Molecular Dynamics Finite Element Research Articles

A study on mechanical properties of 1H-type crystalline nickel ditelluride

We used the molecular dynamic finite element method with Stillinger-Weber potential to study the mechanical behavior of monolayer 1H-type nickel ditelluride (1H-NiTe2) sheets under uniaxial tension. As the size of the pristine 1H-NiTe2 sheet increases, the Young’s modulus in the armchair direction increases by 6.2 %, while that in the zigzag one decreases by 6.0 %. Both tend to be size-independent in larger sheets and approach the same value at around 54 N/m. The ultimate stress in the armchair direction remains almost unchanged but that in the zigzag one reduces by about 9.5 % as the size inclines. Besides the influence of size, our results show that single vacancy defects strongly affect the ultimate stress and strain while having no effect on Young’s modulus and Poisson’s ratio. When a Te atom is missing at the sheet’s center, the ultimate stress in the armchair direction is reduced by 11.7 %, while a decrease of 16.0 % is caused by a Ni atom vacancy

Fracture behavior dependent on crack-tip shapes in nanoscale crack-defect monolayer boron nitride sheets

ABSTRACT Nanoscale defects, including cracks, circular holes, and the triangular-shaped defects, often occur in the growth of boron nitride nanosheets (BNNS). In this study, the fracture behavior of chiral BNNS with different crack-tip shapes and the interactions of nanoscale crack-defects are studied using molecular dynamics (MD) simulations and finite element (FE) analysis. Both MD and FE results indicate that the fracture strength of BNNS with two crack tips (t = 2) is significantly higher than that with one crack tip (t = 1), in which the difference in zigzag (ZZ) direction is more obvious than that in armchair (AC) direction, mainly due to the fact that the change of bond angles near the crack tips is more substantial in the ZZ direction than those in the AC direction. Our results show that the fracture strength of BNNS strongly depends on crack-tip shapes, chiral angles, the defect-to-crack tip spacing and deflection angles. Checking against the current MD simulations and FE analysis shows the present results are reasonable. This study should be of great importance for enhancing the fracture performance of BNNS by modulating their crack-tip shapes and the interactions of nanoscale crack-defects.

Finite element analysis and molecular dynamics simulations of nanoscale crack-hole interactions in chiral graphene nanoribbons

Nanoscale defects (such as cracks, holes) often occur in graphene nanoribbons (GNRs). However, it is still a big challenge to accurately predict crack-hole interactions in them. In this study, the nanocale crack-hole interactions in chiral GNRs are investigated under mode-I loading using molecular dynamics (MD) simulations and finite element (FE) analysis. The carbon-carbon (CC) bond in the FE method is modeled as a nonlinear Timoshenko beam based on the full-atom Reactive Empirical Bond-Order interatomic potential of second generation (REBO potential) for the first time. The present MD and FE results show that the shielding effects on the crack tip stress field are dominated by the angle is θ, the hole-to-crack tip spacing r and the chirality of the GNRs. Checking against the linear-elastic fracture mechanics (LEFM) predictions of some crack-hole configurations shows that the present FE method and MD simulations have high accuracy. This study should be of great help for understanding nanoscale crack-hole interactions in GNRs and providing physical insights into the origins of defect engineering of GNRs.

Mechanical properties of epoxy/boehmite nanocomposites in dependency of mass fraction and surface modification - An experimental and numerical approach

