Smoothed Particle Hydrodynamics Method Research Articles

Numerical simulation research on fragments formation of cylindrical cased charge based on SPH method

In order to obtain the fracture and fragmentation of a cased charge under blast loading, the JWL equation of state of HMX-based PBX was fitted based on a cylinder test firstly, then the smooth particle hydrodynamics (SPH) method was used to perform a simulation of cased charge under interior blast loading, in the meantime, an blast test of cased charge was conducted. The results show that the parameters of JWL equation of state and the simulation method were reasonably. The simulated fragments velocities and calculated results from empirical formula agreed well with each other, the maximum error did not exceed 9.5%. Under the direct loading of the detonation wave, the fragments velocities increased to more than 1000m/s immediately within 5us, and then the fragments were continuously accelerated by detonation products and shock wave until the fragments reached the maximum velocities in the later 250us. Eventually, the shape of expansion contour of the casing tended to be ellipsoid. The method and results can provide references for the power design of the fragment warhead, as well as the protection design against the fragments.

Thermo-Structure Approach to Dissimilar Explosive Cladding with Interlayer

A thermodynamic model capable of predicting the change in internal energy, work done, and thermal energy required during aluminum-stainless steel explosive cladding is presented. The mathematical model is instrumental in determining the temperature and pressure developed at the interface, which characterizes the interface microstructure, compared with the numerical simulation. Numerical simulation is implemented by the Smoothed Particle Hydrodynamics method available in ANSYS Autodyn. Furthermore, the effect of different interlayers, such as Al 1100, copper, and SS 304, on kinetic energy utilization and deformation work is discussed. The increase in ram tensile and shear strengths is also reported.

Numerical analysis of water entry under ocean currents with smoothed particle hydrodynamics method

Water entry is a fluid–structure interaction process closely related to the ocean environment. Repeated water entries take place when ships are sailing in an ocean environment, e.g., ocean currents, which greatly affect the ship's safety and stability in navigation. In this paper, we adopt a smoothed particle hydrodynamics method to numerically study the water entry of a bow-flare ship body section under ocean currents. We simulate the process of water entry under different current velocities and analyze in detail the fluid field regarding the free surface evolution, the velocity and pressure distributions, and the body's forces and motions. It is revealed that the ocean current can induce multidirectional fluid impacts, and a stagnation point with zero velocity occurs at the upstream side. Asymmetric fluid fields including the evolution of the free surface and the velocity and pressure distributions around the body can also be found. In addition, discrepancies are caused in the formation time and the range of the high-pressure region. These fluid field changes greatly affect the ship body's dynamic responses. However, the effects of the ocean current are mainly reflected in the direction of the current flow and are relatively small in the direction perpendicular to the flow.

Bird strike simulation on a bonded Ti/CFRP leading edge of an engine fan blade

Bird strike represents a critical loading scenario for aeronautical structures, especially for engine fan blades. It is, therefore, of great importance both to protect the leading edge of the fan blade from impact damage and to be able to detect impact damage directly. In the present study, an explicit finite element (FE) model was developed using the LS-DYNA software to simulate bird strike on the leading edge of a CFRP fan blade protected by an adhesively bonded Ti layer. The model accounts for damage on the CFRP blade through a progressive damage modeling scheme and for debonding through a cohesive zone modeling scheme but not for damage on the Ti layer. For the modeling of the bird, the smooth particle hydrodynamics (SPH) method was used, due to the large deformations that were expected. Using the model, a parametric study on the effects of bird mass and impact energy was performed. The numerical results show that impact damage depends more on impact velocity than the bird mass. In all cases, debonding of the tip of the leading edge was predicted, while for combinations of small bird mass and large impact velocity a more extensive debonding of the protective layer was predicted. Regarding damage in the CFRP, only matrix cracking on the leading edge has been predicted. Aiming to assess the effectiveness of FBGs to detect debonding of the Ti layer due to bird strike, an FBG network has been modeled into the bondline and a study was performed on the correlation of the measured strains with impact damage.

