Academic literature on the topic 'Atomistic-continuum model parameters'

We consider the wetting of water droplets on substrates with different chemical composition and molecular spacing, but with an identical equilibrium contact angle. A combined approach of large-scale molecular dynamics simulations and a continuum phase field model allows us to identify and quantify the influence of the microscopic physics at the contact line on the macroscopic droplet dynamics. We show that the substrate physico-chemistry, in particular hydrogen bonding, can significantly alter the flow. Since the material parameters are systematically derived from the atomistic simulations, our continuum model has only one adjustable parameter, which appears as a friction factor at the contact line. The continuum model approaches the atomistic wetting rate only when we adjust this contact line friction factor. However, the flow appears to be qualitatively different when comparing the atomistic and continuum models, highlighting that non-trivial continuum effects can come into play near the interface of the wetting front.

This paper focuses on the connections between four stochastic and deterministic models for the motion of straight screw dislocations. Starting from a description of screw dislocation motion as interacting random walks on a lattice, we prove explicit estimates of the distance between solutions of this model, an SDE system for the dislocation positions, and two deterministic mean-field models describing the dislocation density. The proof of these estimates uses a collection of various techniques in analysis and probability theory, including a novel approach to establish propagation-of-chaos on a spatially discrete model. The estimates are non-asymptotic and explicit in terms of four parameters: the lattice spacing, the number of dislocations, the dislocation core size, and the temperature. This work is a first step in exploring this parameter space with the ultimate aim to connect and quantify the relationships between the many different dislocation models present in the literature.

In this paper, a multiscale modeling framework has been established between peridynamics and atomistic models. Peridynamics (PD) formulation is based on continuum theory implying nonlocal force based interactions. Peridynamics (PD) and molecular dynamics (MD) have similarities since both use nonlocal force based interaction. It means continuum points in PD and MD atoms are separated by finite distance and exert force upon each other. In this work PD based continuum model of epoxy polymer is defined by meshless Lagrangian particles. MD is coupled with PD based continuum model through a hierarchical multiscale modeling framework. In this framework, PD particles at coarse scale interact with fine scale PD particles by transferring pressure, displacements and velocities among each other. Based on the same hierarchical coupling method, fine scale PD model is seamlessly interfaced with molecular model through an intermediate mesoscale region i.e. coarse-grain atomic model. At the end of this hierarchical downscaling, the information — such as deformation, energy and other important parameters — were captured in the atomistic region under the applied force at micro and macro regions. A two-dimensional plate of neat epoxy was considered for demonstration of such multiscale simulation platform. The region of interest in the 2D plate was interfaced with atomistic model by applying the proposed hierarchical coupling method. The results show reasonable consistency between PD and MD simulations.

The quasicontinuum (QC) method is a relatively new computational technique, which combines fast continuum and exact atomistic approaches. The key idea of QC is to reduce the computational cost by reducing degrees of freedom of the fully atomistic approach. In this work, a material model based on the idea of microplanes is used to realize the QC simplification. A formulation convenient for numerical simulation of materials with the structure similar to nanotextile is proposed. The relations between microscopic and macroscopic parameters are derived. Numerical tests show that the proposed model can reach a significant reduction of computational cost for the price of an acceptable error.

The key parameter related to the structure of the electric double layer of ionic surfactant micelles – electrostatic potential – is considered. A brief overview of experimental methods and theoretical models for estimating electrostatic potential- is given. The calculating method for the electrostatic potential based on a numerical solution of the Poisson-Boltzmann equation using an atomistic model of anionic surfactant micelle - is proposed. The parameters necessary for the construction of atomistic models - are obtained from molecular dynamic modeling. The electrostatic potentials for the micelles of sodium dodecyl sulfate and cetyltrimethylammonium bromide at different ionic strengths - were calculated by this method. The results are discussed in comparison with the values calculated in the simplified model, the Ohshima – Healy – White equation.

Crack initiation and propagation in a nanostructured nickel film were studied by molecular dynamic simulation as well as an interatomic-potential-based continuum approach. In the molecular dynamic simulation, the interatomic potential was described by using Embedded Atom Method (EAM), and a reduced 2D plane model was employed to simulate the mechanical behavior of nanofilms. Atomistic simulation shows that the reduced plane model in this paper can not only reveal the physical nature of crack initiation clearly but also give the critical time of crack initiation accurately as the continuum fracture analysis does. The normal stress and average atom energy at the crack tip which resulted from atomistic simulation at the time of crack initiation agree well with the analytical results. On the other hand, the crack propagation in nanofilms was studied by interatomic-potential-based continuum fracture mechanics analysis based on Griffith criterion. The coupled continuum-atomic analysis can predict the crack initiation and atomic stress accurately. Continuum analysis with material property parameters determined by interatomic potential is proved to be another promising way of solving failure problem on nanoscale.

