HotQC simulation of nanovoid growth under tension in copper

We apply the HotQC method of Kulkarni et al. (J Mech Phys Solids 56:1417–1449, 2008) to the study of quasistatic void growth in copper single crystals at finite temperature under triaxial expansion. The void is strained to 30% deformation at initial temperatures and nominal strain rates ranging from 150 to 600 K and from 2.5 × 10⁵ to 2.5 × 10¹¹s⁻¹, respectively. The interatomic potential used in the calculations is Johnson’s Embedded-Atom Method potential Johnson (Phys Rev B 37:3924–3931, 1988). The computed pressure versus volumetric strain is in close agreement with that obtained using molecular dynamics, which suggests that inertia effects are not dominant for the void size and conditions considered. Upon the attainment of a critical or cavitation strain of the order of 20%, dislocations are abruptly and profusely emitted from the void and the rate of growth of the void increases precipitously. Prior to cavitation, the crystal cools down due to the thermoelastic effect. Following cavitation dislocation emission causes rapid local heating in the vicinity of the void, which in turn sets up a temperature gradient and results in the conduction of heat away from the void. The cavitation pressure is found to be relatively temperature-insensitive at low temperatures and decreases markedly beyond a transition temperature of the order of 250 K.     

A non-local void filling model to describe its dynamics during processing thermoplastic composites

A model is developed to describe the void dynamics within thermoplastic composite tape during the tape placement process. The model relates the volatile pressure in voids, the applied compaction load, fiber bed response and the resin pressure due to squeeze-flow of resin from resin-rich regions to fill void regions. This model relies on some geometric simplifications, but incorporates the relevant physical phenomena.This void consolidation model was implemented in a numerical code which predicts the void development during the process. The initial void geometry can be introduced either manually, using a random generation algorithm or from actual processed tape micrographs.The model predicts that the final void content depends on the original void content but also on the initial void distribution. Presented results analyze the influence of void distribution on tape consolidation. Limitations of the consolidation process rate by the resin squeeze flow pressures are clearly demonstrated.     

MD simulation of atom-order void formation in Ni fcc metal

Atom-order void formation in a defective crystalline material is studied by using molecular dynamics method (MD). Infinite long cylinder, which is constructed with nickel atoms with a line of vacancies, is subjected to multiaxial tensile strain field by moving periodic boundary and the atoms on the outer surface of the cylinder. When the load exceeds a critical value, sudden appearance of the void is observed and it develops rapidly. The developed void does not disappear by only unloading and relaxation, in spite of the system with the void has higher potential energy than that without void. The biaxial or the triaxial load is necessary to the atom order void formation. Moreover, the results by the MD simulations are compared with theoretical solution for nonlinear elastic solid. Received 26 August 1999     

Numerical study on compression processes of cohesive bimodal particles and their packing structure

In this study, the compression characteristics of bimodal cohesive particles were investigated using a discrete element method (DEM) simulation. The compression and packing processes were simulated under different conditions of size ratios of 1–4 and fine particle mixing ratios of 0–0.5. The cohesive force was expressed using the surface energy proposed by the Johnson-Kendall-Roberts (JKR) cohesion model having a surface energy of 0–0.2 J/m². The calculated results demonstrated that even in the case of cohesive particles, an increase in the particle size ratio reduced the void fraction of the powder bed during the packing and compression processes. In addition, it was found that the cohesive force decreased the contact number, especially the coarse-coarse contacts, although it had little impact on the void fraction. Our DEM simulations suggested that it is necessary to evaluate the contact numbers even under similar void fractions, which will be essential in the case of different material mixtures, such as all-solid-state batteries.     

Effect of the Strain Rate and Microstructure on Damage Growth in Aluminum

Materials used in soldier protective structures, such as armor, vehicles and civil infrastructures, are being improved for performance in extreme dynamic environments. Nanocrystalline metals show significant promise in the design of these structures with superior strengths attributed to the dislocation-based and grain-boundary-based processes as compared to their polycrystalline counterparts. An optimization of these materials, however, requires a fundamental understanding of damage evolution at the atomic level. Accordingly, atomistic molecular dynamics simulations are performed using an embedded-atom method (EAM) potential on three nano-crystalline aluminum atom systems, one a Voronoi-based nano-crystalline system with an average grain size of 10 nm, and the other two single crystals. These simulations are performed under the condition of uniaxial expansion at several strain rates ranging from 10⁶s^-1 to 10¹⁰s^-1. Results for the effective stress are discussed with the aim of establishing the role of the strain rate and microstructure on the evolution of the plastic strain and void volume fraction and the eventual loss of stress carrying capability of the atom systems.     

