Modified Smoothed Particle Hydrodynamics Method Research Articles

Research on the Effect of Particle Distribution on the Crack Propagation in Shaped Energy Blasting Based on the Smoothed Particle Hydrodynamics

Conventional smoothed particle hydrodynamics (SPH) methods suffer from disadvantages, such as difficult initial particle configuration, uneven distribution of generated particles, and low computational efficiency when applied to numerical simulation of shaped charge blasting. In this research, to overcome these problems, a modified SPH method that generates the particle configuration through self-adaptive optimization is developed by the combined application of MATLAB and LS-DYNA. The results presented in this paper demonstrate that the modified configuration method solves the problem of uneven distribution of particles in complex geometry domains by providing a more uniform smoothed particle distribution than the conventional SPH method. Furthermore, the results from the application of these two methods to the bidirectional-shaped charge blasting problem reveal that the defects in the particle configuration in the conventional SPH method lead to the development of main cracks in both the shaped and the unshaped directions. However, with the self-adaptive optimization method, the main cracks develop only in the shaped direction. In addition, the equivalent stress difference between the shaped and unshaped directions, 0.7 ms after detonation, is 120 MPa with the modified method. This is 85 MPa more than that with the conventional method.

A modified SPH method to model the coalescence of colliding non‐Newtonian liquid droplets

SummaryThis paper develops a modified smoothed particle hydrodynamics (SPH) method to model the coalescence of colliding non‐Newtonian liquid droplets. In the present SPH, a van der Waals (vdW) equation of state is particularly used to represent the gas‐to‐liquid phase transition similar to that of a real fluid. To remove the unphysical behavior of the particle clustering, also known as tensile instability, an optimized particle shifting technique is implemented in the simulations. To validate the numerical method, the formation of a Newtonian vdW droplet is first tested, and it clearly demonstrates that the tensile instability can be effectively removed. The method is then extended to simulate the head‐on binary collision of vdW liquid droplets. Both Newtonian and non‐Newtonian fluid flows are considered. The effect of Reynolds number on the coalescence process of droplets is analyzed. It is observed that the time up to the completion of the first oscillation period does not always increase as the Reynolds number increases. Results for the off‐center binary collision of non‐Newtonian vdW liquid droplets are lastly presented. All the results enrich the simulations of the droplet dynamics and deepen understandings of flow physics. Also, the present SPH is able to model the coalescence of colliding non‐Newtonian liquid droplets without tensile instability.

Numerical Study on High Velocity Impact Welding Using a Modified SPH Method

High velocity impact welding (HVIW) involves processes like the impact of metal structures and strong fluid-structure interactions with complex phenomena such as interfacial waves and jet generation. It is very difficult to model the HVIW process with typical physics well captured due to the large deformation and moving interfaces, while the associated mechanisms inherent in HVIW are also not well understood. In this paper, the HVIW process is simulated using a modified smoothed particle hydrodynamics (SPH) model, in which the kernel gradient correction is used to improve computational accuracy and an artificial stress term is used to ease stress instability during the welding process. The mechanisms in HVIW are investigated, and typical phenomena including the wavy interface, jet formation, interfacial temperature and pressure distribution are captured. It is demonstrated that with proper impact welding velocity and initial welding angle, the modified SPH method can well reproduce the morphology evolution of the welding interface from straight to wavy and further to wavy interface with vortex shedding. Based on comprehensive numerical data from SPH simulations, the weldability windows for the HVIW are obtained and are compared with experimental and theoretical results. Welding limits for HVIW are also discussed in detail.

Application of Smoothed Particle Hydrodynamics in analysis of shaped-charge jet penetration caused by underwater explosion

