A robust weakly compressible SPH method and its comparison with an incompressible SPH

This paper presents a comparative study for the weakly compressible (WCSPH) and incompressible (ISPH) smoothed particle hydrodynamics methods by providing numerical solutions for fluid flows over an airfoil and a square obstacle. Improved WCSPH and ISPH techniques are used to solve these two bluff body flow problems. It is shown that both approaches can handle complex geometries using the multiple boundary tangents (MBT) method, and eliminate particle clustering‐induced instabilities with the implementation of a particle fracture repair procedure as well as the corrected SPH discretization scheme. WCSPH and ISPH simulation results are compared and validated with those of a finite element method (FEM). The quantitative comparisons of WCSPH, ISPH and FEM results in terms of Strouhal number for the square obstacle test case, and the pressure envelope, surface traction forces, and velocity gradients on the airfoil boundaries as well as the lift and drag values for the airfoil geometry indicate that the WCSPH method with the suggested implementation produces numerical results as accurate and reliable as those of the ISPH and FEM methods. Copyright © 2011 John Wiley & Sons, Ltd.     

Hypervelocity impacts on thin brittle targets: Experimental data and SPH simulations

The meteoroids and debris environment play an important role in the reduction of spacecraft lifetime. Ejecta or secondary debris, are produced when a debris or a meteoroid impact a spacecraft surface. Brittle materials are particularly sensitive to HVI in term of damages and amount of ejected matter: the ejected fragments total mass is in the order of 100 times bigger than the impacting mass. The French atomic energy commission (CEA) faces the same problem in the Laser MégaJoule project. The lasers optics will be bombarded by hypervelocity debris and shrapnel resulting from target disassembly. Two millimeter thick fused silica disposable debris shields (DDS) located in front of the main debris shields might be used to reduce very small shrapnel cratering on the main debris shields. The aim of this paper is to study the damaging and ejection processes that occur during HVI on thin brittle targets. A two-stage light-gas gun has been used to impact 2 mm DDS with 500 μm steel projectiles. Experimental characterization of ejected matter has also been performed: lightweight paperboards coated with adhesive have been used to collect ejected fragments including spalls. Numerical simulation using the smooth particle hydrodynamics (SPH) method of LS-DYNA and the Johnson Holmquist material model were performed. The results of these calculations are compared to experimental data which include the damage features in the targets (spalled zones and perforation hole) and the ejection clouds. Satisfying agreement between numerical and experimental simulations was obtained for damage characteristics and ejection phenomena.     

A skewed kernel approach for the simulation of shocks using SPH

A wide variety of jump discontinuities, such as shock fronts, are abound in high‐speed flows. An accurate approximation of these fronts may require higher order techniques either under mesh‐based methods or mesh‐free methods. In the latter class, the smoothed particle hydrodynamics (SPH) is becoming popular as a promising method. However, the standard approach in SPH (like any other discrete methods) can result in highly diffusive solutions because of the inevitable use of artificial viscosity to suppress numerical oscillations. On the other hand, the SPH formulation allows innovative ways to model complicated phenomena. In this paper, we introduce the novel idea of a skewed Gaussian kernel, to improve the shock capturing capability in high speed flows. Here, the standard Gaussian kernel function is modified, and its ‘shape’ is altered with a predesigned tunable skewness parameter, while the basic unity property of the kernel function is still preserved. The SPH with the proposed skewed Gaussian kernel is then applied on a number of benchmark problems in computational fluid dynamics, featuring shocks. The simulations have shown significantly better shock capture through the skewed kernel approach as against the standard techniques, with almost no increase in computational time. Copyright © 2016 John Wiley & Sons, Ltd.     

