Multiple time scale method for atomistic simulations

A novel multiple time scale approach is proposed which combines dynamic and static atomistic methods in one numerical simulation. The method is especially effective for modeling processes that consist of two distinct phases: the slow phase when atomic equilibrium positions barely change and the fast phase associated with a rapid change of the system’s configuration. In this case, the slow phase can be effectively modeled using static energy minimization while molecular dynamics (MD) can be applied when specific dynamic effects have to be captured. Compared to direct MD simulations, the new method allows for computational cost savings, and eventually simulation timescale extension, since the major part of the simulation can be modeled as static, without the need to follow vibrations of individual atoms and comply with the critical time step requirement of molecular dynamics. As a result, this approach may allow for modeling loading velocities and strain rates that are more realistic than those currently attainable through direct MD simulations. The fundamental issues in developing this method include the correlation between the MD time scale and quasi-static step-like procedure as well as finding effective criteria for switching between the static and dynamic regimes. The method was inspired by and is applied to simulations of atomic-scale stick-slip friction. Possible applications of the new method to other nano-mechanical problems are also discussed.     

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.     

多场耦合作用下流变液悬浮性态仿真与分析

仿真分析了磁场和剪切场作用下双分散、单分散磁流变液的微观结构演化,从4个方面考察了磁流变液悬浮性态：微观结构相变,链长分布,聚合结构各向异性和悬浮粒子运动涨落。结果表明,在磁场作用下,场强幅值越高,相态迁移的时间越短、簇-墙相越明显;在低磁场时,双分散悬浮较单分散悬浮容易形成长链,而在中、高磁场时,单分散悬浮却较双分散悬浮容易形成长链;磁极粒子具有智能特性,在无剪切场作用下总是寻找最易形成墙的方向排列成簇,而在稳态剪切作用下沿流场方向形成通长墙相以抑制流场的输运;外加磁场有助于减小悬浮粒子的运动涨落,但在剪切场的引导作用下,磁场强度的变化对悬浮粒子运动涨落无明显影响。     

First-principles simulations of removal process in EEM (Elastic Emission Machining)

Interactions between ultra-fine powder [SiO₂] and work [Si (1 0 0) surface] in EEM (Elastic Emission Machining) has been investigated by employing first-principles molecular dynamics (MD) simulations. Calculated results show the possibilities of the atomic removal through the solid phase chemical interaction between surfaces of ultra-fine powders and works.     

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.     

Effect of surface morphology and temperature on the structural stability of nanoscale wavy films

The atomic scale structural stability of freestanding wavy gold (Au) nanofilms was investigated using molecular dynamics simulations. The waviness in the Au film was formed by cleaving sinusoidal surfaces from a [Formula: see text] bulk crystal. The degree of waviness was varied by changing the wavelength of the sinusoidal surface profile. Films were then equilibrated at different temperatures (between 10 and 1080?K) and their structural stability was monitored. The MD simulation results revealed that the stability of films depends on temperature as well as the waviness of the film surface. It was shown that the size-dependent melting point depression of Au plays the dominant role in causing the structural instability of wavy films.     

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.     

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.     

Molecular dynamics simulations of consolidation processes during fabrication of nanophase palladium

Consolidation processes during fabrication of nanophase palladium from atom clusters are simulated using molecular statics (MS), molecular dynamics (MD), and a potential from the emebedded atom ,ethod (EAM). The MD simulations are conducte3d under conditions similar experimental conditions, i.e., at room temperature (300 K) and under compressive pressures of 10–50 kbar (1–5 GPa). Several dynamic phenomena have been observed during the simulations, such as “neck” formation, surface rounding, void formation and shrinking, and cluster extrusion. The effect of applied compressive pressures on the final structures of nanophase materials during considation is demonstrated.     

Silica–silane coupling agent interphase properties using molecular dynamics simulations

In this paper, strength of the interphase between silica and glycidoxypropyltrimethoxy silane (GPS) coupling agent has been studied using molecular dynamics (MD) simulations. Silica–GPS interphase model is created by coupling the hydroxylated silica surface with monolayer-hydroxylated GPS molecules. The interphase model is subjected to mode-I (normal), mode-II (shear) and mixed-mode (normal–shear) mechanical loading to determine the interphase cohesive traction–separation (T–S) response (i.e., cohesive traction law). In MD simulations, atomic interactions are modeled with the reactive force field ReaxFF. Effects of interphase thickness and GPS bond density on the T–S response are studied. Simulation results indicate that interphase strength decreases with increase in the interphase thickness before attaining a plateau level at higher thickness. For a particular thickness, strength improves significantly with increase in the GPS bond density with the silica surface. Damage mode is adhesive at the silica interface at lower thickness and transitions to mixed mode and cohesive failure within the silane interphase at higher thickness. Mixed-mode T–S responses are bounded by the mode-I and mode-II responses. Characteristic parameters of the continuum-level potential-based cohesive zone model (PPR–CZM) are determined by fitting the MD-based mode-I and mode-II T–S responses with PPR–CZM functional. Development of the PPR–CZM parameters enables bridging length scales from the MD to the continuum scale for fracture modeling of the fiber–matrix interphase in composites subjected to mixed-mode loading. Results on mode-I and mode-II unloading are also presented.     