A method for solving high-order real symmetric eigenvalue problems

A new method for solving structural dynamics problems has been proposed by the author in a separate paper.¹ This method of solution produces a high order real symmetric eigenvalue problem of the form ( A ? λ B ? λ² C ? λ³ D …) U = 0. An algorithm for solving such an eigenvalue problem using simultaneous iteration is presented in this paper. Methods of accelerating the convergence and reducing the amount of computation are also described. A numerical example is given in which the algorithm is used to calculate the eigenvalues and eigenvectors of a framed structure.     

The tearing of highly oriented linear polyethylene

The tearing behaviour of oriented linear polyethylene has been studied with particular emphasis on the effects of draw ratio, draw temperature and molecular weight distribution. In all cases the values of fracture surface energy were in the range 10² to 10⁴ Jm^–2. The differences between the low molecular weight grades and high molecular weight grades of linear polyethylene were large. At high molecular weight the energy for crack propagation parallel to the direction of orientation fell by a factor of approximately two as the draw ratio was increased from 10 to 20. At low and medium molecular weights, increasing the draw ratio above a value of 10 had no significant effect on the fracture surface energy. Observation of the fracture surfaces showed a simple relationship between the nature of the fracture surface and the value of the fracture surface energy. In general, the higher the value of fracture surface energy the less fibrillar is the fracture surface. Furthermore the fibrillar nature of the fracture surface is essentially determined by the void content of the material.     

A parallel contact detection algorithm for transient solid dynamics simulations using PRONTO3D

An efficient, scalable, parallel algorithm for treating material surface contacts in solid mechanics finite element programs has been implemented in a modular way for multiple-instruction, multiple-data (MIMD) parallel computers. The serial contact detection algorithm that was developed previously for the transient dynamics finite element code PRONTO3D has been extended for use in parallel computation by utilizing a dynamic (adaptive) load balancing algorithm. This approach is scalable to thousands of computational nodes¹     

Closed loop control-based real-time dispatching heuristic on parallel batch machines with incompatible job families and dynamic arrivals

In this paper, a real-time closed loop control dispatching heuristic (RCLC) algorithm is proposed to address the scheduling problem of parallel batch machines with incompatible job families, limited waiting time constraints, re-entrant flow and dynamic arrivals in the diffusion and oxidation areas of a semiconductor wafer fabrication system (SWFS), which is known to be strongly NP-hard. The basis of this algorithm is the information of lots in the buffer when the parallel batch machines are idle and available. In RCLC, if the number of any family lots is less than the maximum batch size, the dispatching heuristic can be seen as a pull–pull–push–push (P⁴) strategy; otherwise, a genetic algorithm (GA). A look-itself strategy, P⁴ strategy and GA can build a closed loop control system. The experiments are implemented on the Petri nets-based real-time scheduling simulation platform of SWFS, and demonstrate the effectiveness of our proposed method.     

An explicit discontinuous Galerkin method for non‐linear solid dynamics: Formulation,parallel implementation and scalability properties

An explicit‐dynamics spatially discontinuous Galerkin (DG) formulation for non‐linear solid dynamics is proposed and implemented for parallel computation. DG methods have particular appeal in problems involving complex material response, e.g. non‐local behavior and failure, as, even in the presence of discontinuities, they provide a rigorous means of ensuring both consistency and stability. In the proposed method, these are guaranteed: the former by the use of average numerical fluxes and the latter by the introduction of appropriate quadratic terms in the weak formulation. The semi‐discrete system of ordinary differential equations is integrated in time using a conventional second‐order central‐difference explicit scheme. A stability criterion for the time integration algorithm, accounting for the influence of the DG discretization stability, is derived for the equivalent linearized system. This approach naturally lends itself to efficient parallel implementation. The resulting DG computational framework is implemented in three dimensions via specialized interface elements. The versatility, robustness and scalability of the overall computational approach are all demonstrated in problems involving stress‐wave propagation and large plastic deformations. Copyright © 2007 John Wiley & Sons, Ltd.     