A process of target penetration by a shaped-charge jet includes three main stages: charge detonation, formation of a metallic jet and its penetration of the target. With continuously increasing computational power, a numerical approach gradually becomes more prominent (combined with experimental and theoretical methods) in investigations of performance of a shaped-charge jet and its target penetration. This paper presents a meshfree methodology - Smoothed Particle Hydrodynamics (SPH) - for a shaped charge penetrating underwater structures. First, a SPH model of a sphere impacting a plate is developed; its numerical results agree well with the experimental data, verifying the validity of the mentioned developed method. Then, results obtained for different cases - for various materials of explosives and liners - are discussed and compared, and as a result, more suitable parameters of the shaped charge in order to increase the penetration depth are obtained - HMX and copper were chosen respectively as the explosive and the liner material. It follows by validation of a model of a free-field underwater explosion, developed to verify the effectiveness of the modified SPH method in solving problems of underwater explosion; its numerical results are compared with an empirical formula. Finally, the SPH method is applied to simulate the entire process ranging from the detonation of the shaped charge to the target penetration employing the optimal parameters. A fluid around the shaped charge is included into analysis, and damage characteristics of the plate exposed to air and water on its back side are compared.

A novel hybrid solid-like fluid-like (SLFL) method for the simulation of dry granular flows

This paper proposes a novel hybrid method to simulate the dry granular flow of materials over a wide range of inertial numbers that simultaneously covers the quasi-static and dense granular flow regimes. To overcome the lack of incremental objectivity whenever large deformations occur in solid-like regimes and to remove computational singularities in fluid-like regimes close to rest, the elastic–perfectly plastic theory based on the Drucker–Prager yield criterion is combined with the theory of dense granular flows. By implementing some new modifications at the boundaries and removing all ghost particles, smoothed particle hydrodynamics (SPH) is used as the framework for the method. A number of benchmark problems have been solved to show the capabilities of the new modified SPH method. Precise prediction of both location and pressure makes the modifications comparable with the previous works on SPH. Finally, the method is used to solve the classic 2D dry granular cliff collapse problem and to model dry granular material flow inside a rotary drum. The outcomes of the numerical simulation show good agreement with tabletop experiments and published results.

A Modified SPH Method for Dynamic Failure Simulation of Heterogeneous Material

A modified smoothed particle hydrodynamics (SPH) method is applied to simulate the failure process of heterogeneous materials. An elastoplastic damage model based on an extension form of the unified twin shear strength (UTSS) criterion is adopted. Polycrystalline modeling is introduced to generate the artificial microstructure of specimen for the dynamic simulation of Brazilian splitting test and uniaxial compression test. The strain rate effect on the predicted dynamic tensile and compressive strength is discussed. The final failure patterns and the dynamic strength increments demonstrate good agreements with experimental results. It is illustrated that the polycrystalline modeling approach combined with the SPH method is promising to simulate more complex failure process of heterogeneous materials.

Smoothed particle hydrodynamics modeling of linear shaped charge with jet formation and penetration effects

Shaped charge, as a frequently used form of explosive charge for military and industrial applications, can produce powerful metal jet and lead to stronger penetration effects onto targets than normal charges. After the explosion of high explosive (HE) charge, the detonation produced explosive gas can exert tremendous pressure on surrounding metal case and liner with very large deformation and even quick phase-transition. In this paper, the entire process of HE detonation and explosion, explosion-driven metal deformation and jet formation as well as the penetrating effects is modeled using a smoothed particle hydrodynamics (SPH) method. SPH is a Lagrangian, meshfree particle method, and has been widely applied to different areas in engineering and science. A modified scheme for approximating kernel gradient (kernel gradient correction, or KGC) has been used in the SPH simulation to achieve better accuracy and stability. The modified SPH method is first validated with the simulation of a benchmark problem of a TNT slab detonation, which shows accurate pressure profiles. It is then applied to simulating two different computational models of shaped-charge jet with or without charge cases. It is found that for these two models there is no significant discrepancy for the length and velocity of the jet, while the shapes of the jet tip are different. The modified SPH method is also used to investigate the penetrating effects on a steel target plate induced by a linear shaped charge jet. The effectiveness of the SPH model is demonstrated by the good agreement of the computational results with experimental observations and the good energy conservation during the entire process.