Large-scale molecular dynamics simulation of DNA: implementation and validation of the AMBER98 force field in LAMMPS

Molecular modelling played a central role in the discovery of the structure of DNA by Watson and Crick. Today, such modelling is done on computers: the more powerful these computers are, the more detailed and extensive can be the study of the dynamics of such biological macromolecules. To fully harness the power of modern massively parallel computers, however, we need to develop and deploy algorithms which can exploit the structure of such hardware. The Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) is a scalable molecular dynamics code including long-range Coulomb interactions, which has been specifically designed to function efficiently on parallel platforms. Here we describe the implementation of the AMBER98 force field in LAMMPS and its validation for molecular dynamics investigations of DNA structure and flexibility against the benchmark of results obtained with the long-established code AMBER6 (Assisted Model Building with Energy Refinement, version 6). Extended molecular dynamics simulations on the hydrated DNA dodecamer d(CTTTTGCAAAAG)(2), which has previously been the subject of extensive dynamical analysis using AMBER6, show that it is possible to obtain excellent agreement in terms of static, dynamic and thermodynamic parameters between AMBER6 and LAMMPS. In comparison with AMBER6, LAMMPS shows greatly improved scalability in massively parallel environments, opening up the possibility of efficient simulations of order-of-magnitude larger systems and/or for order-of-magnitude greater simulation times.     

Computational modelling of irregular open‐cell foam behaviour under impact loading

Cellular structures represent an important class of engineering materials. Typical representative of such structures are metallic foams, which are being increasingly used in many advanced engineering applications due to their low specific weight, appropriate mechanical properties and excellent energy absorption capacity. For optimal design of cellular structures it is necessary to develop proper computational models for use in computational simulations of their behaviour under impact loading. The paper studies the effects of open‐cell metallic foam irregularity on deformation behaviour and impact energy absorption during impact loading by means of parametric computational simulations, using the lattice‐type modelling of open‐cell material structure. The 3D Voronoi technique is used for the reproduction of real, irregular open‐cell structure of metallic foams. The method uses as a reference a regular mesh structure and utilises an irregularity parameter to reproduce the irregularity of real open‐cell structure. A smoothing technique is introduced to assure proper stability and accuracy of explicit dynamic simulations using the produced lattice models. The effects of the smoothing technique were determined by comparative simulations of smoothed and unsmoothed lattices subjected to dynamic loading.     

Elastic crack propagation model for crystalline solids using a self-consistent coupled atomistic–continuum framework

Deformation and failure processes of crystalline materials are governed by complex phenomena at multiple scales. It is necessary to couple these scales for physics-based modeling of these phenomena, while overcoming limitations of modeling at individual scales. To address this issue, this paper develops self-consistent elastic constitutive and crack propagation relations of crystalline materials containing atomic scale cracks, from observations made in a concurrent multi-scale simulation system coupling atomistic and continuum domain models. The concurrent multi-scale model incorporates a finite temperature atomistic region containing the crack, a continuum region represented by a self-consistent crystal elasticity constitutive model, and a handshaking interphase region. Atomistic modeling is done by the molecular dynamics code LAMMPS, while continuum modeling is conducted by the finite element method. For single crystal nickel a nonlinear and nonlocal crystal elasticity constitutive relation is derived, consistent with the atomic potential function. An efficient, staggered solution scheme with parallel implementation is designed for the coupled problem. The atomistic–continuum coupling is achieved by enforcing geometric compatibility and force equilibrium in the interphase region. Quantitative analyses of the crack propagation process focuses on size dependence, strain energy release rate, crack propagation rate and degradation of the local stiffness. The self-consistent constitutive and crack propagation relations, derived from the concurrent model simulation results are validated by comparing results from the concurrent and full FE models. Excellent accuracy and enhanced efficiency are observed in comparison with pure MD and concurrent model results.     

Molecular dynamics calculation of the J-integral fracture criterion for nano-sized crystals

The critical J-integral is recognized as a valuable criterion for evaluating elastic-plastic fracture behavior of materials. It is, however, computationally complicated at the atomic scale for a nano-sized crystal when using the traditional integral method to reckon the traction force, strain, strain energy, etc. atom by atom. This paper attempts to propose an effective J-integral calculation method based on molecular dynamics (MD) simulations. The proposed method takes advantage of the potential energy interpretation of the J-integral, the main task in which is to calculate the potential energy difference of two identical crystal models with the neighboring crack length. As the potential energy of crystals at the atomic scale can be obtained easily from molecular dynamics simulations, the proposed method is thus computationally simple and especially applicable to complex crystal structures. A nickel crystal having an opening model I crack is investigated using this method. The critical J-integral in the ductile fracture plane (1\bar10) is calculated to be 4.424 Jm^–2. It is also found in this study that the onset of crack propagation does not coincide with the occurrence of the maximum tension stress for nano-sized crystals, which is different from conventional fracture mechanics observation.     

