taken as the basis for the Coulomb explosion in metals. The main feature of the work is the widespread use of modern visualization tools for processing and presenting simulation results.

Atomistic-Continuum Constitutive Modeling Connection for Gold Foams under Compression at High Strain Rates: The Dislocation Density Effect

Constitutive description of the plastic flow in metallic foams has been rarely explored in the literature. Even though the material is of great interest to researchers, its plasticity remains a topic that has a much room for exploration. With the help of the rich literature that explored the material deformation mechanism, it is possible to introduce a connection between the results of the atomistic simulations and the well-established continuum constitutive models that were developed for various loading scenarios. In this work, we perform large-scale atomistic simulations of metallic gold foams of two different sizes at a wide range of strain rates (107−109 s−1) under uniaxial compression. By utilizing the results of those simulations, as well as the results we reported in our previous works, a physical atomistic-continuum dislocations-based constitutive modeling connection is proposed to capture the compressive plastic flow in gold foams for a wide range of sizes, strain rates, temperatures, and porosities. The results reported in this work present curated datasets that can be of extreme usefulness for the data-driven AI design of metallic foams with tunable nanoscale properties. Eventually, we aim to produce an optimal physical description to improve integrated physics-based and AI-enabled design, manufacture, and validation of hierarchical architected metallic foams that deliver tailored mechanical responses and precision failure patterns at different scales.

Modeling laser interactions with aluminum and tantalum targets using a hybrid atomistic-continuum model

A hybrid atomistic-continuum method can model the microstructure evolution of metals subjected to laser irradiation. This method combines classical molecular dynamics (MD) simulations with the two-temperature model (TTM) to account for the laser energy absorption and heat diffusion behavior. Accurate prediction of the temperature evolution in the combined MD-TTM method requires reliable accuracy in electron heat capacity, electron thermal conductivity, and electron–phonon coupling factor across the temperatures generated. This study uses the electronic density of states (DOS) obtained from first-principle calculations. The calculated electron temperature-dependent parameters are used in MD-TTM simulations to study the laser metal interactions in FCC and BCC metals and the phenomenon of laser shock loading and melting. This study uses FCC Al and BCC Ta as model systems to demonstrate this capability. When subjected to short pulsed laser shocks, the dynamic failure behavior predicted using temperature-dependent parameters is compared with the experimentally reported single-crystal and nanocrystalline Al and Ta systems. The MD-TTM simulations also investigate laser ablation and melting behavior of Ta to compare with the ablation threshold reported experimentally. This manuscript demonstrates that integrating the temperature-dependent parameters into MD-TTM simulations leads to the accurate modeling of the laser–metal interaction and allows the prediction of the kinetics of the solid–liquid interface.

Bending and stretching behavior of graphene structures using continuum models calibrated with modal analysis

Two-dimensional nanomaterials exhibit specific mechanical characteristics essential for commercialization and industrial applications, such as nano electro-mechanical systems. When analyzing a mechanical field, it is important to determine these materials' bending stiffness and stretching properties. The apparent bending stiffness and stretching of graphene structures at the macro-scale differ from theoretical predictions at the nano-scale. This discrepancy results from thermally generated dynamic waves in these atomic-based structures. Therefore, characterization methods based on atomistic static methods were unable to capture these effects. This study uses hybrid atomistic-continuum models to apply modal analysis to determine these key parameters. The proposed approach exploits the advantages of both atomistic and continuum models. Our approach is based on optimization techniques such as the simulated annealing algorithm. The unknown parameters of the continuum models, such as the bending stiffness and stretching, were acquired from molecular dynamics simulations and continuum mechanics resonance frequencies. The effects of diameter on the mechanical properties and value of different mode shapes of graphene nanostructures are studied using this method, which incorporates the effects of nano and macro-scale models. The presented approach provides insight into the mechanical vibrational characteristics of two-dimensional graphene structures at an atomic level.