UNIFIED CONSTRUCTION OF FINITE ELEMENT AND FINITE VOLUME DISCRETIZATIONS FOR COMPRESSIBLE FLOWS

A framework for the construction of node-centred schemes to solve the compressible Euler and Navier–Stokes equations is presented. The metric quantities are derived by exploiting some properties of C⁰ finite element shape functions. The resulting algorithm allows to implement both artificial diffusion and one-dimensional upwind-type discretizations. The proposed methodology adopts a uniform data structure for diverse grid topologies (structured, unstructured and hybrid) and different element shapes, thus easing code development and maintenance. The final schemes are well suited to run on vector/parallel computer architectures. In the case of linear elements, the equivalence of the proposed method with a particular finite volume formulation is demonstrated.     

Adjoint design sensitivity analysis of molecular dynamics in parallel computing environment

An adjoint design sensitivity analysis method is developed for molecular dynamics using a parallel computing scheme of spatial decomposition in both response and design sensitivity analyses to enhance the computational efficiency. Molecular dynamics is a path-dependent transient dynamic problem with many design variables of high nonlinearity. Adjoint variable method is not appropriate for path-dependent problems but employed in this paper since the path is readily available from response analysis. The required adjoint system is derived as a terminal value problem. To compute the interaction forces between atoms in different spatial boxes, only atomic positions in the neighboring boxes are required to minimize the amount of data communications. Through some numerical examples, the high nonlinearity of the selected design variables is discussed. Also, the accuracy of the derived adjoint design sensitivity is verified by comparing with finite difference sensitivity and the efficiency of parallel adjoint variable method is demonstrated.     

Morphology and intersections of crazes in polystyrene films

Craze network with interconnecting crazes was produced in thin (~60nm) polystyrene films by using a spherical stretching method. For 30% and 45% radial strain, the average mesh size, defined as the square root of average non-crazed areas enclosed by crazes, decreased from about 28m to 4.6 and 2.7m, respectively, as the molecular weight increased from 46 900 to 1 350 000. At a molecular weight of about 10⁶, the interactions between crazes became evident by the split and change of directions at the end of their propagation. Two types of intersection appeared to exist in parallel. The first type showed void formation at the intersections with no apparent fibril displacement effect. The second type showed that the fibrils at the intersection of two perpendicular crazes reoriented to a new direction which seemed to be determined by the relative displacements of the two crazes at the intersections. This observation suggests that the craze fibrils can be displaced and further stretched by a second crazing process.     

Magnetic field tracking with MCNP5

With the introduction of continuous-energy heavy charged particle transport in MCNP5, the need for tracking charged particles in a magnetic field becomes increasingly important. Two methods for including magnetic field effects on charged particles are included in the proton transport version of the code. The first technique utilises transfer maps produced by the beam dynamics simulation and analysis code COSY INFINITY. This method is fast and accurate; however, its use is limited to void cells only and to ensembles of particles with a fairly small energy spread. The second technique, particle ray tracing, is based on an algorithm adopted from the MARS transport code. This method can be applied to both void and material cells and is valid over a very large range of particle energies. Results from tracking particles in a quadrupole 'identity lens' using the two techniques are compared.     

Concurrent Implementation of the Optimal Incremental Approximation Method for the Adaptive and Meshless Solution of Differential Equations

The optimal incremental function approximation method is implemented for the adaptive and meshless solution of differential equations. The basis functions and associated coefficients of a series expansion representing the solution are selected optimally at each step of the algorithm according to appropriate error minimization criteria. Thus, the solution is built incrementally. In this manner, the computational technique is adaptive in nature, although a grid is neither built nor adapted in the traditional sense using a posteriori error estimates. Since the basis functions are associated with the nodes only, the method can be viewed as a meshless method. Variational principles are utilized for the definition of the objective function to be extremized in the associated optimization problems. Complicated data structures, expensive remeshing algorithms, and systems solvers are avoided. Computational efficiency is increased by using low-order local basis functions and the parallel direct search (PDS) optimization algorithm. Numerical results are reported for both a linear and a nonlinear problem associated with fluid dynamics. Challenges and opportunities regarding the use of this method are discussed.     

Dynamics of fast dislocations

Plastic deformation of crystalline solids at ultra-high strain rates may involve dislocations moving at supersonic speeds, the feasibility of which has been demonstrated via molecular dynamics simulation. The motion of these dislocations in a crystal depends on the defects they encounter, which may slow, or even pin, them down. Recently, we have conducted a series of investigations on the dynamics of transonic dislocations during their interactions with other dislocations, small voids and small interstitial loops, using the molecular dynamics method. The results indicate that a transonic dislocation will be slowed down to subsonic speed by a subsonic dislocation in front of it, and that approaching dislocations at sufficiently high velocities may not form a stable dipole. Small defects, like voids and interstitial clusters, on the other hand, will only temporarily slow down a segment of the transonic dislocation, which absorbs the interstitial loop by forming jogs, and sweeps the void into a few smaller defects of vacancy type. Upon release from the clusters, this segment of dislocation regains speed and becomes transonic again. In view of the possible important role played by high-speed dislocations during high-speed deformation, and from the point of scientific interest, we summarize this series of investigations, and discuss their implications in the present paper.     

