Capturing nanoscale effects by peridynamics

Molecular dynamic simulations inevitably demand large computational resources for structures of liner measures even as small as a few tens or hundreds of nanometers. Thus, a computationally efficient method to simulate larger structures and, at the same time, retain the properties and the mechanical response at the atomic scale is in demand. One such approach is peridynamics, which is a nonlocal extension of continuum mechanics. In this study, we investigate the possibility to efficiently reproduce results from molecular dynamic (MD) simulations by calibration of two parameters inherent in peridynamics: the length scale parameter and the interparticle bond strength. The free-ware LAMMPS supports both numerical approaches, and thus LAMMPS has been used as the common framework. Beams of single-crystal fcc copper of various sizes and under tension along the crystallographic [100]- and [110]-directions act as the modeling example. The force–displacement curves and the elastic–plastic transitions have been compared between the approaches. The conclusion is that proper calibration of the peridynamic two parameters to MD simulations results in proper reproduction of the molecular dynamic results. This in turn allows for geometrical upscaling or simulation of geometrically more complicated structures, without loss of features derived from the atomic scale but to a much lower computational cost.     

Probabilistic Analysis and Design of HCP Nanowires:An Efficient Surrogate Based Molecular Dynamics Simulation Approach

We investigate the dependency of strain rate,temperature and size on yield strength of hexagonal close packed(HCP) nanowires based on large-scale molecular dynamics(MD) simulation.A variance-based analysis has been proposed to quantify relative sensitivity of the three controlling factors on the yield strength of the material.One of the major drawbacks of conventional MD simulation based studies is that the simulations are computationally very intensive and economically expensive.Large scale molecular dynamics simulation needs supercomputing access and the larger the number of atoms,the longer it takes time and computational resources.For this reason it becomes practically impossible to perform a robust and comprehensive analysis that requires multiple simulations such as sensitivity analysis,uncertainty quantification and optimization.We propose a novel surrogate based molecular dynamics(SBMD)simulation approach that enables us to carry out thousands of virtual simulations for different combinations of the controlling factors in a computationally efficient way by performing only few MD simulations.Following the SBMD simulation approach an efficient optimum design scheme has been developed to predict optimized size of the nanowire to maximize the yield strength.Subsequently the effect of inevitable uncertainty associated with the controlling factors has been quantified using Monte Carlo simulation.Though we have confined our analyses in this article for Magnesium nanowires only,the proposed approach can be extended to other materials for computationally intensive nano-scale investigation involving multiple factors of influence.     

A theoretical investigation of thermal effects on vibrational behaviors of single-walled carbon nanotubes

Thermal effects on the vibrational behaviors and dynamic Young’s modulus of single-walled carbon nanotubes (SWCNTs) are investigated through both constant temperature molecular dynamics (MD) simulation and modified molecular structural mechanics (MMSM) modeling. The MD simulation incorporates a modified Nosé-Hoover thermostat model to control the system temperature. In the MMSM modeling, the covalent and nonbonded interactions between carbon atom pairs are modeled with the second generation force field and the Lennard-Jones potential, respectively, where the covalent bonds are treated as Euler-Bernoulli beam and the temperature-dependent bond length and angle are determined through the Badger’s rule and MD simulation. The results derived from these two approaches are compared with each other and the published theoretical and experimental data. Results show that the dynamic Young’s modulus of the SWCNTs tends to be smaller than the published static one obtained from uniaxial tensile tests, and their natural frequency and dynamic Young’s modulus would decrease with increasing temperature. Moreover, a comparable frequency ratio of the first two flexural modes is achieved by these two approaches. The frequency ratio is highly dependent on their aspect ratio but independent of temperature, and would converge to the literature experimental data (about 6.1-6.2) as the aspect ratio becomes very large.     