SPH and FEM Investigation of Hydrodynamic Impact Problems

Simulation of hydrodynamic impact problems and its effect on surrounding structures, can be considered as a fluid structure coupling problem. The application is mainly used in automotive and aerospace engineering and also in civil engineering. Classical FEM and Finite Volume methods were the main formulations used by engineers to solve these problems. For the last decades, new formulations have been developed for fluid structure coupling applications using mesh free methods as SPH method, (Smooth Particle Hydrodynamic) and DEM (Discrete Element Method). Up to these days very little has been done to compare different methods and assess which one would be more suitable. In this paper the mathematical and numerical implementation of the FEM and SPH formulations for hydrodynamic problem are described. From different simulations, it has been observed that for the SPH method to provide similar results as FEM Lagrangian formulations, the SPH meshing, or SPH particle spacing needs to be finer than FEM mesh. To validate the statement, we perform a simulation of a hydrodynamic impact on an elasto-plastic plate structure. For this simple, the particle spacing of SPH method needs to be at least two times finer than FEM mesh. A contact algorithm is performed at the fluid structure interface for both SPH and FEM formulations. In the paper the efficiency and usefulness of two methods, often used in numerical simulations, are compared.     

Creep failure model of a tempered martensitic stainless steel integrating multiple deformation and damage mechanisms

A new model considering both deformation and damage evolution under multiple viscoplastic mechanisms is used to represent high temperature creep deformation and damage of a martensitic stainless steel in a wide range of load levels. First, an experimental database is built to characterise both creep flow and damage behaviour using tests on various kinds of specimens. The parameters of the model are fitted to the results and to literature data for long term creep exposure. An attempt is made to use the model to predict creep time to failure up to 10⁵ h.     

基于SPH方法的剪切流驱动液滴在固体表面变形运动数值模拟研究

光滑粒子流体动力学(SPH)方法是纯拉格朗日粒子方法,可以有效避免网格法在模拟大变形过程中带来的网格扭曲等缺陷,适合模拟含大变形的剪切流驱动液滴在固体表面变形运动过程。在基于CSF模型的表面张力SPH方法基础上,采用新的边界处理方式和界面法向修正方法,引入Brackbill提出的壁面附着力边界条件处理方法,得到了含壁面附着力边界条件的表面张力算法。基于新方法模拟了剪切流驱动液滴在固体表面变形运动过程并与实验结果和VOF方法模拟结果进行了对比验证。结果表明：该方法在处理壁面附着力问题时精度较高,稳定性较好,适合处理工程中剪切流驱动液滴在固体表面变形运动问题。     

Correction and stabilization of smooth particle hydrodynamics methods with applications in metal forming simulations

Smooth particle hydrodynamics (SPH) is a robust and conceptually simple method which suffers from unsatisfactory performance due to lack of consistency. The kernel function can be corrected to enforce the consistency conditions and improve the accuracy. For simplicity in this paper the SPH method with the corrected kernel is referred to as corrected smooth particle hydrodynamics (CSPH). The numerical solutions of CSPH can be further improved by introducing an integration correction which also enables the method to pass patch tests. It is also shown that the nodal integration of this corrected SPH method suffers from spurious singular modes. This spatial instability results from under integration of the weak form, and it is treated by a least‐squares stabilization procedure which is discussed in detail in Section 4. The effects of the stabilization and improvement in the accuracy are illustrated via examples. Further, the application of CSPH method to metal‐forming simulations is discussed by formulating the governing equation associated with the process. Finally, the numerical examples showing the effectiveness of the method in simulating metal‐forming problems are presented. Copyright © 2000 John Wiley & Sons, Ltd.     

SPH Simulation of Low Reynolds Number Planar Shear Flow and Heat Convection

The present study reports on a set of computer programmable SPH formulations, which are used to simulate transient planar shear flows, and in particular Poiseuille flow and Couette flow with different types of body forces. The flows examined have Reynolds numbers within the range 0.05∼50. SPH results agree well with analytical solutions for those situations amenable to an analytical treatment, with the largest deviation being less than 2.0 %. The accuracy of a SPH formulation for heat convection, with particular emphasis in the viscous heat dissipation, is also tested via a steady convective heat transfer case for a combined Poiseuille and Couette flow.     