Voronoi‐based peridynamics and cracking analysis with adaptive refinement

The most common technique for the numerical implementation of peridynamic theory is the uniform discretization together with constant horizon. However, unlike the nonuniform discretization and varying horizons, it is not a natural and intrinsic component of the adaptive refinement analysis and multiscale modeling. Besides, it encounters discretization difficulty in analyzing irregular structures. Therefore, to analyze problems with nonuniform discretization and varying horizons and solve the resulting problems of ghost forces and spurious wave reflection, the dual‐horizon peridynamics based on uniform discretization is extended to the nonuniform discretization based on Voronoi diagrams, for which we call it Voronoi‐based peridynamics. We redefine the damage definition as well. Next, an adaptive refinement analysis method based on the proposed Voronoi‐based peridynamics and its numerical implementation is introduced. Finally, the traditional bond‐based peridynamics and the Voronoi‐based peridynamics with or without refinement are used to simulate 4 benchmark problems. The examples of 2‐D quasi‐static elastic deformation, 2‐D wave propagation, 2‐D dynamic crack growth, and 3‐D simulation of the Kalthoff‐Winkler experiment demonstrate the efficiency and effectivity of the proposed Voronoi‐based peridynamics. Further, the adaptive refinement analysis can be used to obtain reasonable crack path and crack propagation speed with reduced computational burden.     

Tight-binding molecular-dynamics study of a copper oxide Cu4O

The empirical tight-binding molecular dynamic simulations of Cu₄O are performed. It is shown that the atomic and electronic structure can be calculated reasonably with this kind of TB model and repulsive potentials used in this paper. The calculated structures are in good agreement with the results obtained by atomic resolution electron microscope.     

On the effective elastic moduli of carbon nanotubes for nanocomposite structures

A critical review on the validity of different experimental and theoretical approaches to the mechanical properties of carbon nanotubes for advanced composite structures is presented. Most research has been recently conducted to study the properties of single-walled and multi-walled carbon nanotubes. Special attention has been paid to the measurement and modeling of tensile modulus, tensile strength, and torsional stiffness. Theoretical approaches such as molecular dynamic (MD) simulations, finite element analysis, and classical elastic shell theory were frequently used to analyze and interpret the mechanical features of carbon nanotubes. Due to the use of different fundamental assumptions and boundary conditions, inconsistent results were reported. MD simulation is a well-known technique that simulates accurately the chemical and physical properties of structures at atomic-scale level. However, it is limited by the time step, which is of the order of 10⁻¹⁵ s. The use of finite element modeling combined with MD simulation can further decrease the processing time for calculating the mechanical properties of nanotubes. Since the aspect ratio of nanotubes is very large, the elastic rod or beam models can be adequately used to simulate their overall mechanical deformation. Although many theoretical studies reported that the tensile modulus of multi-walled nanotubes may reach 1 TPa, this value, however, cannot be directly used to estimate the mechanical properties of multi-walled nanotube/polymer composites due to the discontinuous stress transfer inside the nanotubes.     

Oligomer Dynamics of LL-37 Truncated Fragments Probed by α-Hemolysin Pore and Molecular Simulations

Oligomerization of antimicrobial peptides (AMPs) is critical in their effects on pathogens. LL-37 and its truncated fragments are widely investigated regarding their structures, antimicrobial activities, and application, such as developing new antibiotics. Due to the small size and weak intermolecular interactions of LL-37 fragments, it is still elusive to establish the relationship between oligomeric states and antimicrobial activities. Here, an α-hemolysin nanopore, mass spectrometry (MS), and molecular dynamic (MD) simulations are used to characterize the oligomeric states of two LL-37 fragments. Nanopore studies provide evidence of trapping events related to the oligomer formation and provide further details on their stabilities, which are confirmed by MS and MD simulations. Furthermore, simulation results reveal the molecular basis of oligomer dynamics and states of LL-37 fragments. This work provides unique insights into the relationship between the oligomer dynamics of AMPs and their antimicrobial activities at the single-molecule level. The study demonstrates how integrating methods allows deciphering single molecule level understanding from nanopore sensing approaches.     

Proper orthogonal decomposition‐based model order reduction via radial basis functions for molecular dynamics systems

Model order reduction for molecular dynamics (MD) systems exhibits intrinsic complexities because of the highly nonlinear and nonlocal multi‐atomic interactions in high dimensions. In the present work, we introduce a proper orthogonal decomposition‐based method in conjunction with the radial basis function (RBF) approximation of the nonlinear and nonlocal potential energies and inter‐atomic forces for MD systems. This approach avoids coordinate transformation between the physical and reduced‐order coordinates, and allows the potentials and inter‐atomic forces to be calculated directly in the reduced‐order space. The RBF‐approximated potential energies and inter‐atomic forces in the reduced‐order space are discretized on the basis of the Smolyak sparse grid algorithm to further enhance the effectiveness of the proposed method. The good approximation properties of RBFs in interpolating scattered data make them ideal candidates for the reduced‐order approximation of MD inter‐atomic force calculations. The proposed approach is validated by performing the reduced‐order simulations of DNA molecules under various external loadings. Copyright © 2013 John Wiley & Sons, Ltd.