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Snapshots of single PE polymer chain equilibrated at 300 K at (a) unfolded state and (b) folded state with the constraint of periodic boundary condition.
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Hardy stress definition has been restricted to pair potentials and embedded-atom method potentials due to the basic assumptions in the derivation of a symmetric microscopic stress tensor. Force decomposition required in the Hardy stress expression becomes obscure for multi-body potentials. In this work, we demonstrate the invariance of the Hardy st...
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In this contribution, we present an overview of the “three-dimensional” (3D) approach that can be used to describe few-nucleon systems. Instead of relying on the partial wave decomposition of quantum mechanical operators related to a specific problem, the 3D approach works directly with the (three-dimensional) momentum degrees of freedom of the nuc...
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... Therefore, the residual stress distribution of scratch with three different crystal orientations is studied. Among the previous related research methods of studying the residual stress distribution of nanoscratching [13, 14,17,39], it is to obtain the stress on the atom through simulation calculation and then directly observe and explore the stress distribution in the scratching region. When the difference in residual stress between atoms is not obvious or the residual stress of the atoms is small, the residual stress distribution law in the scratching region cannot be effectively observed. ...
Molecular dynamics simulation method is carried out to study influence of GaAs crystal anisotropy on deformation behavior and residual stress distribution of nanoscratching. The scratching process of three crystal orientations of GaAs[100], GaAs[110] and GaAs[111] is investigated, respectively. It is found that there exists significant crystal anisotropy of the deformation behavior and residual stress distribution. Meanwhile, atomic pile-up, destruction depth, scratching force, surface topography, internal structure, residual stress are closely related to the GaAs crystal orientations. A new method to study the residual stress distribution of nanoscratching is proposed. It is observed that the residual stress is focused on the scratching region and its limits, and the two sides of the scratch are distributed symmetrically. The component of residual stress at the GaAs[100] scratching bottom is mainly the compressive stress in the y-axis direction. The average scratching force for the GaAs[110] scratch is the smallest and the pile-up height on the upper surface of the GaAs[110] workpiece is the largest. Eventually, the destruction depth of the crystal structure of the GaAs[110] workpiece by the abrasive in the scratching process is the smallest among three crystal orientations, while that of the GaAs[100] scratch is the largest among three crystal orientations.
... Therefore, they determined the thermomechanical quantities from the atomistic scale. In another experiment, Yao Fu et al. [42] elucidated the invariance of the Hardy stress expression for a polymer system modeled with multi-body interatomic potentials including up to four atoms interaction, by applying central force decomposition of the atomic force. Fig. 1 illustrates the initial crack size of 0.32L for a 10% boron doped polycrystalline graphene nanosheet with grain size of 10 nm. ...
This article investigates the effect of different initial crack sizes on the mechanical response of single-layer boron doped polycrystalline graphene nanosheets by Molecular Dynamics (MD) simulations. We study 1%, 3%, 6% and 10% of boron doped polycrystalline graphene nanosheets with grain sizes of 10 and 15 nm for eight different initial crack lengths of 0.02L, 0.04L, 0.08L, 0.12L, 0.16L, 0.2L, 0.24L, and 0.32L, where L is the initial length of the nanosheet. We found that 1. brittle fracture for boron doped polycrystalline graphene as the failure occurs without any sign of plastic deformation and low energy absorption and 2. the ultimate tensile strength is independent of the initial crack size. For identical grain sizes and doping of boron atoms, the ultimate tensile stress and strain decrease as the crack lengths increases. In contrast, a clear trend was not observed in the ultimate tensile strength for the same crack length and doping of boron atoms as the grain size increases. The highest difference of 13.4% in the ultimate tensile strength was observed between grain sizes of 10 and 15 nm for 3% of boron doped nanosheets with an initial crack size of 20Å.
