Highly scalable discrete-particle simulations with novel coarse-graining: accessing the microscale

ABSTRACT

Simulating energetic materials with complex microstructure is a grand challenge, where until recently, an inherent gap in computational capabilities had existed in modelling grain-scale effects at the microscale. We have enabled a critical capability in modelling the multiscale nature of the energy release and propagation mechanisms in advanced energetic materials by implementing, in the widely used LAMMPS molecular dynamics (MD) package, several novel coarse-graining techniques that also treat chemical reactivity. Our innovative algorithmic developments rooted within the dissipative particle dynamics framework, along with performance optimisations and application of acceleration technologies, have enabled extensions in both the length and time scales far beyond those ever realised by atomistic reactive MD simulations. In this paper, we demonstrate these advances by modelling a shockwave propagating through a microstructured material and comparing performance with the state-of-the-art in atomistic reactive MD techniques. As a result of this work, unparalleled explorations in energetic materials research are now possible.     

Multiscale simulations of damage of perfect crystal Cu at high strain rates

We use the molecular dynamics code, large-scale atomic/molecular massively parallel simulator (LAMMPS), to simulate high strain rate triaxial deformation of crystal copper to understand void nucleation and growth (NAG) within the framework of an experimentally fitted macroscopic NAG model for polycrystals (also known as DFRACT model). It is seen that void NAG at the atomistic scales for crystal copper (Cu) has the same qualitative behaviour as the DFRACT model, albeit with a different set of parameters. The effect of material temperature on the nucleation and growth of voids is studied. As the temperature increases, there is a steady decrease in the void NAG thresholds and close to the melting point of Cu, a double-dip in the pressure–time profile is observed. Analysis of this double-dip shows disappearance of the long-range order due to the creation of stacking faults and the system no longer has a face centred cubic (fcc) structure. Molecular dynamics simulation of shock in crystal Cu at strain rates high enough to cause spallation of crystal Cu are then carried out to validate the void NAG parameters. We show that the pre-history of the material affects the void nucleation threshold of the material. We also simulate high-strain-rate triaxial deformation of crystal Cu with defects and obtain void NAG parameters. The parameters are then used in a macroscale hydrodynamic simulation to obtain spallation threshold of realistic crystal Cu. It is seen that our results match experimental results within the limit of 20% error.     

Atomistic simulation analysis of the effects of void interaction on void growth and coalescence in a metallic system

Material deformation caused by the interaction between defects is a significant factor of material fracture failure. The present study employs molecular dynamics simulations of single-void and double-void crystalline Ni atomic systems to investigate inter-void interactions. Furthermore, simulations showing the evolution of dislocations for three different crystallographic orientations are conducted to study the void growth and coalescence. The simulations also consider the effect of the radius of the secondary void on dislocation evolution. The results show that double-void systems are more prone to yield than single-void systems. Further microstructural analysis indicates that the interaction between voids is realized by dislocation reactions. The simulation results of the dislocation evolution of the three orientations reveal that a relationship exists between the evolution of the dislocation density and the stress-strain curve. At the initial stage of dislocation, the dislocation grows slowly, and consists of Shockley partial dislocation. The dislocation growth rate then increases significantly in the sharply declining stage of the stress-strain curve, where most of dislocations are Shockley partial dislocation. Analysis of the dislocation length during the overall simulation indicates that the dislocation length of the [110] orientation is the longest, followed by that of the [111] orientation and the [100] orientation, which has the shortest dislocation length.     

Closing the gap between experiment and theory: crystal growth by temperature accelerated dynamics

We present atomistic simulations of crystal growth where realistic experimental deposition rates are reproduced, without needing any a priori information on the relevant diffusion processes. Using the temperature accelerated dynamics method, we simulate the deposition of 4 monolayers (ML) of Ag/Ag(100) at the rate of 0.075 ML/s, thus obtaining a boost of several orders of magnitude with respect to ordinary molecular dynamics. In the temperature range analyzed (0-70 K), steering and activated mechanisms compete in determining the surface roughness.     

