Smoothed Particle Hydrodynamics Method Research Articles

Thermomechanical bending of functionally graded carbon nanotubes reinforced composite plate by meshless method

AbstractFunctionally graded (FG) carbon nanotubes (CNTs) reinforced composite possessing continuously varied material properties have received extensive concern in the area of aviation, automotive, military, and spaceflight. The nonlinear bending of FG CNT composite is performed by developing a novel meshless model on the base of Smoothed Particle Hydrodynamics (SPH) method. The equivalent temperature relative material properties of composite is established in the light of the extended rule of mixture model. Different gradient dispersions of CNTs are taken into account and modeled. The governing equations are explored using the Mindlin theory and discretized though a symmetric SPH method with high prediction ability. The developed model is verified by analyzed several examples and compared to the solution obtained in literature. Influences of CNT dispersion, content, plate aspect ratio, boundary conditions and lamination angle on the bending response are elaborated. The present study provides an alternative potential method to solve the mechanical performances of FG CNT composites based on the meshless SPH formulation.Highlights Thermo‐mechanics of FG‐CNTRC is firstly solved by SPH method. The model is verified by solving the benchmarks in literature. Nonlinear bending behaviors of FG‐CNTRC are demonstrated. The minimum deflection take place in FG‐X type composite. For laminate plate, the smallest deformation occurs in 0° CNTRC.

Numerical simulation of solidification of molten slag impacting inclined wall in boiler based on smoothed particle hydrodynamics method

In order to study the process of high temperature liquid slag impinging on the wall, the slagging phase change is produced by combustion of high alkali coal in a boiler chamber. In this paper, based on the smoothed particle hydrodynamics (SPH) method, the flow spreading and solidification model of slag particles hitting the inclined wall are established, and the dynamic process of flow spreading and the phase change of slag particles hitting the wall are analyzed by simulating the deposition process of the phase change of slag particles hitting the wall. The effects of different inclination angles of the wall on its deformation and solidification heat transfer are further discussed. It is shown that the change of inclination angle during the impact of single slag on the wall has a greater influence on the spreading flow process. During the impact of single/double slag on the wall with different inclination angles, the time taken by the double slag to reach the final spreading length and complete phase transition is nearly five times longer than that of the single slag. The direction of slag impact also has an effect on the spreading and phase transition. This SPH method provides a novel numerical simulation idea to study the kinetic behavior of molten slag hitting the wall and the problems related to phase change deposition in boilers.

An efficient truncation scheme for Eulerian and total Lagrangian smoothed particle hydrodynamics methods

In smoothed particle hydrodynamics (SPH) method, the particle-based approximations are implemented via kernel functions, and the evaluation of performance involves two key criteria: numerical accuracy and computational efficiency. In the SPH community, the Wendland kernel reigns as the prevailing choice due to its commendable accuracy and reasonable computational efficiency. Nevertheless, there exists an urgent need to enhance computational efficiency while upholding accuracy. In this paper, we employ a truncation approach to limit the compact support of the Wendland kernel to 1.6h. This decision is based on the observation that particles within the range of 1.6h to 2h make negligible contributions to the SPH approximation. To decrease numerical errors from SPH approximation and the truncation method, we incorporate the Laguerre–Gauss kernel for particle relaxation to obtain the high-quality particle distribution with reduced residue [Wang et al., “A fourth-order kernel for improving numerical accuracy and stability in Eulerian and total Lagrangian SPH,” arXiv:2309.01581 (2023)], and the kernel gradient correction to rectify integration errors. A comprehensive set of numerical examples including fluid dynamics in Eulerian formulation and solid dynamics in total Lagrangian formulation are tested and have demonstrated that truncated and non-truncated Wendland kernels enable achieving the same level of accuracy but the former significantly increases the computational efficiency.

Progressive failure and quantitative stability analysis of rock slope with cross-type discrete fracture network using spring-based smoothed particle hydrodynamics method