MPP并行机上数亿粒子规模的分子动力学模拟

提出一种基于“块-单元-链表”数据结构和HSFC动态负载平衡的并行分子动力学算法,实现了大规模、非均匀分子动力学模拟的基于MPI的可扩展并行计算,以辅助物理学家实现具有实验意义的纳米级模拟。具体地,在某MPP并行机的240个CPU上,计算3．84亿(二维)和2．76亿(三维)个粒子规模的金属微喷射问题,均获得了209倍以上的加速比。     

Intensity dependence of nonsequential double ionization of aligned asymmetric molecules

The electron correlation in nonsequential double ionization (NSDI) from aligned HeH⁺ molecules by intense laser pulses at various intensities has been investigated with the three-dimensional classical ensemble model. The results show that the correlated emission from NSDI for the parallel alignment is asymmetric. By back analysis the contribution of Coulomb focusing from H⁺ to this asymmetry has been also demonstrated besides the permanent dipole moment of the HeH²⁺ molecule. Moreover, the asymmetry of correlated emissions enhances sharply with decreasing laser intensity. This is attributed to the intensity dependence of the effects of the permanent dipole moment of the HeH²⁺ molecule and Coulomb focusing from H⁺ on the recollision dynamics. Besides the two electrons involved in NSDI of HeH⁺, molecules aligned parallel to the laser polarization are more likely to exit the molecule into the opposite hemispheres compared with the perpendicular alignment at some laser intensities, which is different from the case of symmetric molecules.     

Study of Interatomic Potentials Using the Crystal-GRID Method on Oriented Single Crystals of Ni,Fe, and Cr

The Crystal-GRID method is used to study interatomic collisions at low energy in metals and such to probe the repulsive interatomic potential. Line shapes of gamma rays, emitted by the recoiling ⁵⁹Ni isotope after thermal neutron capture in Ni single crystals, were measured and compared to results obtained by molecular dynamics simulations of the slowing down. The same procedure is also used for recoiling ⁵⁷Fe and ⁵⁴Cr atoms in Fe and Cr single crystals, respectively. Different potentials (including several from the embedded atom method) are investigated using the observed fine structure of the line shape which depends on the crystal orientations. From the detailed study of the lineshapes measured in two different orientations, a new potential is then derived for each element. Nuclear state lifetimes for the excited isotopes are also deduced with a higher precision than obtained with standard nuclear techniques.     

Nonequilibrium Molecular Dynamics Simulation of the Rheology of Linear and Branched Alkanes

Liquid alkanes in the molecular weight range of C₂₀–C₄₀ are the main constituents of lubricant basestocks, and their rheological properties are therefore of great concern in industrial lubricant applications. Using massively parallel supercomputers and an efficient parallel algorithm, we have carried out systematic studies of the rheological properties of a variety of model liquid alkanes ranging from linear to singly branched and multiply branched alkanes. We aim to elucidate the relationship between the molecular architecture and the viscous behavior. Nonequilibrium molecular dynamics simulations have been carried out for n-decane (C₁₀H₂₂), n-hexadecane (C₁₆H₃₄), n-tetracosane (C₂₄H₅₀), 10-n-hexylnonadecane (C₂₅H₅₂), and squalane (2, 6, 10, 15, 19, 23-hexamethyltetracosane, C₃₀H₆₂). At a high strain rate, the viscosity shows a power-law shear thinning behavior over several orders of magnitude in strain rate, with exponents ranging from –0.33 to –0.59. This power-law shear thinning is shown to be closely related to the ordering of the molecules. The molecular architecture is shown to have a significant influence on the power-law exponent. At a low strain rate, the viscosity behavior changes to a Newtonian plateau, whose accurate determination has been elusive in previous studies. The molecular order in this regime is essentially that of the equilibrium system, a signature of the linear response. The Newtonian plateau is verified by independent equilibrium molecular dynamics simulations using the Green–Kubo method. The reliable determination of the Newtonian viscosity from non-equilibrium molecular simulation permits us to calculate the viscosity index for squalane. The viscosity index is a widely used property to characterize the lubricant's temperature performance, and our studies represent the first approach towards its determination by molecular simulation.