Stochastic homogenization of nano-thickness thin films including patterned holes using structural perturbation method

The aim of this paper is to investigate the statistical response of the homogenized mechanical behavior of nano-thickness thin films with circular holes. For this purpose, a stochastic multiscale framework is proposed. The proposed framework involves molecular dynamics simulation, surface modeling, asymptotic homogenization, moving-mesh technique, Monte-Carlo simulation, and a reduced computational scheme. The surface effect of thin-film material is predicted by the molecular dynamics (MD) approach. The volume fraction and location of each circular hole are considered as geometric uncertainties of a model. In order to investigate the statistical response of the homogenized mechanical behavior, Monte-Carlo simulation is performed to show the probability density distribution of the homogenized elastic modulus against geometric uncertainties. The reduced computational schematic based on the static reduction method and the structural perturbation method is proposed in order to overcome the issues of a cumbersome remeshing procedure and computational inefficiency of Monte-Carlo simulations involving a high number of repetitive trials. A guideline to minimize the coefficient of variation (CV) of the mechanical properties is suggested based on the parametric study.     

Computer simulations for the design of microstructural developments in ceramics

This paper is to study the computer simulation of microstructural developments in ceramics mainly by Monte Carlo (MC) model and partly by molecular dynamics (MD). Plural mechanisms of mass transfer were introduced in the MC simulation of sintering and grain growth in ceramics at micron-size particle. The MC simulations were performed at the array of two-dimensional triangular lattices and were developed to sintering and grain growth in the complex systems involving a liquid phase and the second solid phase. The MD simulation was applied to the sintering of nano-size particles of ionic ceramics and showed the characteristic features in sintering process at atomic levels. The MC and MD simulations for sintering process are useful for microstructural design for ceramics.     

包装材料中化学物质迁移分子动力学模拟研究进展

概述了分子动力学模拟的基本原理及其应用方法,在此基础上,综述了分子动力学模拟在高阻隔包装材料、缓释包装材料、高性能聚合包装材料中化学物质迁移的研究现状,并提出分子动力学技术在包装材料化学物质迁移方面未来的应用方向:深入研究模型处于缺陷状态、复杂环境下的建模方法,不断完善迁移模型库,采用更高性能的计算机来构建更大分子量的模型,以验证和改进模型并提供更多的物性数据,得到一些极限条件或实验无法实现情况下的信息。     

An embedded statistical method for coupling molecular dynamics and finite element analyses

The coupling of molecular dynamics (MD) simulations with finite element methods (FEM) yields computationally efficient models that link fundamental material processes at the atomistic level with continuum field responses at higher length scales. The theoretical challenge involves developing a seamless connection along an interface between two inherently different simulation frameworks. Various specialized methods have been developed to solve particular classes of problems. Many of these methods link the kinematics of individual MD atoms with finite element (FE) nodes at their common interface, necessarily requiring that the FE mesh be refined to atomic resolution. Some of these coupling approaches also require simulations to be carried out at 0 K and restrict modelling to two‐dimensional material domains due to difficulties in simulating full three‐dimensional material processes. In the present work, a new approach to MD–FEM coupling is developed based on a restatement of the standard boundary value problem used to define a coupled domain. The method replaces a direct linkage of individual MD atoms and FE nodes with a statistical averaging of atomistic displacements in local atomic volumes associated with each FE node in an interface region. The FEM and MD computational systems are effectively independent and communicate only through an iterative update of their boundary conditions. Thus, the method lends itself for use with any FEM or MD code. With the use of statistical averages of the atomistic quantities to couple the two computational schemes, the developed approach is referred to as an embedded statistical coupling method (ESCM). ESCM provides an enhanced coupling methodology that is inherently applicable to three‐dimensional domains, avoids discretization of the continuum model to atomic scale resolution, and permits finite temperature states to be applied. Published in 2009 by John Wiley & Sons, Ltd.     

