Axisymmetric Smoothed Particle Hydrodynamics Research Articles

Tip splitting and ring formation in impact of hollow Al-6061 cylinders on Al-6061 plates

Numerous ductile failure models have been proposed in literature and it is useful to compare them for test problems. We compare three simple failure models on projectile impact problem in which hollow cylindrical Al-6061 projectiles, strike 5 mm thick Al-6061 plates at 403 m/s and undergo fracture in the projectile tip with high speed ejection of a ring-shaped fragment. High resolution simulations employing an axisymmetric formulation of smoothed particle hydrodynamics (SPH) are carried out using three different failure models: (1) a standard Johnson–Cook fit of Leuser (JC); (2) a novel Johnson–Cook fit of Ghahremaninezhad and Ravi-Chandar (GR) based upon grain-level plastic strain measurements; and (3) the Bao-Wierzbicki (BW) failure model. Numerically, the projectile tip splits and a ring is ejected when the SPH interparticle spacing 62 μm or lower, with JC or BW failure. However, simulations using JC model show further splitting of projectile tip contrary to the experiment. Grain-level GR fit produces failure of projectile tip with SPH interparticle spacing of 24 μm. This length is roughly the grain size in Al-6061. Thus, it confirms the idea of Ghahremaninezhad and Ravi-Chandar that high resolution simulations require caliberation of the failure model at the same scale. The ring dimensions obtained through simulations have a discrepancy of about 20 percent with experimental values. Hence, simple BW and GR ductile failure models reproduce experimental results in a relatively complex projectile impact. However, residual discrepancies show need for further investigation of axisymmetric SPH and failure models.

Damage characteristics of ship structures subjected to shockwaves of underwater contact explosions

The damage process of ship structures subjected to underwater contact explosions is characterized by strong nonlinearity, thus there are great challenges in solving such problems. Firstly, the full Smoothed Particle Hydrodynamics (SPH) method for the fluid and structure interaction (FSI) is established based on compressible SPH fluid dynamics and SPH shell. Furthermore, the normal flux method is introduced to treat the interface. However, given the immaturity of the SPH shell in dealing with the fracture of complex structures, an SPH-FEM (Finite Element Method) coupling method for FSI is proposed with the “glue” treatment applied at the interface. The above two methods are verified by an underwater contact explosion experiment. Afterwards, the pressure-time relationship within six charge radii is fitted based on the axisymmetric SPH simulation. On this basis, the flat plates subjected to underwater contact explosions are studied in detail with the application of a combined damage variable. Three stages in the damage process, namely localized bulging, discing and petaling, are observed, and the crack and deflection are found to be sensitive to the changes of peak pressure and impulse respectively. Finally, complex models of a stiffened plate and a ship are established to further study the damage characteristics.

Stable axisymmetric SPH formulation with no axis singularity

SummaryThe axisymmetric formulation of the governing equations for geomechanics in the framework of smoothed particle hydrodynamics (SPH) is presented in this study. Two forms of SPH discretization for the motion equations, which are labeled as form I and form II, are proposed, and the methods to compute the hoop stress and strain terms including hoop strain rate and the acceleration introduced by the hoop stress are compared. To avoid possible singularity problem near the axis of symmetry, a perfectly smooth contact along with ghost particles are applied to prevent the real particles from overly approaching the axis of symmetry to remove this potential singularity. In addition, the Mohr–Coulomb constitutive model is implemented into the SPH formulation in describing soil behavior. Four numerical tests are carried out to validate and compare the accuracy and stability of the proposed algorithms, and their results are compared with analytical solutions and results from FEM analysis. The performance in these comparisons suggests that SPH II with hoop terms computed through direct hoop method is more stable than the others, and the adoption of contact for the symmetric axis is efficient in eliminating the singularity problem. Copyright © 2015 John Wiley & Sons, Ltd.

Perforation of Aluminum Plates with Ogive-Nose Projectiles Using Axisymmetric Smoothed Particle Hydrodynamics

The 2D axisymmetric smoothed particle hydrodynamics (ASPH) has been adopted to study the perforation of AA5083-H116 aluminum plates with ogive-nose hard steel projectiles. The deceleration history curves of the projectile by the ASPH were presented for three impact conditions. Impact vs. residual velocity curves were constructed and the ballistic limit velocity was determined. The computational residual velocities and the ballistic limit velocities from the ASPH agree well with available experimental data. The study shows that the ASPH is able to emulate the perforation of aluminum plates as observed in the experimental investigations of high velocity impact.

Investigation on charge parameters of underwater contact explosion based on axisymmetric SPH method

This paper investigates the effects of charge parameters of the underwater contact explosion based on the axisymmetric smoothed particle hydrodynamics (SPH) method. The dynamic boundary particle is proposed to improve the pressure fluctuation and numerical accuracy near the symmetric axis. An in-depth study is carried out over the influence of charge shapes and detonation modes on the near-field loads in terms of the peak pressure and impulse of shock waves. For different charge shapes, the cylindrical charge with different length-diameter ratios may cause strong directivity of peak pressure and impulse in the near field. Compared with spherical charge, the peak pressure of cylindrical charge may be either weakened or enhanced in different directions. Within a certain range, the greater the length-diameter ratio is, the more obvious the effect will be. The weakened ratio near the detonation end may reach 25% approximately, while the enhanced ratio may reach around 20% in the opposite direction. However, the impulse in different directions seems to be uniform. For different detonation modes, compared with point-source explosion, the peak pressure of plane-source explosion is enhanced by about 5%. Besides, the impulse of plane-source explosion is enhanced by around 5% near the detonation end, but close to those of the point-source explosion in other directions. Based on the material constitutive relation in the axisymmetric coordinates, a simple case of underwater contact explosion is simulated to verify the above conclusions, showing that the charge parameters of underwater contact explosion should not be ignored.