Boehmite nanoparticles show great potential in improving the matrix dominated mechanical properties of fiber reinforced polymers. For the material design process and the prediction of the nanocomposite's properties, knowledge about the material behavior of the constituent phases and their interactions is crucial. Since the chemical composition of the particle surface can strongly affect the interaction between particle and matrix, the influence of particle surface modification and mass fraction on mechanical properties (tensile modulus, tensile strength, fracture toughness) and failure mechanisms of nanoparticle reinforced epoxy resins is investigated using experimental and numerical methods. In the present work, unmodified and thus chemically reactive boehmite particles are compared to acetic acid modified particles with supposedly lower chemical reactivity and thus worse particle-matrix bonding. A linear relationship between particle mass fraction and tensile modulus/fracture toughness is experimentally found with a maximum increase of 26% in tensile modulus and 62% in critical energy release rate for a particle content of 15 wt%. Furthermore, the experiments indicate that the acetic acid surface modification increases the tensile modulus (up to 6% compared to the unmodified boehmite particles), but at the same time not significantly affects the tensile strength or the fracture toughness. Molecular Dynamic Finite Element Method (MDFEM) simulations are conducted to identify and understand the mechanisms induced by nanoparticles. The material properties of both, modified and unmodified, nanoparticle systems are discussed in relation to the change of particle-matrix bonding strength and interphase morphology. While simulation results of the unmodified system show an outstanding agreement with the experiments, the acetic acid modified system deviates significantly. In conclusion, it seems that additional effects have to be considered to completely understand the material behavior.

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.

Uniaxial deformation of polystyrene–silica nanocomposites studied by hybrid molecular dynamics–finite element simulations

This contribution investigates, based on molecular dynamics (MD), the mechanical deformation behavior of polystyrene-silica nanocomposites and focuses on the influence of micromechanical properties as e.g. filler particle size and filler mass fraction. With regard to simulations of macroscopic problems with system sizes not capable by pure MD approaches, our investigations are complemented by hybrid molecular dynamics – finite element (MD-FE) simulations. Our computational approach shows that an increasing total interfacial area between the nanoparticles and the polymer matrix stiffens the nanocomposite. As expected, small nanoparticles have more significant impact on the macroscopic mechanical properties of nanocomposites than large ones. We show that, for the same mass fraction of nanoparticles, the Young’s modulus increases by about 4–5% when the nanoparticle diameter is decreased from 5 to 2nm. Furthermore, we find that: (i) the end-to-end distances of free polymer chains in the vicinity of nanoparticles are larger than in the bulk; (ii) the addition of nanoparticles slows down the global dynamics of free polymer chains; and (iii) the interphase thickness of nanocomposites is about 1–1.5nm. Beyond that, we study structural properties at the microscale under uniaxial tension and find that the presence of nanoparticles hinders the orientation of free polymer chains under deformation. This hindrance is more pronounced for small nanoparticles and high mass fractions. Polymer structural descriptors as the chain end-to-end vector and a molecular anisotropy parameter largely change in line with the geometrical transformation of the whole sample.

Mechanical Properties of Boehmite Evaluated by Atomic Force Microscopy Experiments and Molecular Dynamic Finite Element Simulations

Boehmite nanoparticles show great potential in improving mechanical properties of fiber reinforced polymers. In order to predict the properties of nanocomposites, knowledge about the material parameters of the constituent phases, including the boehmite particles, is crucial. In this study, the mechanical behavior of boehmite is investigated using Atomic Force Microscopy (AFM) experiments and Molecular Dynamic Finite Element Method (MDFEM) simulations. Young’s modulus of the perfect crystalline boehmite nanoparticles is derived from numerical AFM simulations. Results of AFM experiments on boehmite nanoparticles deviate significantly. Possible causes are identified by experiments on complementary types of boehmite, that is, geological and hydrothermally synthesized samples, and further simulations of imperfect crystals and combined boehmite/epoxy models. Under certain circumstances, the mechanical behavior of boehmite was found to be dominated by inelastic effects that are discussed in detail in the present work. The studies are substantiated with accompanying X-ray diffraction and Raman experiments.