A Brief Sketch of Different Models for the Calculation of Defect Parameters in Metals and Alloys, Comparison of Data and Limitations Has Been Reviewed here; Especially Relaxations due to a Vacancy Type of Point Defect, its Formation, Migration, Activation Energies and Related other Parameters Based upon the Present Experimental Status. the Models Reviewed Are the Bond Model, Continuum Model, Semi-Discrete Model, Jellium Model, Thermodynamic Model, Lattice Statics Model, Atomistic Continuum Model and Pseudopotential Model. the Main Thrust Concerns the Last Model. the Taylor, Vashishta and Singwi, Harrison, Kleinmann and King and Kutler Form of Exchange and Correlation Function Are Almost Similar, Give Moderate Results and May Be Trusted for Better Results.

In this paper, we derive a continuum variational model for a two-dimensional deformable lattice of atoms interacting with a two-dimensional rigid lattice. The starting point is a discrete atomistic model for the two lattices which are assumed to have slightly different lattice parameters and, possibly, a small relative rotation. This is a prototypical example of a three-dimensional system consisting of a graphene sheet suspended over a substrate. We use a discrete-to-continuum procedure to obtain the continuum model which recovers both qualitatively and quantitatively the behaviour observed in the corresponding discrete model. The continuum model predicts that the deformable lattice develops a network of domain walls characterized by large shearing, stretching and bending deformation that accommodates the misalignment and/or mismatch between the deformable and rigid lattices. Two integer-valued parameters, which can be identified with the components of a Burgers vector, describe the mismatch between the lattices and determine the geometry and the details of the deformation associated with the domain walls.

Twinning plays a critical part in the plastic deformation of the materials and the strengthening mechanisms and is hence considered as one of the most prevalent deformation mechanisms in metals. Because to the high stacking fault energy of the fcc metals like Al, Pd, and Pt, the extended dislocations are believed to be energetically favored over isolated partials, thereby rendering deformation twinning unfeasible. Nevertheless, some recent experimental researches have confirmed a potential deformation twinning pathway in nanocrystalline platinum. This alternate-shear mechanism has a much lower energy barrier than the usual layer-by-layer twinning. We utilize computations involving atomistic calculations and continuum modeling in this study to examine the genesis of deformation twins in Pt. Atomistic simulations provides the generalized planer fault energy using an EAM (embedded-atom-model) potential. Moreover, a potential energy-based method, namely; a nudged-elastic band (chain of states) has been used to compute the activation energy barrier for the nucleation of the twinning dislocation loop in the alternate-shear model. The critical stress needed for the nucleation of the twinning dislocation loop in platinum is estimated using some of the parameters acquired from atomistic calculations and using them as fitting parameters in the continuum model. The minimum-energy path between the two end states can be identified using this methodology. Through the unusual alternate-shear approach, the results provide a rudimentary but essential dislocationbased perspective of the occurrence of deformation twins in fcc metals.

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.

An equivalent continuum-atomistic algorithm is proposed for carbon-based structures such as nano-scale graphene platelets (NGPs) and carbon nanotubes (CNTs) individually or as stiffeners with polymers. This equivalent continuum-atomistic model will account for the nonlocal effect at the atomistic level and will be a highly accurate mean to determine the bulk properties of graphene-structured materials from its atomistic parameters. In the model, the equivalent continuum and atomic domains are analyzed by finite elements and molecular dynamics finite element-based where atoms stand as nodes in discretized form. Micromechanics idea of representative volume elements (RVE) will be used to determine averaged homogenized properties. In the procedure, a unit hexagonal cell will be the RVE. A minimum volume of material containing this RVE and the neighboring hexagonal cells will be chosen. The size of this volume should cover all the atoms, which have bonded, and nonbonded interaction with the atoms of the RVE unit cell. This minimum volume will be subjected to several load cases. Determination of the response of the RVE hexagonal unit cell contained within the minimum volume, and its potential energy density under the defined load cases, will lead to the determination of mechanical parameters of an equivalent, continuum geometrical shape. For a single layer NGP the thickness of the hexagonal continuum plate is assumed to be 0.34 nm, while in three-dimension and multilayered the actual thickness of layers can be implemented. Under identical loading on the minimum volumes, identical potential (strain) energies for both models will be assumed. Through this equivalence a linkage between the molecular force field constants and the structural elements stiffness properties will be established.