Effect of ramming initial state on band engraving in smooth-bore guns

Most modern tank guns are high bore pressure smooth-bore guns that often use High Explosive Antiarmor (HEAA) projectile in combat. This paper focuses on the coupled smoothbore gun- HEAA projectile system, and analyses the projectile ramming-band engraving process when a tank fires HEAA projectile. First, a finite element mesh model of the coupling dynamics of a large-calibre tank gun smoothbore barrel and HEAA projectile was established, and the band was discretized by using the Smoothed Particle Hydrodynamics (SPH) method based on the Lagrange mesh. Then, the propellant gas pressure acting on the bore and the base of the projectile was defined by ABAQUS user’s subroutine. Finally, the ramming-engraving process simulations were carried out for the ramming residual stress and strain, ramming tilt and different ramming misalignment distances working conditions respectively. According to the simulation results, the effect of different ramming initial states on the band engraving process was obtained. The conclusion provides some reference for the simulation of the band engraving process.

Numerical investigation on the coupled vibrations of piezoelectric energy harvester with a liquid-filled proof mass

Replacing the solid tip mass of a piezoelectric cantilever beam with a liquid-filled mass can increase its frequency bandwidth due to the effect of nonlinear liquid sloshing. To investigate the coupled vibrations of the piezoelectric beam and the sloshing liquid, as well as their contributions to the output power, a coupled two-dimensional finite element method-smoothed particle hydrodynamics model has been developed in this study. Using this model, the dynamic behavior of a piezoelectric beam with a liquid-filled rectangular container as the tip mass, subjected to vertical harmonic excitation, has been investigated. The effects of parametric sloshing, excitation level, and geometric nonlinearity on the output voltages have been studied in detail. The simulation results indicate that: (a) the parametric sloshing in the liquid container exhibits subharmonic characteristics, which can be triggered by matching the excitation frequency to twice the natural frequency of the sloshing mode; (b) the piezoelectric beam exhibits subharmonic or harmonic oscillations at parametric resonance; (c) due to the effect of coupled vibrations, the energy harvester with a liquid-filled proof mass has a broader bandwidth compared to the traditional harvester; (d) the frequency response diagram of the output voltage shows multiple peaks at high excitation amplitudes, and the bifurcations are caused by parametric sloshing.

An energy stable incompressible SPH method with consistent solid boundary treatment

We propose two novel solid wall boundary treatments on the energy-stable Smoothed Particle Hydrodynamics (SPH) method for the Navier–Stokes system which models single-phase incompressible flows. In this work, the solid wall is discretized with dummy particles, and an external force is introduced to restrict the motion of solid particles, whose physical significance and numerical necessity are analyzed. We construct consistent fluid–solid coupling schemes based on the approaches so that the boundary condition is involved in the same equations system with particular constraints. Furthermore, the schemes are unconditionally energy-stable, which allows large time step sizes and leads to efficient computation. A variety of examples are demonstrated to verify the corresponding numerical analysis result, which shows that the approaches can easily handle no-slip and moving boundaries. Finally, we highlight that the energy-stable ISPH with consistent boundary treatments greatly benefits solving long-term problems with steady states.

FEM-SPH Coupling Approach for Impact Response Analysis of Composite Plates with Brick-and-Mortar Structure