... Finite element method is a typical success of continuum mechanics in predicting materials' response and failure at macroscopic level. To extend the concepts of continuum mechanics, i.e., stress and strain, to the nano-scale for exploring the microscopic behavior, attracts increasing attention [20,21].Inspired by this, we make an attempt to construct the extensional-shear coupled flow in DPD simulation, for the first time. In Reference [18], based on the Souza-Martins method [22], the extensional flow was driven by an external pressure along the length Lz of the simulation box. ...
This paper presents our study on the use of dissipative particle dynamics (DPD) simulations to discover the flow behavior in ultra high molecular weight polyethylene/polyamide 6 (UHMWPE/PA6) blends associated with extensional-shear coupled flow, based on the Souza-Martins method, for the first time. By way of simulations, we aimed at investigating the mesoscopic morphology and alignment behavior in response to extensional-shear coupled flow, in comparison with simple shear flow and simple extensional flow. Our results reveal that the aggregation of polymers is noticeable under zero flow, as expected. Within the considered range of extensional-shear coupled rates, the morphology transforms from micelle-like clusters to a chain-like network structure by increasing coupled rates from 0.01 to 2.0. Furthermore, it shows a linear distribution along the flow direction at a high coupled rate. It can be concluded that the flow behaviors in UHMWPE/PA6 blends are significantly impacted by extensional-shear coupled rates. The orientation behavior induced by extensional-shear coupled flow is more obvious than shear flow, even though flow variations and mass fractions yield less effects on the distribution behaviors of UHMWPE/PA6 blends. The DPD results are verified by mean square displacement (MSD) as a function of simulation time and relative concentration distribution along Z direction.
... It has been demonstrated that these two methods are equivalent, as VA expression can be obtained by spatially averaging the MOP expression [51]. Although both MOP and VA methods are straightforward for pairwise interactions, many-body interactions require more involved treatment, such as central force decomposition [5,11,12]. ...
... Note that in other literature the kinetic term, i.e., the first right-hand side term of Eq. (1), is sometimes included, the 1/2 coefficient can be omitted, various definitions of atomic volume are used, and stress might be exchanged to pressure. For many-body interactions, similarly to MOP and VA methods, the more involved central force decomposition can be used [5,11,12]. Although Thompson et al. admitted in their paper that there is no strict physical basis [10], it is often simpler and more convenient to equally distribute the virial from many-body interaction to the each atom in the group in accordance to Eq. (3), ...
Although the computation of heat flux and thermal conductivity either via Fourier's law or the Green-Kubo relation has become a common task in molecular dynamics simulation, contributions of three-body and larger many-body interactions have always proved problematic to compute. In recent years, due to the success when applying to pressure tensor computation, atomic stress approximation has been widely used to calculate heat flux, where the lammps molecular dynamics package is the most prominent propagator. We demonstrated that the atomic stress approximation, while adequate for obtaining pressure, produces erroneous results in the case of heat flux when applied to systems with many-body interactions, such as angle, torsion, or improper potentials. This also produces incorrect thermal conductivity values. To remedy this deficiency, by starting from a strict formulation of heat flux with many-body interactions, we reworked the atomic stress definition which resulted in only a simple modification. We modified the lammps package accordingly to demonstrate that the new atomic stress approximation produces excellent results close to that of a rigid formulation.
... The stress tensor and heat flux vector are then obtained through the molecular description of the transport equations as point functions. Over the past 68 years, more than two thousand papers whose works were inspired by IK's formalism of fluxes have been published; many of these replacing the Dirac delta with a spatial-averaging functions such as Hardy [13,14] and several others [43][44][45][46]. Additionally, a form of the stress formula in terms of pair density can be noted in the Appendix [6], in which IK ultimately expressed the pair density stress formula using Taylor series expansion with the intent to connect the pair density expression for stress to that in terms of singlet density. ...