A numerical analysis of drop impact on solid surfaces by using smoothed particle hydrodynamics method

In this paper, we present a numerical simulation of a single liquid drop impacting onto solid surface with smoothed particle hydrodynamics (SPH). SPH is a Lagrangian, meshfree particle method, and it is attractive in dealing with free surfaces, moving interfaces and deformable boundaries. The SPH model includes an improved approximation scheme with corrections to kernel gradient and density to improve computational accuracy. Riemann solver is adopted to solve equations of fluid motion. An new inter-particle interaction force is used for modeling the surface tension effects, and the modified SPH method is used to investigate liquid drop impacting onto solid surfaces. It is demonstrated that the inter-particle interaction force can effectively simulate the effect of surface tension. It can well describe the dynamic process of morphology evolution and the pressure field evolution with accurate and stable results. The spread factor increases with the increase of the initial Weber number. The numerical results are in good agreement with the theoretical and experimental results in the literature.

Numerical simulation of droplet impact onto liquid films with smoothed particle hydrodynamics

In this paper, we present a modified smoothed particle hydrodynamics (SPH) method. In order to well predict the morphology change of liquid drop, the presented SPH method employs a kernel gradient correction and a coupled solid boundary treatment algorithm. An inter-particle interaction force is used to model surface tension, and an artificial stress model is used to deal with tensile instability. The process of droplet impacting on liquid film is numerically simulated by the modified SPH method, which can well predict the pressure field evolution process of the drop impacting onto the liquid film and capture the variation of the free surface at different instants. Effects of Web number and surface stress on droplet impacting are also investigated, and mechanism of droplet splashing is analyzed. It is clearly demonstrated that the modified SPH method can effectively describe the dynamics of droplet splashing and the variation of the free surface. The obtained liquid drop morphology accords well with the results from other sources.

Numerical simulation of droplet impact on liquid with smoothed particle hydrodynamics method

In this paper, we present a modified smoothed particle hydrodynamics (SPH) method. The kernel approximation and the particle approximation are corrected to ensure that polynomial functions are exactly interpolated up to a given degree. Riemann solver is adopted to solve equations of fluid motion. A surface tension calculation program is used for considering the surface tension effects in droplets splashing. The process of droplet impact on liquid surface is numerically simulated by the modified smoothed particle hydrodynamics method. The numerical results clearly demonstrate that the modified SPH method can effectively describe the dynamics of droplet splashing and the variation of the free surface, and that the accuracy of the results can be stable.

Numerical simulation of water mitigation effects on shock wave with SPH method

The water mitigation effect on the propagation of shock wave was investigated numerically. The traditional smoothed particle hydrodynamics (SPH) method was modified based on Riemann solution. The comparison of numerical results with the analytical solution indicated that the modified SPH method has more advantages than the traditional SPH method. Using the modified SPH algorithm, a series of one-dimensional planar wave propagation problems were investigated, focusing on the influence of the air-gap between the high-pressure air and water and the thickness of water. The numerical results showed that water mitigation effect is significant. Up to 60% shock wave pressure reduction could be achieved with the existence of water, and the shape of shock wave was also changed greatly. It is seemly that the small air-gap between the high-pressure air and water has more influence on water mitigation effect.

Symmetric smoothed particle hydrodynamics (SSPH) method and its application to elastic problems

We discuss the symmetric smoothed particle hydrodynamics (SSPH) method for generating basis func- tions for a meshless method. It admits a larger class of kernel functions than some other methods, including the smoothed particle hydrodynamics (SPH), the modified smoothed parti- cle hydrodynamics (MSPH), the reproducing kernel particle method (RKPM), and the moving least squares (MLS) meth- ods. For finding kernel estimates of derivatives of a function, the SSPH method does not use derivatives of the kernel func- tion while other methods do, instead the SSPH method uses basis functions different from those employed to approxi- mate the function. It is shown that the SSPH method and the RKPM give the same value of the kernel estimate of a function but give different values of kernel estimates of deriv- atives of the function. Results computed for a sine function defined on a one-dimensional domain reveal that the L 2 ,t he H 1 and the H 2 error norms of the kernel estimates of a func- tion computed with the SSPH method are less than those found with the MSPH method. Whereas the L 2 and the H 2 norms of the error in the estimates computed with the SSPH method are less than those with the RKPM, the H 1 norm of the error in the RKPM estimate is slightly less than that found with the SSPH method. The error norms for a sam- ple problem computed with six kernel functions show that their rates of convergence with an increase in the number of uniformly distributed particles are the same and their magni- tudes are determined by two coefficients related to the decay rate of the kernel function. The revised super Gauss function has the smallest error norm and is recommended as a ker- nel function in the SSPH method. We use the revised super