Bioinspired nacre-like composites have attracted increasing research interests recently. They are typical composites with brick-and-mortar structure and usually employ a combination of hard material and soft material to achieve a good balance between stiffness and toughness. Impact response analysis of such composites is difficult due to their complex structure and interface. In this work, an effective finite element method-smoothed particle hydrodynamics (FEM-SPH) coupling approach is developed for impact response analysis of composite plates with brick-and-mortar structure. In the approach, hard material taking up the bulk of the composite plate is modeled with the SPH method, and soft material forming thin layer structures in the composite plate is modeled with FEM. A coupling algorithm considering failure behavior is proposed to model bonding interfaces between FEM parts and SPH parts. A particle-to-particle SPH contact algorithm is employed to handle contacts between SPH parts, and a penalty-based FEM-SPH contact algorithm is implemented to treat contacts between FEM parts and SPH parts. The developed coupling approach is used to calculate stress wave propagation in two bonded plates of the same material and different materials and a composite plate with brick-and-mortar structure. The accuracy of the coupling approach is validated by comparing the calculated results with those of analytical method and FEM. The coupling approach is then used to simulate the effects of some factors on the impact damage of composite plates with brick-and-mortar structure. The coupling approach can conveniently model the complex structure and bonding interface of the composite plates and is capable of capturing interface failure and fragmentation of the major composition of the composite plates during impact events. It provides a promising alternative for the impact response analysis of brick-and-mortar composite structures.

An improved SPH scheme for the 3D FEI (Fluid-Elastomer Interaction) problem of aircraft tire spray

The problem of aircraft tire spray produced by taking off or landing on wet runways is widely concerned. When simulating this kind of FEI(Fluid-Elastomer Interaction) problem with traditional SPH((Smoothed Particle Hydrodynamics) method, there are some drawbacks in both fluid and elastomer calculation. For the elastomer simulation, the TL-SPH(Total Lagrangian-SPH) is used to deal with the deformation of tire under complicated motion and load. For the fluid simulation, a new SPH scheme of Riemann solver combined with transport velocity is proposed to solve the problem of particle clumping when the free surface is suffering from violent splash. Then the tire spray model by unified SPH is established, in which both the tire deformation and the spray pattern are validated by experiments. Finally, based on the large-scale tire spray simulation, the phenomenon of tire hydroplaning is studied.

Using an improved SPH algorithm to simulate thermo-hydro-mechanical-damage coupling problems in rock masses

The Thermo-Hydro-Mechanical-Damage (THMD) process inside rock structures is a complex multi-field coupling problem, which is also regarded as the hotspot worldwide. In view of this situation, a fracture mark ξ is introduced to reflect the “active” or “failure” mode of Smoothed Particle Hydrodynamics (SPH) particles, which can simulate rock progressive cracking characteristics. The solid-water interaction modes and the damaged particles - water particles transformation algorithms are embedded into traditional SPH program to simulate the water-stress coupling problems. The heat conduction equations are programmed into SPH, which can reach the goal of modeling the temperature-stress coupling problems. Results show that: By coupling the parameter transformations between water and solid particles, the thermo-hydro-mechanical-damage simulation is then realized. Three numerical examples are carried out to validate the improved THMD method. Finally, an engineering numerical model of a typical tunnel is established, and the THMD coupling processes under complex conditions are simulated, which shows that the improved SPH method can simulate rock THMD multi-field coupling problems. The research results will help understanding the rock THMD coupling mechanisms, meanwhile, it can also promote the applications of SPH method into THMD modeling.

Influence of printing conditions on the extrudate shape and fiber orientation in extrusion deposition additive manufacturing

A numerical framework was developed in this study to investigate the influence of relevant Extrusion Deposition Additive Manufacturing (EDAM) processing conditions on the final fiber orientation, inter-bead void and cross-sectional geometry of the bead laid down as the extrudate. Specifically, four key processes of the EDAM process are studied, namely: (i) flow of 90° angle turn as the extrudate exits the nozzle and is laid down on the previous layer or the substrate, (ii) flow of the bead during compaction, (iii) flow of an extrudate deposited adjacent to the previously compacted bead, and (iv) flow of the adjacent bead during compaction. The simulations utilize an anisotropic viscous flow model implemented using the smoothed particle hydrodynamics method in Abaqus and fiber orientation vectors are evolved under the assumption of affine motion. The simulation results are compared with experiments for printed bead geometries produced and this comparison was shown to validate the modeling approach as useful for predicting fiber orientation, bead geometry, and bead-to-bead contact interface geometry. The processing parameters considered are nozzle height from the substrate, the ratio of the print speed to the extrusion speed (Vb/Ve), and the bead-to-bead lateral overlap distance. A series of virtual experiments were conducted, and the following observations were noted: (i) the bead printed with a high nozzle height has significantly more fiber alignment in the printing direction than the lower nozzle height, (ii) the ratio of the print speed and extrudate speed, Vb/Ve, of greater than unity results in greater fiber alignment than for Vb/Ve <1. The developed model illuminates the roles of process parameters in determining the microstructure of the printed bead and bead geometry.