Bayesian statistics is a quintessential tool for model validation in many applications including smart materials, adaptive structures, and intelligent systems. It typically uses either experimental data or high-fidelity simulations to infer model parameter uncertainty of reduced order models due to experimental noise and homogenization of quantum or atomistic behavior. When heterogeneous data is available for Bayesian inference, open questions remain on appropriate methods to fuse data and avoid inappropriate weighting on individual data sets. To address this issue, we implement a Bayesian statistical method that begins with maximizing entropy. We show how this method can weight heterogeneous data automatically during the inference process through the error covariance. This Maximum Entropy (ME) method is demonstrated by quantifying uncertainty in 1) a ferroelectric domain structure model and 2) a finite deforming electrostrictive membrane model. The ferroelectric phase field model identifies continuum parameters from multiple density functional theory calculations. In the case of the electrostrictive membrane, parameters are estimated from both mechanical and electric displacement experimental measurements.

Fluid transport with diffusion through micro-/nano-channels is found in many natural phenomena and industrial processes, including fluid transport or diffusion through nano-materials, molecular/atomistic transfer across nuclear pores or in the MEMS devices among other applications. Those nano-pores can be treated as nano-channels in the thin layers of the membranes. The transport phenomena of fluid in such small confined channels, usually in the size of ten molecular diameters or less, differs significantly from its bulk behaviors and cannot be described with continuum theory. In this case, molecular dynamics (MD) simulation, rather than continuum methods, is better suited to study the phenomena. The surface diffusion, related to both the fluid and solid material properties and the flow rate, can be used as a parameter for estimating the adsorbing capacity of a porous nano-material. The transport of fluids through porous materials occurs mainly by diffusion. In this study, a molecular-continuum hybrid scheme is used for the study of the diffusion in a representative Couette flow problem. By varying the velocity of the moving-solid wall, we investigated the effect of the shearing condition on the mass flux going through the pores. The relationship of the physical mechanisms and the transport phenomena (e.g. Fick’s law) were then linked among the different length scales. Activated carbon with its high surface area has been emerging as a promising candidate for an adsorbent due to not only its stable thermodynamic and mechanical properties but also its homogenous and isotropic porous distribution and relatively even pore size. In this study, we focus on the characteristics of the permeation and the adsorption process between different gases and the carbon substrate under various shearing conditions. The investigation of the diffusion process of fluids through the pores of the nano-materials has become an interesting topic in recent decades. This investigation has been divided into two major areas: 1) the diffusivity estimation and 2) the transient diffusion rate. We apply a continuum/MD hybrid scheme to a model problem of various gases transport through a carbon substrate with several pores in a channel flow under different shear rates. Instead of inserting and deleting particles from the control volumes used in the DCV-GCMD method, we keep the number of particles in the simulation system constant. The interactions between fluid/fluid, fluid/solid and solid/solid are all assumed to be under Lennard-Jones potentials. In the modeled Couette flow, the two solid walls are constructed with nano-pores that allow fluids to go through the substrate to study the transient diffusion rate (flux). Before simulating the fluid transport through the nano-pores, we need to validate the natural diffusion properties of the bulk fluid. To do this, a system (as a cube) consisting of pure liquid argon molecules is used to perform the pure MD simulation. The radial distribution function (RDF) is used as the parameter to verify the natural diffusion of the liquid argon fluid in the bulk flow, which is a structural correlation. It describes the spherically averaged local organization around any given molecule. Figure 1 shows a good comparison of the radial distribution functions between the MD prediction and the experimental measurement of Eisenstein and Gingrich (1942). By comparing our calculation to Wu et al. (2008) under similar circumstances, we found that the average (from 8 pores) and corrected mass flux J · (RTh) is linearly proportional to the average pressure gradient along the pore. And the slope of this relationship is the transport diffusivity, which is 4.6 × 10−7m2/s under 273K and 4.9 × 10−7m2/s under 300K. This indicates that the current simulation follows the Fick’s law exactly. Similarly, for other gases, the same linear relationships can also be obtained. These calculations are listed in Table 1 that shows the transport diffusivity increases with temperature. The mass fluxes of three gases at various pore widths are calculated as shown in Fig. 2. Generally, with larger pores, the mass fluxes increase. However, among three gases, the increase of H2 is much faster than the other two gases because of hydrogen’s smaller molecular size. In another word, smaller molecules as H2 have faster diffusion rates during the adsorption process.