Toward a predictive atomistic model of ion implantation and dopant diffusion in silicon

We review the development and application of kinetic Monte Carlo simulations to investigate defect and dopant diffusion in ion implanted silicon. In these types of Monte Carlo models, defects and dopants are treated at the atomic scale, and move according to reaction rates given as input parameters. These input parameters can be obtained from first principles calculations and/or empirical molecular dynamics (MD) simulations or can be extracted from fits to experimental data. Time and length scales differing several orders of magnitude can be followed with this method, allowing for direct comparison with experiments. The different approaches are explained and some results presented.     

A study on the prediction of the mechanical properties of nanoparticulate composites using the homogenization method with the effective interface concept

A sequential multi‐scale homogenization method combined with molecular dynamics (MD) simulation is developed for the mechanical characterization of nanoparticulate composites. In order to characterize the particle‐size effect of nanocomposites, the effective interface, which has been adopted in continuum micromechanics approaches, is considered as the characteristic phase. Owing to the existence of the interface and the size‐dependent elastic modulus that is observed from MD simulations, an analysis of the mechanical properties of nanocomposites with continuum micromechanics requires careful consideration of the particle‐concentration effect. Therefore, this study focuses on hierarchical information transfer from the molecular model to the continuum model through the homogenization method in lieu of an analytical micromechanics bridging method. Using the present multi‐scale homogenization method, the elastic properties of the effective interface are numerically evaluated and compared with the analytically obtained micromechanics solutions. In addition, the overall elastic modulus of nanocomposites is obtained from the present model and compared with the results of MD simulation, the micromechanics bridging model, and finite‐element analysis (FEA). Copyright © 2010 John Wiley & Sons, Ltd.     

Modeling of radiation hardening in ferritic/martensitic steel using multi-scale approach

Fe-Cr based ferritic/martensitic (FM) steels are the candidate structural materials for future fusion reactors. In this work, a multi-scale approach comprising atomistic and dislocation dynamic simulations are used to understand the hardening of these materials due to irradiation. At the atomic scale, molecular dynamics (MD) simulations are used to study the mobility of an edge dislocation and its interaction with irradiation induced voids and bubbles. The dislocation dynamics (DD) simulations are used to estimate the change in flow stress of the material as a result of irradiation hardening. The key input to the DD simulations are the friction stress and maximum shear stress for the edge dislocation to overcome the defects as determined from atomistic simulations. The results obtained from the MD and DD simulations are in qualitative agreement with experimental results of hardening behavior of irradiated FM steels.     

Molecular dynamics and atomistic based continuum studies of the interfacial behavior of nanoreinforced epoxy

In this study, we investigate the interfacial mechanical characteristics of carbon nanotube (CNT) reinforced epoxy composite using molecular dynamics (MD) simulations. The second-generation polymer consistent force field (PCFF) is used in the MD simulations. In particular, we compare MD results with those obtained by atomistic-based continuum (ABC) multiscale modeling technique, which makes use of the appropriate constitutive relations derived solely from interatomic potentials. The results of our comparative investigation suggest that (i) the ABC multiscale model and MD simulation provides almost identical predictions for the interfacial properties of the nanocomposite for smaller diameter of CNTs, (ii) the ABC model slightly over predict the interfacial properties of the nanocomposite for larger diameter of CNTs, and (iii) the MD simulations represents the real nanocomposite structure with the minimum assumptions compared to that of the ABC multiscale model but with much greater computer requirements and limited length scale.     

杜仲胶/天然橡胶共混物的分子动力学模拟和耗散粒子动力学模拟

应用分子动力学(MD)和耗散粒子动力学(DPD)模拟方法对杜仲胶(TPI)、天然橡胶(NR)的相容性进行了研究。采用MD模拟方法,在COMPASS力场下,对纯物质在不同聚合度下的溶度参数、一系列共混比的TPI/NR共混物内聚能密度、Flory-Huggins作用参数进行了模拟计算,确定了纯物质单链的聚合度,经判断各比例共混物的相容性均较好;采用DPD模拟方法对TPI/NR共混体系的相结构进行了研究,从等密度图可以进一步判断共混体系的相容性;分析比较两种纯物质的径向分布函数,揭示了其相互作用的本质;经过分析比较静态力学性能,发现共混比为1/3的TPI/NR共混物性能最佳,其结论与实验结果一致。     