Simulation of non-cohesive soil turning based on an SPH model

Soil turning is an infrastructure activity in the field of geotechnical engineering. In this study, we propose a new soil turning numerical model based on the Smoothed Particle Hydrodynamics (SPH) method, in which an elastoplastic constitutive model is implemented. To validate the model, firstly, a landslide benchmark test is studied, the error of the maximum sliding distance is only 1.5 % compared to the experimental data. Next, a combined experimental numerical investigation on the soil turning process is carried out. We compare the experimental observations with the numerical modeling results and find that the numerical error of the peak height and the horizontal distance of the soil is about 2.56 % and 3.37 %, respectively, indicating that the proposed SPH model can reproduce the soil turning process accurately. The simulation results also demonstrate that: (1) When the turning speed is increased, the turning resistance does not change significantly but leads to a more sufficient mixing of the soil; (2) There exists a critical turning angle above which the resistance increase significantly associates with a larger angle; (3) Increasing the burying depth of the tool helps to improve the mixing effect; however, leads to larger resistance as well.

Simulation of collapse failure process of rock slope based on the smoothed particle hydrodynamics method

The limit equilibrium method (LEM) or finite element method (FEM) for slope problems most frequently focusses on the stability analysis. There are, however, still some problems with the LEM or FEM when considering damage and failure evolution of a rock slope because of the distortion of mesh. In this work, a mesh-free particle approach, named the smoothed particle hydrodynamics (SPH) method, is presented and is improved to analyze the damage and failure process of a rock slope. In order to better describe the cause and mechanism of brittle failure for a rock slope, the plastic factor was suggested and introduced into the SPH algorithm, and the conservation equations of SPH for brittleness characteristics were obtained. Based on the variation of displacement and time, an effective criterion was proposed to define the factor of safety in SPH simulation. The Drucker-Prager Mohr-Coulomb strength criterion was implemented into the SPH algorithm to describe the elastic-plastic behavior. Then, three rock-slope models with different precast cracks were analyzed to illustrate the performance of the proposed method. It is shown that the proposed SPH algorithm can be effectively applied in the prediction of the deformation and failure process of rock slope.

Three-Dimensional Numerical Modeling of Lava Dynamics Using the Smoothed Particle Hydrodynamics Method

Lava domes and lava flows are major manifestations of effusive volcanic eruptions. Less viscous lava tends to flow long distances, depending on the volcanic slope topography, the eruption rate, and the viscosity of the erupted magma. When magma is highly viscous, its eruption to the surface leads to the formation of lava domes and their growth. The meshless smoothed particle hydrodynamics (SPH) method is used in this paper to simulate lava dynamics. We describe the SPH method and present a numerical algorithm to compute lava dynamics models. The numerical method is verified by solving a model of cylindrical dam-break fluid flow, and the modelled results are compared to the analytical solution of the axisymmetric thin-layer viscous current problem. The SPH method is applied to study three models of lava advancement along the volcanic slope, when the lava viscosity is constant, depends on time and on the volume fraction of crystals in the lava. Simulation results show characteristic features of lava flows, such as lava channel and tube formation, and lava domes, such as the formation of a highly viscous carapace versus a less viscous dome core. Finally, the simulation results and their dependence on a particle size in the SPH method are discussed.