单晶铜在动态加载下空洞增长的分子动力学研究

冲击载荷下延性材料的损伤是材料中微空洞的产生和长大演化的结果.利用分子动力学模拟 方法对延性金属单晶铜中单个空洞在动态加载下的演化发展进行了研究，得到了空洞增长过 程中的应力分布及空洞增长演化随冲击强度变化的规律.模拟结果表明，动态加载下的前期 压缩过程对后期拉伸应力场作用下的空洞增长演化特征有不可忽视的影响，微空洞增长的阈 值则与单晶实验中层裂强度随拉伸应力作用时间减少而增加的趋势相一致. 关键词： 层裂 分子动力学 动态加载 空洞     

Multiscale simulation from atomistic to continuum – coupling molecular dynamics (MD) with the material point method (MPM)

A new multiscale simulation approach is introduced that couples atomistic-scale simulations using molecular dynamics (MD) with continuum-scale simulations using the recently developed material point method (MPM). In MPM, material continuum is represented by a finite collection of material points carrying all relevant physical characteristics, such as mass, acceleration, velocity, strain and stress. The use of material points at the continuum level provides a natural connection with the atoms in the lattice at the atomistic scale. A hierarchical mesh refinement technique in MPM is presented to scale down the continuum level to the atomistic level, so that material points at the fine level in MPM are allowed to directly couple with the atoms in MD. A one-to-one correspondence of MD atoms and MPM points is used in the transition region and non-local elastic theory is used to assure compatibility between MD and MPM regions, so that seamless coupling between MD and MPM can be accomplished. A silicon single crystal under uniaxial tension is used in demonstrating the viability of the technique. A Tersoff-type, three-body potential was used in the MD simulations. The coupled MD/MPM simulations show that silicon under nanometric tension experiences, with increasing elongation in elasticity, dislocation generation and plasticity by slip, void formation and propagation, formation of amorphous structure, necking, and final rupture. Results are presented in terms of stress–strain relationships at several strain rates, as well as the rate dependence of uniaxial material properties. This new multiscale computational method has potential for use in cases where a detailed atomistic-level analysis is necessary in localized spatially separated regions whereas continuum mechanics is adequate in the rest of the material.     

Effects of void shape and orientation on the elastoplastic properties of spheroidally voided single-crystal and nanotwinned copper

ABSTRACT

Void nucleation, growth and coalescence have been identified as the leading cause of ductile damage in metallic materials. To understand the underlying deformation and damage mechanisms, extensive theoretical, experimental and simulation efforts have been attempted on spherically voided metals. In this work, molecular dynamics simulations are performed to analyze the uniaxial straining deformation behaviours of both single-crystal and nanotwinned copper materials embedded with a preexisting spheroidal void. The coupling effects among twin boundary, spheroidal void aspect ratio and orientation on unidirectional elastoplastic behaviours are systematically examined. The dislocation-induced plastic deformation mechanism is also examined and compared with the one due to a perfectly spherical cavity. Simulation results show that elastic modulus increases with both spheroidal void aspect ratio and orientation. So do the yield stress, the first peak stress and the plasticity index. Another peak stress exists for most cases, except for a prolate void embedded in nanotwinned specimens. The slope between peak stresses decreases with both the spheroidal aspect ratio and orientation. The incorporation of a twin boundary results in lower elastic modulus, higher yield strength and smaller plasticity index. For an oblate void, the twin boundary gives rise to more severe strain softening behaviour. The dislocation extraction algorithm illustrates that the continuous nucleation, propagation and reaction of dislocations emanated from both the void front and twin boundary are responsible for the ductile damage of spheroidally voided crystals. The lower dislocation densities found in nanotwinned specimens indicate the desired suppression effects of twin boundary on dislocation activities.     

Multiscale modeling of nanoindentation in copper thin films via the concurrent coupling of the meshless Hermite-Cloud method with molecular dynamics

This paper investigates the 2D nanoindentation of a copper thin film using a concurrent multiscale method. The method uses molecular dynamics (MD) simulation in the atomistic region, the strong-form meshless Hermite-Cloud method in the continuum region and a handshaking algorithm to concurrently couple them. A fully atomistic simulation is also carried out to validate the multiscale method. The results, namely the load versus indentation depth graph obtained from the multiscale method shows only slight quantitative variation from that of the full atomistic model. More importantly, the graphs from both simulations show a similar trend thus validating the 2D multiscale method. The displacement profile without discontinuities further supports the efficiency of the multiscale method in ensuring smooth exchange of information between the atomistic and continuum domains. The material properties extracted from the simulation include the force/unit length values obtained by dividing the maximum load on the indenter by its contact perimeter, instead of the hardness value obtained in 3D simulations. By restricting the atomic scale detail to the critical regions beneath the indenter, the multiscale method effectively saves computational resources to more than one order (close to 13 times less for this problem), thus making it feasible to simulate problems of larger dimensions that are not amenable to complete atomistic simulations.     