The propagation and coalescence of discontinuous cross-type joints are often the primary drivers of rock slope failures. Due to the inherent randomness of these joints, identifying suitable methods to accurately characterize progressive failure and quantitatively assess the stability of slopes with cross-type joints is particularly challenging. To address this, a Discrete Fracture Network-Spring Based-Smoothed Particle Hydrodynamics (DFN-SB-SPH) method is proposed, which considers cross-type DFN generation, rock matrix heterogeneity, cracking, block contact, and deposition within a unified SPH framework. In this approach, damage and contact of blocks are achieved by introducing a fracture sign to enhance the kernel function and applying Newton's law to the damaged particles to realize the point to point contact. A uniaxial compression test on rock samples with double fissures is carried out to verify the accuracy of the proposed method. The influence of joint density, geometric parameters (i.e., trace length, dominate dip angle) of cross joints, and rock mass heterogeneity on the failure characteristics of RSCD are investigated. The results revealed that the DFN-SB-SPH model possesses robust capabilities for crack tracking, mass movement, and contact slipping along fracture surfaces. Moreover, DFN generation, heterogeneous characterization, shear and tensile fractures within a single SPH framework without mesh distortion are realized. Five typical failure modes calculated by DFN-SB-SPH are primarily determined by the combination of joint dip angles and trace lengths. Furthermore, the dip angle, trace length, joint density, and rock mass heterogeneity significantly alter the stability of RSCD with sensitivity coefficients for factor safety of 27.7 %, 44.6 %, 72.9 % and 35.0 %, respectively. Higher dominant dip angles (above 60°) lead to significantly longer run-out distances for RSCD compared to lower angles (below 30°) once instability occurs. The sudden rise in major principal stress at the slope's top and toe, along with the shift of tensile stress concentration towards the middle, predicts the stages of crack propagation and sliding in slope failure.

Numerical simulation of melt flow and heat transfer in casting filling process based on SPH

There is a great influence of the melt filling process on the quality of castings. Smoothed particle hydrodynamics (SPH) that materials are approximated by free particles rather than by fixed grids is applied to accurately predict fluid flows involving complex free surfaces. In this paper we present a mathematical model of melt flow and heat transfer by using SPH method. A novel approach is used in the governing equations to ensure stable numerical schemes and homogeneous particle distributions. The SPH heat equation takes into account the thermal release during phase transition and is more suitable for alloy solidification. The solid wall boundary conditions are slightly modified to satisfy the filling simulations. Several case studies are carried out to predict significant details about the filling order and flow structures in the mold cavity. The velocity and temperature distributions during different stages of melt filling are also given. The results show that this proposed model allows us to understand the predisposition of defects such as gas porosity and weld lines in the castings. These predictions can be used as inputs for improving process parameters, venting and cooling systems design.

A numerical study on a winglet floating breakwater: Enhancing wave dissipation performance

Box-type floating breakwaters (FBs), widely used for marine protection, face challenges in their wave dissipation capabilities. Although the effectiveness of the winglet-type floating breakwater in improving wave dissipation has been recognized, the specific mechanisms involved are not fully understood. This research presents an innovative winglet breakwater design, featuring three unique winglet configurations: 4-wings, Down-wings, and Up-wings. The study examines its performance against both regular and irregular waves using the Smooth Particle Hydrodynamics (SPH) method, taking into account factors such as the wave period, FB immersion depth, and FB relative density. Numerical simulations indicate a marked enhancement in wave dissipation for the FB equipped with four winglets compared to a baseline model without winglets. The Response Amplitude Operator (RAO) amplitude for the winglet-equipped FB is notably lower, approximately half that observed in the baseline scenario. Notably, the winglet FB's performance in irregular waves outperforms that in regular wave conditions. The insights gained from the design of these winglets provide significant contributions to practical engineering applications.

Stability analysis of layered circular rock tunnels considering anchor reinforcement based on an enhanced mesh-free method

The impact of geotechnical structure and support construction on the stability of a layered circular rock tunnel was investigated based on an improved mesh-free method. The Smoothed Particle Hydrodynamics (SPH) was improved by incorporating a total bridge broken strategy into the kernel function and was validated through analysis of the mechanical behavior in circular opening problem and uniaxial compression tests. The Particle Domain Search (PDS) method is utilized to create crack pathways and implement anchor reinforcement in specific areas without the requirement for grid division. An SPH model of the Muzhailing tunnel was established to investigate the stability of the surrounding rock considering different anchor lengths and spacing. The result indicated that the enhanced SPH method provides a feasible approach for the rapid assessment of tunnel convergence displacement and damage coefficients. Furthermore, this method was validated through laboratory experiments and analytical solutions. For layered tunnels with other different dip angles, this approach offers a general optimization strategy for anchor reinforcing surrounding rock. These findings suggest that the enhanced mesh-free method, owing to its characteristics of efficient parameter calibration and computation, can be further expanded to the rapid assessment of the stability of layered slopes and foundations considering anchor reinforcement.