SIMULATION OF NORMAL PERFORATION OF ALUMINUM PLATES USING AXISYMMETRIC SMOOTHED PARTICLE HYDRODYNAMICS WITH CONTACT ALGORITHM

An axisymmetric smoothed particle hydrodynamics (ASPH) with contact algorithm is presented to simulate the normal perforation of aluminum plates. Traditional ASPH considering contact implicitly by conservation equations has the problem of virtual tensile stresses and shear stresses for perforation simulation. To overcome the problem, a particle-to-particle contact algorithm is employed to treat contact interfaces explicitly in the present method. An artificial stress method is extended for the method to remove tensile instability. The present method is firstly validated by three test cases. Then, it is used to simulate the normal perforation of aluminum plates with ogive-nose steel projectiles. Numerical simulation results show that the method predicted residual velocities of projectiles in good agreement with the experimental data.

Numerical simulation of column charge underwater explosion based on SPH and BEM combination

Underwater explosion detonated by column charge can generate exceedingly high-pressure shock wave, bubble pulsing and high-speed jet formed by bubble. Its physical course involves many complicated problems such as transient state, high temperature and high pressure, large distortion and multi-medium flow. For this reason, axisymmetric Smoothed Particle Hydrodynamics (SPHs) numerical model was established combined with Boundary Element Method (BEM) to simulate the whole process of underwater explosion detonated by column charge in this paper. Calculation results of various phases such as shock wave propagation, bubble pulsing and jet formation agree well with the experiment values. In this study, column charge detonation and bubble jet are successfully simulated via axisymmetric SPH method. The calculation results are still of highly precise at the symmetrical axis, verifying the feasibility of the axisymmetric SPH method established in this paper in the computation of three-dimensional underwater explosion, bubble jet and other physical problems. Meanwhile, axisymmetric SPH method and BEM are successfully combined in this paper to fully utilize their advantages, which is favorable in the solution of other hydrodynamic problems.

Characterization of the ballistic limit curve for metallic Whipple shield

It has been known that space debris or meteoroid impact damage can have significant effects on spacecraft. Experimental test has been conducted up to 7 km/s, and numerical simulations are performed at higher velocities. Studies on the hypervelocity impact onto single plate, double spaced plates (Whipple shield), and multiple plates (MS shield) have been performed and ballistic limit curves (BLCs) are proposed. Last 15 years SPH (Smoothed Particle Hydrodynamics) has been applied to the hypervelocity impact problems because of cost of test and numerical efficiency especially in the hypervelocity impact regime. Although most of the simulations captured the debris shape well, somehow they do not seem to match well with the empirical ballistic limit curves. We have recently developed a new axisymmetric SPH hydrocode. In order to assess the confidence that should be placed in such simulations we simulated the hypervelocity impacts on aluminum Whipple shields and compared with the empirical BLCs. The SPH simulations indicated an improved accuracy compared with the previously published SPH simulation results. Other effort we put was using different types of equation of state, however no further improvement was achieved.

IS THERE A HIDDEN HOLE IN TYPE Ia SUPERNOVA REMNANTS?

In this paper we report on the bulk features of the hole carved by the companion star in the material ejected during a Type Ia supernova explosion. In particular we are interested in the long term evolution of the hole as well as in its fingerprint in the geometry of the supernova remnant after several centuries of evolution, which is a hot topic in current Type Iasupernovae studies. We use an axisymmetric smoothed particle hydrodynamics code to characterize the geometric properties of the supernova remnant resulting from the interaction of this ejected material with the ambient medium. Our aim is to use supernova remnant observations to constrain the single degenerate scenario for Type Ia supernova progenitors. Our simulations show that the hole will remain open during centuries, although its partial or total closure at later times due to hydrodynamic instabilities is not excluded. Close to the edge of the hole, the Rayleigh-Taylor instability grows faster, leading to plumes that approach the edge of the forward shock. We also discuss other geometrical properties of the simulations, like the evolution of the contact discontinuity.

Axisymmetric smoothed particle hydrodynamics with self-gravity

The axisymmetric form of the hydrodynamic equations within the smoothed particle hydrodynamics (SPH) formalism is presented and checked using idealized scenarios taken from astrophysics (free fall collapse, implosion and further pulsation of a Sun-like star), gas dynamics (wall heating problem, collision of two streams of gas) and inertial confinement fusion (ablative implosion of a small capsule). New material concerning the standard SPH formalism is given. That includes the numerical handling of those mass points which move close to the singularity axis, more accurate expressions for the artificial viscosity and the heat conduction term and an easy way to incorporate self-gravity in the simulations. The algorithm developed to compute gravity does not rely in any sort of grid, leading to a numerical scheme totally compatible with the Lagrangian nature of the SPH equations.

Axisymmetric SPH simulation of elasto-plastic contact in the low velocity impact

This paper presents a new contact algorithm to analyze an elasto-plastic contact problem using the SPH (Smoothed Particle Hydrodynamics) method. This algorithm is available to both contact types, which are the particle-to-particle contact and the surface-to-particle one. It is employed to determine the actual boundary normal vector and apply the reproducing condition in the cylindrical coordinate. The variational equation based on the virtual work principle is derived and its solution is obtained by the penalty method, which includes both a penetration and a penetration rate. Numerical simulations are presented to show that the proposed algorithm can be applied to the elasto-plastic contact problem for the case that either both bodies are deformable or one is a rigid wall and the other is deformable. Two colliding bodies can be separated with the expected rebound velocity and the total contact force acting on between them similar to theoretical value. Results of the rod impact analysis are shown to be in agreement with the ones obtained by other solution and experiment.