A concurrent multi-scale technique in modeling heterogeneous FCC nano-crystalline structures

In this paper, a multi-scale molecular dynamics–finite element coupling is presented to study the mechanical behavior of heterogeneous nano-crystalline structures. The stiffness and mass matrices of the continuum sub-domain are generated by applying a linear transformation on the matrices obtained via the atomic structure underlying the FE mesh. A Lagrange multiplier method is employed to the transition zone imposing velocity resemblance of the coupling regions. The constraint equations of motion are solved by the multi-time-step decomposition thus giving the opportunity to ascribe different time steps to each individual zone. The molecular dynamics is performed by employing the Sutton–RafiiTabar many body potential (Raffi-Tabar and Sutton, 1991) for FCC metallic alloys, and its integrity is attained by calculating the effective lattice parameter of different random alloys by minimizing the general form of Sutton–RafiiTabar interatomic potential energy. The authenticity and accuracy of the renovated concurrent scheme is remarkably acquired by comparing some numerical results of the proposed multi-scale model to those of implemented and validated molecular dynamics.

The role of defects in the tensile properties of silicene

Effects of vacancies and Stone–Wales defects on the mechanical properties of silicene are investigated through molecular dynamic finite element method with Tersoff potential. Young’s modulus, Poisson’s ratio and uniaxial tensile stress–strain curves are considered in the armchair and zigzag directions. It is found that pristine and lowly defective silicene sheets exhibit almost the same elastic nature up to fracture points. However, a single defect weakens significantly the silicene sheet, resulting in a considerable reduction in the fracture strength. One 2-atom vacancy in the sheet’s center reduces 18–20 % in fracture stress and 33–35 % in fracture strain. The weakening effects of Stone–Wales defects vary with the tensile direction and the orientation of these defects.

A coupled mechanical‐charge/dipole molecular dynamics finite element method, with multi‐scale applications to the design of graphene nano‐devices

SUMMARYA new Molecular Dynamics Finite Element Method (MDFEM) with a coupled mechanical‐charge/dipole formulation is proposed. The equilibrium equations of Molecular Dynamics (MD) are embedded exactly within the computationally more favourable Finite Element Method (FEM). This MDFEM can readily implement any force field because the constitutive relations are explicitly uncoupled from the corresponding geometric element topologies. This formal uncoupling allows to differentiate between chemical‐constitutive, geometric and mixed‐mode instabilities. Different force fields, including bond‐order reactive and polarisable fluctuating charge–dipole potentials, are implemented exactly in both explicit and implicit dynamic commercial finite element code. The implicit formulation allows for larger length and time scales and more varied eigenvalue‐based solution strategies.The proposed multi‐physics and multi‐scale compatible MDFEM is shown to be equivalent to MD, as demonstrated by examples of fracture in carbon nanotubes (CNT), and electric charge distribution in graphene, but at a considerably reduced computational cost. The proposed MDFEM is shown to scale linearly, with concurrent continuum FEM multi‐scale couplings allowing for further computational savings. Moreover, novel conformational analyses of pillared graphene structures (PGS) are produced. The proposed model finds potential applications in the parametric topology and numerical design studies of nano‐structures for desired electro‐mechanical properties (e.g. stiffness, toughness and electric field induced vibrational/electron‐emission properties). Copyright © 2014 John Wiley & Sons, Ltd.

Computation of thermal properties of a copper–copper nano interface structure using a MD–ISE–FE method

A multiscale modeling method is put forward to investigate the interfacial characteristic of copper nano interface structures. The ISE (Interface Stress Element) method is set as a coupling button to a span-scale model combined with MD (Molecular Dynamics) and FE (Finite Element) methods. Those three methods are effectively coupled by MD–ISE and ISE–FE handshake regions. The thermal properties of copper nano structures are investigated by using this multiscale model. The results show that the accuracy of the MD–ISE–FE model is better than that of MD–FE model; the thermal resistance decreases with the temperature increase. Compared with the MD–FE model, the MD–ISE–FE multiscale model can provide better accuracy to investigate the interface prosperities for MEMS design and manufacturing.