Coupled DEM-SPH simulations of wet continuous screening

During screening, a liquid stream, besides the vibration, can be applied for the acceleration of the separation. The discrete element method coupled with the smoothed particle hydrodynamics (DEM-SPH) is used to numerically analyse wet continuous screening here. Within the applied DEM-SPH a new simple model for the representation of the screening surface is suggested in this study. In this model, the influence of the screening surface on the fluid is represented using external forces, which act on the SPH particles in close vicinity of the screen. A required validation of the DEM-SPH method for the analysis of a vibrated particle-laden system is performed by comparing obtained DEM-SPH results with the results derived using the DEM coupled with finite volume method. The performed simulations of dry and wet continuous screening demonstrate that flowing water, in most simulated cases, accelerates the separation of particles. The presented study demonstrates the potential of the coupled DEM-SPH method for the analysis of wet screening processes. To our best knowledge, the simulation of wet screening using a two-way coupled numerical DEM-SPH approach not resolving the flow around individual particles is demonstrated in the scientific literature for the first time.     

A model of continuum damage mechanics for fatigue failure

This paper describes the development of a generalized model of continuum damage mechanics for fatigue fracture. With the introduction of a new damage effect tensor, the necessary constitutive equations of elasticity and plasticity coupled with damage are for the first instance derived. This is followed by the formulations of fatigue damage dissipative potential function and a fatigue damage criterion which are required for the development of a fatigue damage evolution equation. The fatigue evolution model is based on the hypothesis that the overall fatigue damage is induced by the summation of elastic and plastic damages.The validity of the damage model proposed is verified by comparing the predicted and measured number of cycles to failure for ten tensile specimens each applied with different load ranges and excellent agreement has been achieved.University of Science and Technology of China     

A synergistic creep fatigue failure model damage (case of the alloy Z5NCTA at 550 °C)

Creep-fatigue tests have been performed on nickel base alloy Z5NCTA 33-21 grade 1. Hold time varied from 0, 10, 30, 90, 300, 1440 and 10,080 min at two values of strain range. It was found that the number of cycles to failure N_R decreases with holding time t_m, according to a power law:

N_R=1.88×10³·(t_m)^-0.39.     

A composite ply failure model based on continuum damage mechanics

A material model including the failure behaviour is derived for a thin unidirectional (UD) composite ply. The model is derived within a thermodynamic framework and the failure behaviour is modelled using continuum damage mechanics. The following features describe the model: (i) The ply is assumed to be in a plane state of stress. (ii) Three damage variables associated with the stress in the fibre-, transverse and shear directions, respectively, are used. (iii) The plastic behaviour of the matrix material is modelled. (iv) The difference in the material response in tensile and compressive loading is modelled. (v) Rate dependent behavior of plasticity and damage (i.e. strength) is modelled.     

A combined elastoplastic damage model for progressive failure analysis of composite materials and structures

The paper is concerned with the development and verification of a combined elastoplastic damage model for the progressive failure analysis of composite materials and structures. The model accounts for the irreversible strains caused by plasticity effects and material properties degradation due to the damage initiation and development. The strain-driven implicit integration procedure is developed using equations of continuum damage mechanics, plasticity theory and includes the return mapping algorithm. A tangent operator consistent with the integration procedure is derived to ensure a computational efficiency of the Newton–Raphson method in the finite element analysis. The algorithm is implemented in Abaqus as a user-defined subroutine. The efficiency of the constitutive model and computational procedure is demonstrated using the analysis of the progressive failure of composite laminates containing through holes and subjected to in-plane uniaxial tensile loading. It has been shown that the predicted results agree well with the experimental data reported in the literature.     