The Molecular Dynamic Finite Element Method (MDFEM)

In order to understand the underlying mechanisms of inelastic material behavior and nonlinear surface interactions, which can be observed on macroscale as damping, softening, fracture, delamination, frictional contact etc., it is necessary to examine the molecular scale. Force fields can be applied to simulate the rearrangement of chemical and physical bonds. However, a simulation of the atomic interactions is very costly so that classical molecular dynamics (MD) is restricted to structures containing a low number of atoms such as carbon nanotubes. The objective of this paper is to show how MD simulations can be integrated into the finite element method (FEM) which is used to simulate engineering structures such as an aircraft panel or a vehicle chassis. A new type of finite element is required for force fields that include multi-body potentials. These elements take into account not only bond stretch but also bending, torsion and inversion without using rotational degrees of freedom. Since natural lengths and angles are implemented as intrinsic material parameters, the developed molecular dynamic finite element method (MDFEM) starts with a conformational analysis. By means of carbon nanotubes and elastomeric material it is demonstrated that this pre-step is needed to find an equilibrium configuration before the structure can be deformed in a succeeding loading step.     

Optimization approach in variable-charge potential for metal/metal oxide systems

Earlier attempts on minimizing the total system energy of metal/metal oxide systems with given charge constraints appear to be indirect and unnecessarily complicated. The energy minimization problem is in fact a constrained optimization problem and hence can be solved by a constrained optimization method. We propose a new direct approach for finding charge distributions among ions in molecular dynamics simulations. The approach is based on an optimization algorithm, called the Generalized Reduced Gradient (GRG) Method. This efficient approach can be readily employed in molecular dynamic simulations for metal/metal oxide systems.     

Hybrid molecular dynamics–finite element simulations of the elastic behavior of polycrystalline graphene

In this paper, we develop an efficient multiscale molecular dynamics (MD)–finite element (FE) modeling scheme capable of determining the elastic and fracture properties of polycrystalline graphene. The local elastic properties of a grain boundary (GB) connecting two adjacent graphene grains, with different lattice orientations, were first determined using MD simulations. In a two-dimensional medium, randomly distributed grains connected with GBs were then created using the Voronoi tessellation method. The constructed Voronoi diagrams were used to create FE models of the polycrystalline graphene, where the GBs were represented by interphase regions with their local properties determined using MD. The grains were modeled as pristine graphene and the accuracy of the polycrystalline FE model was validated with MD simulations of a geometrically identical polycrystalline graphene. The results reveal good agreement between MD and FE simulations. They further show that the elastic and fracture properties of polycrystalline graphene are greatly influenced by the grain size and the misorientation angle. They also indicate that the predicted elastic properties are in agreement with earlier reported experimental and MD results. We believe that this newly proposed multiscale scheme could be easily integrated into current design software to model graphene based nano- and micro-devices.     

Molecular dynamics simulation of asphalt-aggregate interface adhesion strength with moisture effect

This study developed an atomistic simulation framework based on the classical molecular dynamics (MD) method to study the moisture-induced damage at the asphalt-aggregate interface. The interface adhesion strength of the asphalt–quartz system was predicted using MD simulation for the first time. The interface stress-separation curve under tension that was obtained from MD simulation resembles the failure behaviour measured from the pull-off strength conducted at the macroscopic scale. The results show that the presence of moisture at the asphalt–quartz interface significantly reduces the interface adhesion strength. The interface failure process is affected by the chemical compositions of asphalt. The interface adhesion strength decreases as the moisture content increases or the temperature increases. It was found that the atomistic model size (number of atoms) and the loading rate in MD simulation have considerable effects on the predicted interface adhesion strength. The findings from MD simulation provide fundamental understanding of material failure at the atomistic scale that cannot be observed at the normal experimental testing environment for asphalt materials. The MD simulation results can be potentially calibrated and utilised as inputs for higher scale micromechanical models to predict bulk mechanical responses of asphalt mixtures.     