Although there are numerous formulae for atomic-level fluxes, they are expressed either in terms of a singlet density, resulting from Irving and Kirkwood's statistical mechanics formulation of hydrodynamical equations, or a pair density, proposed in kinetic theories of transport processes. Flux formulae using singlet density have been further developed and widely implemented in molecular dynamics (MD) simulations by either replacing the Dirac delta with a volumetric averaging function or performing a surface average of the flux operators. Pair density-based flux formulae have also been further developed by using spatial-averaging kernels; these formulae, however, have rarely been implemented or used in modern MD. In this work, distributional calculus is used to reformulate the fluxes in momentum and energy transport processes. The formulation results demonstrate that these two types of existing flux formulae are mathematically equivalent when expressed with the Dirac delta. The lasting confusion regarding these two different types of flux formulae from two different formalisms is thus resolved. © 2019 The Author(s) Published by the Royal Society. All rights reserved.
... However, the transfer of information across the length scales for problems involving material failure and finite temperatures still remains a challenging task. A thermodynamically consistent continuum stress fields from discrete atomistic model can be estimated, for example: based on an extended Hardy's methodology as proposed in [15,16]. ...
A three dimensional concurrently coupled adaptive multiscale method is introduced here to simulate complex crack growth patterns in Silicon, by combining several numerical techniques across the length scales. The coarse scale material is modeled using the virtual atom cluster approach. The strong kinematic discontinuities in the bulk are simulated based on a three dimensional version of the phantom node method. A molecular statics model placed around the crack tip is concurrently coupled with the phantom-based discontinuous formulation, where the coupling between the fine and coarse scales is realized through the use of ghost atoms, whose positions are interpolated based on the coarse scale solution. The boundary conditions to the fine scale model, at the coupling region, are assigned by enforcing the interpolated displacements of ghost atoms. In order to optimize the computation costs, adaptivity schemes for adjustment of the fine scale region as the crack propagates, and coarse graining of the region behind the crack tip, are proposed. The crack tip location is detected based on an energy criterion. All the molecular simulations in the pure atomistic as well as the multiscale model are carried out using the LAMMPS software, triggered through the system command in MATLAB. The performance of the developed framework in terms of computation cost, robustness and versatility, is assessed through several numerical examples concerning crack growth in Silicon. Therefore, the diamond cubic lattice structure of Silicon is used at the fine scale, where the atom-atom interactions are modeled based on the Tersoff potential function. According to the numerical examples presented in this study, savings in computational time using the present multiscale method are observed to be up to 87%, as compared to the pure atomistic model.
... Worthy to note that the investigation of local thermodynamics quantities [45][46][47], during the creation of nanopore in the polycrystalline boron nitride nanohseet may reveal interesting physics which can be considered in the future studies. ...
Abstract In this paper, molecular dynamic simulations have been performed to fabricate nanopores in a polycrystalline boron-nitride nanosheet applied to DNA sequencer devices by using Si clusters bombardment. Three different sizes of Si clusters with ten different kinetic energies and impacts at five different locations of the polycrystalline boron-nitride nanosheet have been simulated. Our results show that desired nanopores with expected size and topography can be created by controlling the kinetic energy and size of the cluster. The area size of nanopores also increase by rising the kinetic energy of the cluster. We have also observed that the existing grain boundary in the incident location highly affects the shape and size of the nanopores. Therefore, we subsequently applied an external tensile strain on the boron-nitride nanosheet and determined the effect of straining nanosheet on the area, quality and the shape of fabricated nanopores. We find that increasing the external tensile strain leads to a large increase in the area of nanopores, but the shape and quality of fabricated nanopores remains nearly unaffected, particularly compared to drilling nanopores in the unstrained nanosheet. In order to investigate the effect of the cluster type, two new type of clusters (SiC and diamond) have been used to generate nanopores. Our results reveal that SiC and diamond clusters bombardment lead to fabricate almost the same shape and quality of nanopores as well as the Si cluster. On the other hand, increasing the kinetic energy of the SiC and diamond cluster barely influences the area size of the nanopores. Among all clusters, the diamond cluster bombardment leads to fabricate the largest average area size of the nanopores.