A heterogeneous space–time full approximation storage multilevel method for molecular dynamics simulations

A heterogeneous space–time full approximation storage (HFAS) multilevel formulation for molecular dynamics simulations is developed. The method consists of a waveform Newton smoothing that produces initial space–time iterates and a coarse model correction. The formulation is coined as heterogeneous since it permits different interatomic potentials to be applied at different physical scales. This results in a flexible framework for physics coupling. Time integration is performed in windows using the implicit Newmark predictor–corrector method that permits larger time integration steps than the explicit method. The size of the time steps is governed by accuracy rather than by stability considerations of the algorithm. We study three different variants of the method: the Picard iteration, constrained dynamics and force splitting. Numerical examples show that FAS based on force splitting provides significant time savings compared to standard explicit methods and alternative implicit space–time schemes. Parallel studies of the Picard iteration on harmonic problems illustrate the time parallelization effect that leads to a superior parallel performance compared to explicit methods. Copyright © 2007 John Wiley & Sons, Ltd.     

A saturated discrete particle model and characteristic-based SPH method in granular materials

Based on the discrete particle model for solid-phase deformation of granular materials consisting of dry particulate assemblages, a discrete particle–continuum model for modelling the coupled hydro-mechanical behaviour in saturated granular materials is developed. The motion of the interstitial fluid is described by two parallel continuum schemes governed by the averaged incompressible N–S equations and Darcy's law, respectively, where the latter one can be regarded as a degraded case of the former. Owing to the merits in both Lagrangian and mesh-free characters, the characteristic-based smoothed particle hydrodynamics (SPH) method is proposed in this paper for modelling pore fluid flows relative to the deformed solid phase that is modelled as packed assemblages of interacting discrete particles. It is assumed that the formulation is Lagrangian with the co-ordinate system transferring with the movement of the solid particles. The assumed continuous fluid field is discretized into a finite set of Lagrangian (material) points with their number equal to that of solid particles situated in the computational domain. An explicit meshless scheme for granular materials with interstitial water is formulated. Numerical results illustrate the capability and performance of the present model in modelling the fluid–solid interaction and deformation in granular materials saturated with water. Copyright © 2007 John Wiley & Sons, Ltd.     

带有限等待的动态HFS调度的拉格朗日松弛算法

作为基于最优化的近似算法,分析了拉格朗日松弛算法的分解策略,设计了算法的实现优化过程.针对从钢铁生产提炼出的带有限等待时间要求的动态HFS调度,采用基于工件解耦的分解策略,应用拉格朗日松弛算法进行求解,以最小化总加权完成时间和工件等待惩罚之和.该算法将工件耦合约束松弛到目标函数中,将形成的松弛问题分解成多个更易求解的工件级子问题,进而利用动态规划求解这些子问题,通过拉格朗日乘子的更新迭代过程获得原问题的近优解.对不同问题规模的测试结果表明,该算法能在较短的计算时间内得到较好的近优解,说明了拉格朗日松弛算法求解等待时间受限的HFS调度的可行性和有效性.     

基于SPH方法对不同药型罩线性聚能射流形成及后效侵彻过程的模拟

为了解决传统基于网格的数值方法在模拟线性聚能射流问题时因大变形而导致网格畸变使计算难以进行的问题,本文通过自编程实现的光滑粒子法（SPH）对不同药型罩线性聚能装药射流形成及其侵彻金属靶板的过程开展了数值模拟研究,所实现的算法可以为线性聚能射流数值模拟研究提供新途径。本文所开展的研究首先基于已有的线性聚能射流试验模型进行模拟分析,采用SPH方法有效实现了线性聚能射流的形成过程,数值模拟获得的射流头部速度与试验比对误差在10%以内。然后建立了装药质量、药型罩质量和装药横截面宽度相同的前提下不同药型罩线性聚能射流模型,数值模拟获得不同药型罩形成的射流特征以及侵彻金属靶板的开口宽度和侵彻深度随时间的变化规律。研究得到的不同药型罩线性聚能射流形成及后效侵彻规律可为线性聚能射流的设计提供参考。