On the hybrid atomistic-continuum model for vibrational analysis of α-, β-, and γ-graphyne circular nano-plates

The natural frequency of graphyne structures for all phases is calculated by molecular dynamics simulation. Tersoff potential function was used in molecular dynamics (MD) simulations. In this paper, the vibration behavior of α-, β-, and γ-graphyne circular nano-plates was investigated using a hybrid atomistic-continuum Model. The MD frequencies are higher than those obtained from the classical local plate model, so the use of the Eringen-nonlocal elasticity model is practically unusable. The obtained equations based on the stress-driven elasticity, modified couple stress theory, and strain gradient theory were solved by generalized differential quadrature rule (GDQR), which has a faster convergence than generalized differential quadrature method (GDQ). The value of the size parameter for each diameter was calculated using the molecular dynamics results. By changing the phase from alpha to beta and beta to gamma, value of stiffness is increased. Therefore, for a smaller size parameter, continuum mechanics results match the molecular dynamics results. The results show that the size effect parameter is not a fixed value and has different values in different conditions. For all three phases and all diameters, the calculated frequencies are greater than those from classical theory. This result shows that the graphyne structure is fantastic and peculiar.

Temperature-dependent multiscale modeling of graphene sheet under finite deformation

The homogenized constitutive models that have been utilized to simulate the behavior of nanostructures are typically based on the Cauchy–Born hypothesis, which seeks the fundamental properties of material via relating atomistic information to an assumed homogeneous deformation field. It is well known that temperature has a profound effect on the validity and size-dependency of the Cauchy-Born hypothesis in finite deformations. In this study, a temperature-related Cauchy–Born formulation is established for graphene sheets and its performance is examined through a direct comparison between the continuum-based constitutive model and molecular dynamics analysis. It is demonstrated that if the temperature increases, the validity surfaces shrink, which is not highly dependent on the size of specimen. At finite strains, graphene sheet exhibits material softening and hardening, which are manifested in the elastic constants. The developed constitutive model is used to study the effect of applied deformations at various temperature levels on the elastic constants of graphene sheets. Finally, a novel multiscale finite element approach is developed for the analysis of graphene sheets in finite strain regime based on the proposed atomistic-continuum model. The method can be used efficiently in the simulation of large specimens where the application of molecular dynamics requires considerable computational efforts. The efficiency and robustness of the proposed multiscale approach are shown through several numerical examples.

Surface- and nonlocality-dependent vibrational behavior of graphene using atomistic-modal analysis

Classical continuum theories are incapable of accurately describing the behavior of nanostructures due to their size dependence. Size-dependent effects such as surface and non-local are among these phenomena, and their study at the nano-scale is essential. Despite advances in modeling and characterization of graphene's material properties, the surface and nonlocality effects of circular graphene nano-plates have not been calibrated for continuum mechanics theories. Based on a hybrid model that combines the advantages of continuum and atomic models, the present study is primarily focused on developing a method for calculating and estimating the effect of these parameters. A non-local surface elasticity model for graphene has been developed using a modal analysis derived from molecular dynamics simulations based on genetic algorithm optimization. In this research, both asymmetric and axisymmetric linear vibrational modes are studied. The parameters of the model, including surface residual stress, surface elasticity, surface density, and size parameter, are extracted from the results of the atomistic modal. Subsequently, this hybrid atomistic-continuum model has been employed to characterize the vibrational behavior of graphene. Based on the conducted simulations, the surface elasticity model with the nonlocality effect is calibrated with the lowest error for all radii and vibration modes. Moreover, this research suggests using a non-local surface elasticity model for very small radii since its findings are remarkably similar to the molecular dynamics simulations for the same diameters. On the other hand, the error is highest for the continuum model that does not incorporate surface and non-local effects. The findings of this study can be valuable in evaluating the crucial parameters regarding the surface and non-local elasticity of two-dimensional structures.