Smoothed particle hydrodynamics method for pinch plasma simulation with non-ideal MHD model

When plasma is compressed by magnetic forces, a pinch phenomenon is observed. Pinch plasma has received significant attention as an efficient source of radiation and a way for high-density plasma physics analysis. In this study, a non-ideal magnetohydrodynamics (MHD) model is applied to a smoothed particle hydrodynamics (SPH) framework to analyze pinch plasmas whose local resistivity varies with temperature and pressure. The proposed SPH model incorporates several numerical treatments, such as a correction term to satisfy the ∇·B constraint and some artificial dissipation terms to govern the shock wave. Moreover, it includes the evaluation of a novel SPH discretization for non-ideal MHD terms, including current density calculations. Furthermore, the proposed model is validated with three benchmark cases: (1) Brio and Wu shock tube (ideal MHD), (2) resistive MHD shock simulation, and (3) magnetized Noh Z-pinch problem. The simulation results are compared with the results of some reference Eulerian MHD simulations and analytical solutions. The simulations agree well with the reference data, and the introduced numerical treatments are effective. Finally, X-pinch simulations are performed using the proposed model. The simulations well produce the micro Z-pinch and jet shapes, which are important X-pinch features. Overall, the proposed SPH model has extensive potential for studying the complex pinch plasma phenomena.

Hydraulic fracturing modelling of glutenite formations using an improved form of SPH method

Due to the low permeability and high heterogeneity properties of glutenite formations, the hydraulic fracture morphologies are extremely distorted during hydraulic fracturing operations, which is difficult to predict by traditional numerical method. Based on the existing limitations (i.e., the mesh re-division problems in FEM, complex parameter calibrations in DEM), an improved Smoothed Particle Hydrodynamics (SPH) method for modelling the hydraulic fracturing of glutenite formations was proposed. The interaction modes between the liquid and solid particles were first defined and the transformation algorithms of liquid, particles and damaged particles were also proposed. Then, the fracture mark ξ was introduced and the traditional kernel function in SPH was improved to simulate the hydraulic fracturing process. The “random gravel generation” algorithm combined with the “searching radius method” were proposed to well reproduce the meso-structures of glutenite. After that, the SPH model of glutenite was established, based on which, the influence of factors such as gravel size, content, strength as well as confining pressure were investigated. Results show that the crack patterns mainly include: 1) Propagating through the gravel; 2) Propagating around the gravel; 3) Stopping inside the gravel; 4) Crack bifurcation. The research results can provide some references for the comprehensive understandings of the internal mechanisms of glutenite hydraulic fracturing processes as well as the applications of SPH method into the simulations of glutenite hydraulic fracturing.

Regularized SPH model for soil–structure interaction with generalized frictional boundary

AbstractThis paper proposes a regularized smoothed particle hydrodynamics (SPH) scheme to solve the problems of tensile instability and stress noise in large‐deformation soil–structure interaction. Particle shifting and stress regularization are combined to maintain uniform stresses and particle distributions. A generalized frictional boundary condition is presented to model soil–structure interfaces with abitrary friction coefficients. A modified particle shifting technique is developed to regularize particles near the frictional boundaries. Furthermore, GPU acceleration algorithm is adopted to improve the efficiency. The proposed scheme is compared with the conventional SPH methods using numerical examples, including the collapse of three‐dimensional granular column, the collapse of the cohesive soil, and pipe penetrates into soft clay. The comparison indicates that the proposed regularized SPH model can give highly accurate results for large‐deformation soil–structure interaction problems with arbitrary friction coefficient.