Interaction of voids and nanoductility in silica glass

Multimillion-to-billion-atom molecular dynamics simulations are performed to investigate the interaction of voids in silica glass under hydrostatic tension. Nanometer size cavities nucleate in intervoid ligaments as a result of the expansion of Si-O rings due to a bond-switching mechanism, which involves bond breaking between Si-O and bond formation between that Si and a nonbridging O. With further increase in strain, nanocracks form on void surfaces and ligaments fracture through the growth and coalescence of ligament nanocavities in a manner similar to that observed in ductile metallic alloys.     

Harnessing atomistic simulations to quantify activation parameters for dislocation nucleation from a grain boundary in Nickel

We perform atomistic simulations and nudged elastic band calculations to quantify activation energy barriers for dislocation nucleation from ∑3 grain boundary containing a pre-existing void in Ni. By changing the void size, we offer a phenomenological relationship between the activation free energy at zero stress and boundary porosity. Simulations at different temperatures are also conducted to gain some insights into the inherent intricacies of activation energy landscape. It is envisioned that the approach can be pushed forward to guide the flow rules of physics based crystal plasticity models at higher length scales that account for grain boundary effects.     

Internally consistent verification of mean-field models for aggregation using large-scale molecular dynamics

The underlying atomistic mechanisms that govern vacancy aggregation in crystalline silicon are probed using a parametrically consistent, two-scale approach. The essential ingredient in this framework is a direct, quantitative comparison between the predictions of atomistic and continuum simulations for the transient size distribution of vacancy clusters. The former is carried out with parallel molecular dynamics simulation of a silicon system containing 215?000 atoms and 1000 vacancies. The continuum model is based on a sequence of coupled Master equations and is parametrized based on the same empirical potential used to perform the atomistic aggregation simulation. An excellent representation of the cluster size distribution can be obtained with consistent parameters only if the relevant physical mechanisms are captured correctly. The inclusion of vacancy cluster diffusion and a model to capture the dynamic nature of cluster morphology at high temperature are necessary to reproduce the results of the large-scale atomistic simulation. Finally, the continuum model is used to investigate cluster evolution for longer times, which are relevant for process simulation of defect-optimized silicon substrates for microelectronic device fabrication.     

〈111〉晶向冲击加载下单晶铜中纳米孔洞增长的早期动力学行为

利用分子动力学方法模拟计算了单晶铜中纳米孔洞在沿〈111〉晶向冲击加载下增长的早期过程.测量发现不同加载强度下等效孔洞半径随时间近似成线性变化.观测到单孔洞增长的两种位错生长机理：加载强度较低时，只在沿着冲击加载方向的孔洞顶点附近区域有位错的成核和运动；而随着加载强度超过一定阈值，在沿冲击加载和其垂直方向的孔洞顶点区域都观察到位错的成核和运动.在前一种机理作用下，孔洞只沿加载方向增长；在后一种机理作用下，孔洞同时沿加载和垂直于加载方向增长.分析孔洞表面原子的位移历史，发现沿加载及与其垂直方向的孔洞顶点沿径向的速度基本恒定，由此提出了一个孔洞生长模型，可以解释孔洞增长的线性生长规律. 关键词： 纳米孔洞 分子动力学 冲击加载 位错     

Atomic mechanisms of superionic conductivity in fluorite

The subsequent melting/crystallization of the two sub-lattices of CaF₂ is explored by molecular dynamics simulations. Both, heating from 100 K and cooling from 2500 K encompasses two transitions, i.e. the melting/recrystallization of the fluoride sub-lattice and the of whole crystal at different temperatures. Solid state F^? ion conductivity is observed in a temperature range of about 1500–2000 K which reflects a reasonable agreement with the experiment. A systematic study of fluoride migration revealed the atomistic mechanisms of the spontaneous formation of Frenkel defects, followed by void translocation and terminated by recombination of interstitial fluoride ions and vacancies.     