Modified Smoothed Particle Hydrodynamics (MSPH) basis functions for meshless methods, and their application to axisymmetric Taylor impact test

The Modified Smoothed Particle Hydrodynamics (MSPH) method proposed earlier by the authors and applied to the analysis of transient two-dimensional (2-D) heat conduction, 1-D transient simple shearing deformations of a thermoviscoplastic material, 1-D wave propagation in a functionally graded plate, and 2-D elastodynamic crack propagation is extended to the analysis of axisymmetric deformations of a thermoviscoplastic material. In the MSPH method, different shape functions are used to find kernel estimates of the function, and of its first and second derivatives. It differs from the classical finite element method in which derivatives of a function are usually obtained by differentiating the shape function used to approximate the function. It is shown that results computed with the MSPH method for the Noh problem agree well with its analytical solution. The MSPH basis functions can be used in any meshless method to numerically solve either static or dynamic problems. The method is then applied to analyze transient deformations of a cylindrical rod impacting at normal incidence a rigid smooth stationary flat plate. The computed solution is found to agree very well with those obtained by analyzing axisymmetric and 3-D transient deformations of the rod with the commercial code LS-DYNA. The final length of the deformed rod, the final radius of the impacted face, and the final length of the relatively undeformed portion of the rod for twelve test configurations computed with the MSPH method are also found to agree well with their corresponding experimental values.

Search algorithm, and simulation of elastodynamic crack propagation by modified smoothed particle hydrodynamics (MSPH) method

We first present a nonuniform box search algorithm with length of each side of the square box dependent on the local smoothing length, and show that it can save up to 70% CPU time as compared to the uniform box search algorithm. This is especially relevant for transient problems in which, if we enlarge the sides of boxes, we can apply the search algorithm fewer times during the solution process, and improve the computational efficiency of a numerical scheme. We illustrate the application of the search algorithm and the modified smoothed particle hydrodynamics (MSPH) method by studying the propagation of cracks in elastostatic and elastodynamic problems. The dynamic stress intensity factor computed with the MSPH method either from the stress field near the crack tip or from the J-integral agrees very well with that computed by using the finite element method. Three problems are analyzed. One of these involves a plate with a centrally located crack, and the other with three cracks on plates’s horizontal centroidal axis. In each case the plate edges parallel to the crack are loaded in a direction perpendicular to the crack surface. It is found that, at low strain rates, the presence of other cracks will delay the propagation of the central crack. However, at high strain rates, the speed of propagation of the central crack is unaffected by the presence of the other two cracks. In the third problem dealing with the simulation of crack propagation in a functionally graded plate, the crack speed is found to be close to the experimental one.

Wave propagation in functionally graded materials by modified smoothed particle hydrodynamics (MSPH) method

We use the modified smoothed particle hydrodynamics (MSPH) method to study the propagation of elastic waves in functionally graded materials. An artificial viscosity is added to the hydrostatic pressure to control oscillations in the shock wave. Computed results agree well with the analytical solution of the problem. It is shown that, for the same placement of particles/nodes the MSPH method gives better results than the finite element method when the initial smoothing length in the MSPH method is 1.1 times the distance between two adjacent particles. Effects of the artificial viscosity are also examined, and the optimum value of the linear artificial viscosity that minimizes the relative error in computed stresses is found.

Analysis of adiabatic shear bands in elasto-thermo-viscoplastic materials by modified smoothed-particle hydrodynamics (MSPH) method

We use the modified smoothed-particle hydrodynamics (MSPH) method to analyze shear strain localization in elasto-thermo-viscoplastic materials that exhibit strain- and strain-rate hardening and thermal softening. A homogeneous solution of simple shearing deformations of the body is perturbed and the resulting initial-boundary-value problem analyzed by the MSPH method. It is found that the deformation localizes into a narrow region of intense plastic deformation. In materials exhibiting enhanced thermal softening, an elastic unloading shear wave emanates from this region and propagates outwards. The time when the deformation localizes decreases exponentially with an increase in the thermal softening coefficient. Results have been computed without adding an artificial viscosity and compared with those obtained by the finite element method.