Smoothed Particle Hydrodynamics-Based Study of 3D Confined Microflows

In this study, we investigate the performance of the smoothed particle hydrodynamics (SPH) method regarding the computation of confined flows in microchannels. Modeling and numerical simulation with SPH involve the representation of flowing matter as distinct mass points, leading to particle discretization of the Navier–Stokes equations. The computational methodology exhibits similarities with other well-established particle methods, such as molecular dynamics (MD), dissipative particle dynamics (DPD), and smooth dissipative particle dynamics (SDPD). SPH has been extensively tested in the simulation of free-surface flows. However, studies on the performance of the method in internal flow computations are limited. In this work, we study flows in microchannels of variable cross-sections with a weakly compressible SPH formulation. After preliminary studies of flows in straight constant cross-section ducts, we focus on channels with sudden expansion and/or contraction. Flow models based on periodic or various inlet/outlet boundary conditions and their implementations are discussed in the context of 2D and 3D simulations. Numerical experiments are conducted to evaluate the accuracy of the method in terms of flowrate, velocity profiles, and wall shear stress. The relation between f and Re for constant cross-section channels is computed with excellent accuracy. SPH captured the flow characteristics and achieved very good accuracy. Compressibility effects due to the weakly compressible smoothed particle hydrodynamics (WCSPH) formulation are negligible for the flows considered. Several typical difficulties and pitfalls in the application of the SPH method in closed conduits are highlighted as well as some of the immediate needs for the method’s improvement.

Restoring particle consistency in discontinuous smoothed particle hydrodynamics

As an important improvement of the smoothed particle hydrodynamics (SPH) method, the finite particle method (FPM) and the kernel gradient free SPH (KGF-SPH) method possess high order accuracy and have shown practicability in processing large deformation, movable boundary, and severe convection modeling problems. However, they might still be unreliable due to the inevitable discontinuous physical phenomena in some real engineering applications. Given that, two improved SPH methods considering interface discontinuity – FPM-DSPH and KGF-DSPH – are proposed based on FPM and KGF-SPH. One- and two-dimensional numerical tests of discontinuous functions are conducted to analyze the approximate accuracy of SPH, DSPH, FPM-DSPH and KGF-DSPH. The results indicate that the new methods enable recovering the zero- and first-order consistency of particles even in the case of strong discontinuity, and possess higher accuracy in reproducing higher-order functions. In addition, the reliability of the proposed methods in dealing with boundary and discontinuous interface is verified by a series of numerical examples, including two-dimensional shear flow in cavity, aluminum block collision, elastic cylinder water entry, droplet oscillation, and droplet impact on the cantilever. This paper provides two attractive alternative approaches for simulating discontinuous physical phenomena.

Simulation of droplet bouncing on flexible substrate in 2D and 3D with WC-TL SPH method

Droplet impacts on super-hydrophobic surfaces play an important role in many fields. Previous studies have focused on rigid substrates and ignored the effect of substrate deformation. Simulating droplet impacts on a flexible substrate is a challenge to numerical methods due to the coupling of free surface, elasticity, large deformation and surface tension. In this study, a fully meshfree model of fluid–solid interaction is developed based on the smoothed particle hydrodynamics (SPH) method. The liquid droplet is modeled by the weakly compressible (WC) SPH method, and the flexible substrate is modeled by the total Lagrangian (TL) SPH method. Liquid surface tension is modeled by the continuum surface force (CSF) method through reconstructing the free surface of the droplet. The surface geometry reconstruction process is given for both 2D and 3D cases, enabling the model to simulate the bouncing of droplets in both 2D and 3D cases. Furthermore, in order to reduce the computational cost of 3D simulation, the TL-SPH model combined with shell theory established the TL-SPH-shell model, thus achieving the simulation of 3D droplet impact on thin plates. For verification and testing, the established WC-TL SPH model is used to simulate the process of droplet impact on various substrates, including fixed-fixed and curved beams, micro-pillar substrates, and cantilever beams. The results show that the spreading, retraction and bouncing processes of the droplets interact with the deformation and recovery of the flexible substrate, accompanied by large deformation and dynamic characteristics, which can be effectively simulated by the model.