Irradiation-induced void evolution in iron:A phase-field approach with atomistic derived parameters

A series of material parameters are derived from atomistic simulations and implemented into a phase field(PF) model to simulate void evolution in body-centered cubic(bcc) iron subjected to different irradiation doses at different temperatures.The simulation results show good agreement with experimental observations — the porosity as a function of temperature varies in a bell-shaped manner and the void density monotonically decreases with increasing temperatures; both porosity and void density increase with increasing irradiation dose at the same temperature. Analysis reveals that the evolution of void number and size is determined by the interplay among the production, diffusion and recombination of vacancy and interstitial.     

Wormlike chain theory and bending of short DNA

The probability distributions for bending angles in double helical DNA obtained in all-atom molecular dynamics simulations are compared with theoretical predictions. The computed distributions remarkably agree with the wormlike chain theory and qualitatively differ from predictions of the subelastic chain model. The computed data exhibit only small anomalies in the apparent flexibility of short DNA and cannot account for the recently reported AFM data. It is possible that the current atomistic DNA models miss some essential mechanisms of DNA bending on intermediate length scales. Analysis of bent DNA structures reveal, however, that the bending motion is structurally heterogeneous and directionally anisotropic on the length scales where the experimental anomalies were detected. These effects are essential for interpretation of the experimental data and they also can be responsible for the apparent discrepancy.     

Supercoiling and denaturation of DNA loops

We study the statistical mechanics of small DNA loops emphasizing the competition between elasticity, supercoiling, and denaturation. Motivated by recent experiments and atomistic molecular dynamics simulation, we propose a new coarse-grained phenomenological model of DNA. We extend the classical elastic rod models to include the possibility of denaturation and nonlinear twist elasticity. Using this coarse-grained model, we obtain a phase diagram in terms of fractional overtwist and loop size that can be used to rationalize a number of experimental results which have also been confirmed by atomistic simulations.     

Beyond finite-size scaling in solidification simulations

Although computer simulation has played a central role in the study of nucleation and growth since the earliest molecular dynamics simulations almost 50 years ago, confusion surrounding the effect of finite size on such simulations has limited their applicability. Modeling solidification in molten tantalum on the Blue Gene/L computer, we report here on the first atomistic simulation of solidification that verifies independence from finite-size effects during the entire nucleation and growth process, up to the onset of coarsening. We show that finite-size scaling theory explains the observed maximal grain sizes for systems up to about 8 000 000 atoms. For larger simulations, a crossover from finite-size scaling to more physical size-independent behavior is observed.     

Atomistic simulations of the effect of a void on nanoindentation response of nickel

Three-dimensional molecular dynamics simulations have been performed to investigate the effect of a void on the nanoindentation of nickel thin film.The radius and depth of the void are varied to explore how they influence the nanoindentation.The simulation results reveal that the presence of a void softens the material and allows for a larger indentation depth at a given load compared to the no void case.The radius and depth of the void have a major effect on the indentation behaviors of the thin film.It is also observed that the void will collapse during the nanoindentation of crystal with void.And when the indentation depth is sufficiently large,the void will disappear.It is found that the indentation depth needed to make the void disappear depends on the void size and location.     

Atomistic mechanisms of fatigue in nanocrystalline metals

We investigate the mechanisms of fatigue behavior in nanocrystalline metals at the atomic scale using empirical force laws and molecular level simulations. A combination of molecular statics and molecular dynamics was used to deal with the time scale limitations of molecular dynamics. We show that the main atomistic mechanism of fatigue crack propagation in these materials is the formation of nanovoids ahead of the main crack. The results obtained for crack advance as a function of stress intensity amplitude are consistent with experimental studies and a Paris law exponent of about 2.     

Symmetry-adapted graph neural networks for constructing molecular dynamics force fields

Molecular dynamics is a powerful simulation tool to explore material properties. Most realistic material systems are too large to be simulated using first-principles molecular dynamics. Classical molecular dynamics has a lower computational cost but requires accurate force fields to achieve chemical accuracy. In this work, we develop a symmetry-adapted graph neural network framework called the molecular dynamics graph neural network(MDGNN) to construct force fields automatically for molecular dynamics simulations for both molecules and crystals. This architecture consistently preserves translation, rotation, and permutation invariance in the simulations. We also propose a new feature engineering method that includes high-order terms of interatomic distances and demonstrate that the MDGNN accurately reproduces the results of both classical and first-principles molecular dynamics. In addition, we demonstrate that force fields constructed by the proposed model have good transferability.The MDGNN is thus an efficient and promising option for performing molecular dynamics simulations of large-scale systems with high accuracy.