Development of a Hybrid Intelligent Process Model for Micro-Electro Discharge Machining Using the TTM-MDS and Gaussian Process Regression.

This paper proposed a hybrid intelligent process model, based on a hybrid model combining the two-temperature model (TTM) and molecular dynamics simulation (MDS) (TTM-MDS). Combined atomistic-continuum modeling of short-pulse laser melting and disintegration of metal films [Physical Review B, 68, (064114):1–22.], and Gaussian process regression (GPR), for micro-electrical discharge machining (micro-EDM) were also used. A model of single-spark micro-EDM process has been constructed based on TTM-MDS model to predict the removed depth (RD) and material removal rate (MRR). Then, a GPR model was proposed to establish the relationship between input process parameters (energy area density and pulse-on duration) and the process responses (RD and MRR) for micro-EDM machining. The GPR model was trained, tested, and tuned using the data generated from the numerical simulations. Through the GPR model, it was found that micro-EDM process responses can be accurately predicted for the chosen process conditions. Therefore, the hybrid intelligent model proposed in this paper can be used for a micro-EDM process to predict the performance.

Spatiotemporal insights into the femtosecond laser homogeneous and heterogeneous melting aluminum by atomistic-continuum modeling

Spatiotemporal insights into the femtosecond laser homogeneous and heterogeneous melting aluminum by atomistic-continuum modeling

Unfolding the mechanical properties of buckypaper composites: nano- to macro-scale coupled atomistic-continuum simulations

Carbon-based nanostructures are receiving increasing attention over the past two decades due to their unprecedented multi-functional features. However, the macro-scale structural applications of these nanostructures have not yet come to full fruition due to the involvement of complex multi-scale computations and manufacturing. Recently, the research community has started investigating buckypaper, which can be described as a sheet or membrane developed using a network of bundles of single-wall carbon nanotubes, multi-wall carbon nanotubes, or a mixture of both. This article aims to focus on the computational bridging of different length scales involving six levels in the range of nano- to macro-scale behaviour concerning buckypaper composites. The sequential derivatives of carbon at six levels, as analyzed in this paper, involve graphene, CNT, CNT bundle, buckypaper, and buckypaper composite automotive components. Here, we adopt a coupled atomistic-continuum modelling approach for the multi-level simulations. Graphene, CNTs, and CNT bundles are modelled using atomistic simulations, while the buckypaper and its composites are modelled using equivalent beam representations for the bundles and continuum solid representation for resin. At the macro-scale, an industry-relevant multi-material composite automotive component has been investigated, wherein the buckypaper is proposed to be embedded involving sheet moulding compound and carbon prepreg. The current simulations have led to the determination of mechanical properties at each level of the carbon-based materials and their mutual dependence. The numerical results demonstrate that a buckypaper composite can enhance the natural frequency and stiffness up to 25 and 37% with respect to conventional monolithic metallic designs, while reducing the weight by 57%. Such outcomes lead to the realization that carbon-based nanostructural derivative in the form of buckypaper can significantly improve the mechanical properties of advanced lightweight structural components as reinforcements for the next generation of aerospace and automotive structures.Graphical abstract

A continuum–atomistic multi-scale analysis of temperature field problems and its application in phononic nano-structures

In this paper, a novel coupling technique is developed in continuum–atomistic multi-scale analysis of temperature field problems. In this manner, a new thermostat is introduced based on the single-atom sub-system, where its capability to control the temperature and produce the canonical ensemble is investigated. Moreover, the performance of proposed thermostat is verified by comparing the distribution of velocities to the Maxwell-Boltzmann distribution. The single-atom sub-system thermostat is then incorporated into the concurrent multi-scale model to relate the temperature field between the continuum and atomistic domains with complex lattice thermal fields. In order to illustrate the capability of proposed coupling continuum–atomistic model, the multi-scale analysis is performed through several numerical examples at various temperature fields and the results are compared with those obtained from the full atomistic model and finite element simulation. Finally, the continuum–atomistic multi-scale technique is applied in numerical simulation of the lattice heat conduction in two-dimensional phononic nano-structures. • A single-atom sub-system thermostat is developed that presents the canonical ensemble. • The performance of proposed thermostat is verified by comparing the velocities distribution to the Maxwell-Boltzmann distribution. • A concurrent multi-scale technique is presented based on the proposed single-atom thermostat. • The concurrent multi-scale technique is applied to model the lattice heat conduction in phononic nano-structures. • The behavior of thermal decay time is investigated for various model parameters in a phononic crystal.