... The practical onerousness of this procedure depends on the complexity of the functional form of the considered potential. These inconveniences are the reason why till now CFDs have been found only for potentials of low or moderate complexity, such as embedded atom method potentials [37], spline based modified embedded atom method potentials [33] and rather simple three-body [38] and four-body potentials [39,40]. ...
... which after plugging formulas for 1 , 2 and 3 (see Equations (39), (42) and (48), respectively) will read: ...
Central forces play important role in the analysis of results obtained with particle simulation methods, since they allow evaluating stress fields. In this work we derive expressions for a central-force decompositon of the Tersoff potential, which is often used to describe interatomic interactions in covalently bonded materials. We simplify the obtained expressions and discuss their properties.
... Computational approaches provide an excellent route to characterize materials properties by reducing the cost of exhaustive hit-and-miss experimentation and by providing insightful information at the molecular and microscopic scales not easily extracted from experiments [13,14]. Recently, several theroretical studies based on the understanding of the atomistic behaviors of polymeric structures have contributed to the modeling of thermoset polymers such as an epoxy resin system that builds a crosslinked network between the polymer chains during the curing (cross-linking) process. ...
... Due to the importance of cross-linked polymers in various applications [13,14,[19][20][21], there have been increasing studies on polymer networks in addition to linear homopolymers or copolymers [22][23][24][25][26][27]. Wu and Xu [25] investigated a computational method for the construction of a polymer network based on diglycidyl ether bisphenol A (DGEBA) and isophorone diamine (IPD). ...
In this work, we demonstrate the feasibility of a computational approach based on first principles for estimating various thermomechanical quantities of a cross-linked epoxy resin. In particular, this work is focused on determining estimated values of the variation of glass transition temperature, the coefficient of thermal expansion, the volume shrinkage due to curing, the Young’s modulus, the Poisson’s ratio, the yield strength and the viscosity as a function of temperature and degree of curing via molecular dynamics simulations. In most cases it has been demonstrated that the values predicted by the proposed approach as in good agreement with the respective experimentally measured values. In addition, the validity of the proposed models describing the dependence of the thermomechanical quantities on temperature and curing degree is also examined. Throughout this study, we demonstrate that the molecular dynamics based computational predictive framework can serve as an excellent infrastructure that can enable numerical prediction of materials properties and thereby can reduce the costs of associated with physical experimentation. In addition, we also demonstrate that insightful information can also be generated at the molecular and microscopic scales that is not easily extractable from experiments.
... The approach of [43,44] (termed the Murdoch-Hardy procedure, with the corresponding quantity known as Hardy stress) was later further generalised [45][46][47][48][49][50][51][52][53][54]. Owing to its many advantages, Hardy stress has since found widespread use in atomistic simulations [55][56][57][58][59][60][61][62][63][64]. ...
... The possibility of applying Hardy stress to three-body potentials has also been discussed [56]. Only recently applications of Hardy stress to systems described by four-body potentials have been reported [63,64]. To our best knowledge, there are no examples in the literature of the use of Hardy stress in systems described by many-body potentials more involved than the original EAM potential. ...
... In some formulations [63,64], most often for systems in equilibrium, time averaging is employed for both of the above terms. In the absence of time averaging the instantaneous stress tensor is obtained. ...
Central-force decompositions are fundamental to the calculation of stress fields in atomic systems by means of Hardy stress. We derive expressions for a central-force decomposition of the spline-based modified embedded atom method (s-MEAM) potential. The expressions are subsequently simplified to a form that can be readily used in molecular-dynamics simulations, enabling the calculation of the spatial distribution of stress in systems treated with this novel class of empirical potentials. We briefly discuss the properties of the obtained decomposition and highlight further computational techniques that can be expected to benefit from the results of this work. To demonstrate the practicability of the derived expressions, we apply them to calculate stress fields due to an edge dislocation in bcc Mo, comparing their predictions to those of linear elasticity theory.