An atomic-continuum multiscale modeling approach for interfacial thermal behavior between materials

The aim of this paper is to provide a systematic method to perform interfacial thermal behavior between materials. A multiscale modeling method is proposed to investigate the interfacial thermal properties about copper nano interface structure. The interface stress element (ISE) method is set as a coupling button to a span-scale model combined with molecular dynamics (MD) and finite element (FE) methods. The handshake regions can simulate the structure transfer properties between the transition with MD and ISE, ISE and FE. The multiscale model is used to calculate the interfacial thermal characters under different temperatures. Some examples about numerical experiments with copper materials demonstrate the performance of MD–ISE–FE multiscale model is more successful compared with the approach applying MD–FE model. The results indicate that the accuracy of the MD–ISE–FE model is higher than that of MD–FE mode. This investigation implies a potential possibility of multiscale analysis from atomic to continuum scales.

A multiscale MD–FE model of diffusion in composite media with internal surface interaction based on numerical homogenization procedure

Mass transport by diffusion within composite materials may depend not only on internal microstructural geometry, but also on the chemical interactions between the transported substance and the material of the microstructure. Retrospectively, there is a gap in methods and theory to connect material microstructure properties with macroscale continuum diffusion characteristics. Here we present a new hierarchical multiscale model for diffusion within composite materials that couples material microstructural geometry and interactions between diffusing particles and the material matrix. This model, which bridges molecular dynamics (MD) and the finite element (FE) method, is employed to construct a continuum diffusion model based on a novel numerical homogenization procedure. The procedure is general and robust for evaluating constitutive material parameters of the continuum model. These parameters include the traditional bulk diffusion coefficients and, additionally, the distances from the solid surface accounting for surface interaction effects. We implemented our models to glucose diffusion through the following two geometrical/material configurations: tightly packed silica nanospheres, and a complex fibrous structure surrounding nanospheres. Then, rhodamine 6G diffusion analysis through an agarose gel network was performed, followed by a model validation using our experimental results. The microstructural model, numerical homogenization and continuum model offer a new platform for modeling and predicting mass diffusion through complex biological environment and within composite materials that are used in a wide range of applications, like drug delivery and nanoporous catalysts.

An Arlequin-based method to couple molecular dynamics and finite element simulations of amorphous polymers and nanocomposites

A new simulation technique is introduced to couple a flexible particle domain as encountered in soft-matter systems and a continuum which is solved by the Finite Element (FE) method. The particle domain is simulated by a molecular dynamics (MD) method in coarse grained (CG) representation. On the basis of computational experiences from a previous study, a staggered coupling procedure has been chosen. The proposed MD–FE coupling approximates the continuum as a static region while the MD particle space is treated as a dynamical ensemble. The information transfer between MD and FE domains is realized by a coupling region which contains, in particular, additional auxiliary particles, so-called anchor points. Each anchor point is harmonically bonded to a standard MD particle in the coupling region. This type of interaction offers a straightforward access to force gradients at the anchor points that are required in the developed hybrid approach. Time-averaged forces and force gradients from the MD domain are transmitted to the continuum. A static coupling procedure, based on the Arlequin framework, between the FE domain and the anchor points provides new anchor point positions in the MD–FE coupling region. The capability of the new simulation procedure has been quantified for an atactic polystyrene (PS) sample and for a PS-silica nanocomposite, both simulated in CG representation. Numerical data are given in the linear elastic regime which is conserved up to 3% strain. The convergence of the MD–FE coupling procedure has been demonstrated for quantities such as reaction forces or the Cauchy stress which have been determined both in the bare FE domain and in the coupled system. Possible applications of the hybrid method are shortly mentioned.