Key role of surface plasmon polaritons in generation of periodic surface structures following single-pulse laser irradiation of a gold step edge

Abstract Understanding the mechanisms and controlling the possibilities of surface nanostructuring is of crucial interest for both fundamental science and application perspectives. Here, we report a direct experimental observation of laser-induced periodic surface structures (LIPSS) formed near a predesigned gold step edge following single-pulse femtosecond laser irradiation. Simulation results based on a hybrid atomistic-continuum model fully support the experimental observations. We experimentally detect nanosized surface features with a periodicity of ∼300 nm and heights of a few tens of nanometers. We identify two key components of single-pulse LIPSS formation: excitation of surface plasmon polaritons and material reorganization. Our results lay a solid foundation toward simple and efficient usage of light for innovative material processing technologies.

Lattice dislocation induced misfit dislocation evolution in semi-coherent {111} bimetal interfaces

The study of dislocation plasticity mediated by semi-coherent interfaces can aid in the design of certain heterostructured materials, such as nanolaminates. The evolution of interface misfit patterns under complex stress fields arising from dislocation pileups can influence local dislocation/interface interactions, including effects of multiple incoming dislocations. This work utilizes the Concurrent Atomistic-Continuum modeling framework to probe the evolution of misfit structures at semi-coherent Ni/Cu and Cu/Ag interfaces impinged by dislocation pileups generated via nanoindentation. A continuum microrotation metric is computed at various stages of the indentation process and used to visualize the evolution of the interface misfit dislocation pattern. The stress state from approaching dislocations induces mixed contraction and expansion of misfit dislocation structures at the interface. A lower number of misfit nodes per unit interface area coincides with greater localized deformation with regard to atoms near misfit nodes for Ni/Cu. The decreased misfit node spacing for Cu/Ag alternatively distributes the restructuring associated with plastic deformation over a larger percentage of atoms at the interface. Interface sliding facilitated by misfit dislocation motion is found to facilitate deformation extending into the bulk lattices centered on misfit nodes. The depth of penetration of those fields is found to be greater for Ni/Cu than for Cu/Ag. The study of dislocation plasticity mediated by semi-coherent interfaces can aid in the design of certain heterostructured materials, such as nanolaminates. The evolution of interface misfit patterns under complex stress fields arising from dislocation pileups can influence local dislocation/interface interactions, including effects of multiple incoming dislocations. This work utilizes the Concurrent Atomistic-Continuum modeling framework to probe the evolution of misfit structures at semi-coherent Ni/Cu and Cu/Ag interfaces impinged by dislocation pileups generated via nanoindentation. A continuum microrotation metric is computed at various stages of the indentation process and used to visualize the evolution of the interface misfit dislocation pattern. The stress state from approaching dislocations induces mixed contraction and expansion of misfit dislocation structures at the interface. A lower number of misfit nodes per unit interface area coincides with greater localized deformation with regard to atoms near misfit nodes for Ni/Cu. The decreased misfit node spacing for Cu/Ag alternatively distributes the restructuring associated with plastic deformation over a larger percentage of atoms at the interface. Interface sliding facilitated by misfit dislocation motion is found to facilitate deformation extending into the bulk lattices centered on misfit nodes. The depth of penetration of those fields is found to be greater for Ni/Cu than for Cu/Ag.