A new approach to production regularity assessment in the oil and chemical industries

This article presents a new approach to production regularity assessment in the oil and chemical industries. The production regularity is measured by the throughput capacity distribution. A brief survey of some existing techniques is presented, and the structure of the new approach is introduced. The proposed approach is based on analytical methods, i.e. no simulation is necessary. The system modeling is split into three levels: components, basic subsystems, and merged subsystems, and two modeling methods are utilized: Markov modeling and a rule-based method. The main features of the approach are as follows: (1) short calculation time; (2) systems of dependent components can be modeled; (3) maintenance strategies can be modeled; and (4) a variety of system configurations can be modeled. A simple case study is used to demonstrate how the proposed approach can be applied.     

The Topology Sampling of H2SO4·NH3 with Meta-Dynamics Method

The configurations of molecular clusters have significant impacts on their growth into fine particles in atmosphere. In this paper, we explore the topology space of the structure of H2SO4·NH3 dimer with a novel sampling technique of meta-dynamics (MTD) method and ab initio molecular dynamics simulations. The simulations are carried out at the temperatures of both 50 K and 242 K, which represent the typical high and low latitudes of troposphere. The results show that, compared with only traditional MD simulations, the structure samplings are significantly accelerated with MTD method. Therefore, more isomers of the dimer are discovered within the same simulation time scale. In addition, the results show that MTD is more efficient for circumstances with high temperature.     

Predictive multiscale theory for design of heterogeneous materials

A general multiscale theory for modeling heterogeneous materials is derived via a nested domain based virtual power decomposition. Three variations on the theory are proposed; a concurrent approach, a simplified hierarchical approach and a statistical power equivalence approach. Deformation at each scale of analysis is solved either (a) by direct numerical simulation (DNS) of the microstructure or (b) by higher order homogenization of the microstructure. If the latter approach is chosen, a set of multiscale homogenized constitutive relations must be derived. This is demonstrated using a computational cell modeling technique for a four scale metal alloy. In each variation of the theory, a transfer of information occurs between the scales giving a coupled formulation. The concurrent approach achieves a more comprehensive coupling than the hierarchical approach, making it more accurate for dynamic fast time scale simulations. The power equivalence approach is strongly coupled and is useful for performing larger scale simulations as the expensive multiple scale DNS boundary value problems are replaced with statistical higher order continua. Furthermore, these continua may be solved on a single spatial discretisation using an extended finite element framework, making the theory applicable within existing high performance computing codes. Submitted to a Special Issue of Computational Mechanics in Honor of Professor Ladeveze’s 60th Birthday.     

Nonlinear Dynamic Behavior of Granular Materials in Base Excited Silos

Nonlinear behavior of granular materials stored in steel silos subjected to dynamic base excitation due to earthquake is presented in the current article. Three-dimensional finite element (FE) modeling of the granular material silo is carried out under three-directional earthquake ground acceleration time histories. Granular material is modeled by adopting a continuum approach. The nonlinearity of the granular materials is represented by a hypoplastic material law in the FE approximation. The interface between the granular material and the silo wall is modeled by using surface-to-surface based contact formulation. The horizontal and vertical displacements of the granular material under earthquake ground acceleration at various depths of the silo are studied. Moreover, the stresses induced in the steel silo are also investigated. The static FE simulation and the analytical solution obtained by using Janssen's theory are observed to be in close agreement. Also, the dynamic FE simulations compare with the calculated results using Eurocode 8 part 4 with reasonable accuracy. The stresses in the steel silo wall are higher for loose packing of the granular material as compared to that for the dense packing.