An adaptive FE–MD model coupling approach

This contribution introduces an adaptively coupled finite element (FE)–molecular dynamics (MD) model based on the Quasicontinuum (QC) method. The idea for obtaining constitutive laws from the underlying lattice structure (local QC model) will be discussed in detail. The outline of the formulation for the quasi-static MD model (nonlocal QC model) will also be derived in the same mathematical structure. A new type of element is proposed to solve the boundary problems and to couple the FE and MD models. The interpolation techniques for the atomic stress and strain fields are introduced. A two-step adaptive mechanism is applied to the multiscale model, including the mesh refinement step for the FE model and the FE–MD conversion step. A 3D nanoindentation example is used for demonstrating accuracy and the efficiency of the coupled FE–MD model at the end.

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

AbstractThe 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.

Multiscale modeling of intergranular fracture in aluminum: constitutive relation for interface debonding

Intergranular fracture is a dominant mode of failure in ultrafine grained materials. In the present study, the atomistic mechanisms of grain-boundary debonding during intergranular fracture in aluminum are modeled using a coupled molecular dynamics—finite element simulation. Using a statistical mechanics approach, a cohesive-zone law in the form of a traction–displacement constitutive relationship, characterizing the load transfer across the plane of a growing edge crack, is extracted from atomistic simulations and then recast in a form suitable for inclusion within a continuum finite element model. The cohesive-zone law derived by the presented technique is free of finite size effects and is statistically representative for describing the interfacial debonding of a grain boundary (GB) interface examined at atomic length scales. By incorporating the cohesive-zone law in cohesive-zone finite elements, the debonding of a GB interface can be simulated in a coupled continuum–atomistic model, in which a crack starts in the continuum environment, smoothly penetrates the continuum–atomistic interface, and continues its propagation in the atomistic environment. This study is a step toward relating atomistically derived decohesion laws to macroscopic predictions of fracture and constructing multiscale models for nanocrystalline and ultrafine grained materials.

A coupled MD–FE approach for contact at microscopic length–scales (Poster Presentation)

AbstractContact at very tiny length–scales is characterized by atomic force interaction. A technical application of interest is the atomic force microscope (AFM). A coupled molecular dynamics (MD) – finite element (FE) approach is outlined to tackle the multi–scale problem by numerical simulation. Guidelines for the spatial discretization are derived from convergence studies. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Multiscale simulation on nanometric cutting of single crystal copper

Molecular dynamics (MD) simulation and finite element (FE) method have been successfully applied in the simulation of the machining process, but the two methods have their own limitations. For example, the MD simulation can only explain the phenomena occurring at nanometric scale because of the computational cost and nanoscale, while the FE method is suited to model meso-macroscale machining and to simulate macro parameters such as the temperature in cutting zone, the stress/strain distribution, and cutting forces. With the successful application of multiscale simulation in many research fields, the multiscale simulation of the machining process is becoming possible in relation to the machined surface generation including the surface roughness, residual stress, microhardness, microstructure, and fatigue. Based on the quasicontinuum (QC) method, this paper presents the multiscale simulation of nanometric cutting of crystal copper to demonstrate that a combined MD—FE technique can be applied to a multiscale simulation of the machining process. The study shows that the multiscale simulation is feasible, not withstanding that there is still more work needing to be done to make the multiscale simulation more practical.

A scheme for hybrid molecular dynamics/finite element analysis of thin film lubrication

Impressive strides have recently been made in the field of tribology through molecular dynamics (MD) simulations. A convergence of MD and experiment has led to optimism in scientific circles that the mechanisms of friction and boundary lubrication, studied for centuries, can soon be understood and predicted by first principles. However, from the engineering point of view, practical predictive ability seems far away. Toward the eventual goal of applying MD analysis to practical tribological design, we propose a hybrid molecular dynamics–finite element method. Similar approaches have been used in simulating dislocations and other defects in crystalline solids under nano-indenting, and in simulation of reacting flows. In our preliminary study, linkage to MD is established through a variable effective viscosity which increases near the surfaces due to molecular forces. Preliminary results are presented showing an increase in pressure due to the presence of nearby surfaces.