An SPH framework for drained and undrained loading over large deformations

AbstractWe propose a new approach for performing drained and undrained loading of elastoplastic geomaterials over large deformations using smoothed particle hydrodynamics (SPH), a meshfree continuum particle method, combined with the modified Cam Clay (MCC) model of critical state soil mechanics. The numerical approach draws upon a novel one‐particle two‐phase penalty‐method based formulation for handling undrained loading in saturated soils, which allows tracking of the buildup of pore‐water pressures under combined shearing and compression. Large‐scale parallelized simulations are employed to accommodate a significant number of degrees of freedom in a three‐dimensional setting. After verification and benchmark testing, the SPH based formulation is used to analyze the propagation of reverse faults through fluid‐saturated clay deposits and the rupture of strike‐slip faults across earthen embankments. The computational methodology tests the robustness of the meshfree approach in situations where the soil tends to dilate on the ‘dry’ side of the critical state line and to compact on the ‘wet’ side, but cannot, because of the incompressibility constraint imposed by undrained loading. Our results extend the current understanding of fault rupture modeling and further demonstrate the potential of our framework together with the SPH method for large deformation analyses of complex problems in geotechnics.

Numerical simulation of the damage and ignition responses of high explosives under low-velocity impact using the SPH method

The damage evolution and ignition mechanism of high explosives are of great importance in assessing the safety of munitions and guiding the design of munitions. In this study, the smoothed particle hydrodynamics (SPH) method is combined with a viscoelastic–viscoplastic-damage constitutive model and a hot spot model to explore the damage and ignition responses of high explosives under low-velocity impact. In particular, the sub-particle method is developed in the SPH method to combine the macroscopic constitutive model with the mesoscopic hot spot model. First, the damage evolution of a compressed plate containing a cavity and the ignition response of a single particle at a given pressure and strain rate are studied separately, and the simulation results are validated by experimental results and existing finite element method simulations. Subsequently, the impact shear and crack extrusion tests of high explosives with complex stress states are explored, respectively. For typical pressed PBX under impact-shear loading, a large damage region is formed in the high explosives due to the tensile stress formed by the meeting of rarefaction waves, and the initial ignition region is mainly located in the region where the outer edge of the rod is in contact with the high explosives and extends in a circular shape to the inside of the explosives. For typical pressed PBX under crack extruded loading, the damage region is mainly concentrated in the materials squeezed into the crack, and the initial ignition region is mainly located around the crack and gradually extends above the crack. The results indicate that the proposed SPH method is capable of modeling the damage and ignition responses of high explosives under complex stress states.

Systematic Literature Review on Smoothed Particle Hydrodynamic Method for Coastal Protection Optimizing

Systematic Literature Review on Smoothed Particle Hydrodynamic Method for Coastal Protection Optimizing

A coupled FD-SPH method for shock-structure interaction and dynamic fracture propagation modeling

Shock wave propagation and their damage to solid structures, which involve complex multiphase and multiphysics phenomena, are difficult problems to address. In this paper, a three-dimensional graphics processing unit (GPU)-accelerated finite difference-smoothed particle hydrodynamics (FD-SPH) method was developed for the prediction of strongly compressible fluid flow and strong fluid-structure interactions. The conventional mesh-based finite difference method was used to simulate shock wave propagation, while the smoothed particle hydrodynamics method was employed to predict the dynamic behavior of solid materials. In addition, the immersed boundary method (IBM) was implemented in the GPU-accelerated FD-SPH solver for the boundary treatment of the interface between solid and fluid materials. Four numerical cases, namely shock-cylinder obstacle interaction, elastic panel deformation induced by shock wave propagation, the response of stainless steel tubes under internal blast loading, and the damage of blast loading on reinforced concrete slab, were conducted for verification of the GPU-accelerated FD-SPH solver. The numerical results were compared against the available experimental data, which shows that the GPU-accelerated FD-SPH solver is capable of capturing the shock wave propagation and its damage to structures very well.

SPH modeling and investigation of the effect of the carbon dioxide entry form on its absorption rate in a microchannel containing absorbent aqueous solution

Carbon capture technology is a rapidly growing and developing field that has seen extensive research conducted in both experimental and numerical studies. The majority of numerical simulations conducted thus far have primarily concentrated on mesh-based methods, disregarding the potential of full Lagrangian methods in accurately simulating multiphase and intricate flows. Consequently, this research aims to address this gap by introducing, for the first time, the application of the Lagrangian Smoothed Particle Hydrodynamics (SPH) method to simulate and analyze the process of carbon dioxide absorption in an aqueous solution. The first step in this study involves developing a suitable and relatively accurate algorithm based on the governing equations of carbon dioxide absorption. These equations encompass mass and momentum conservation, heat transfer, mass transfer, and chemical reactions. Once the algorithm is developed, it is validated through computational code and the optimal grid of particles is selected for calculations. Subsequently, three different scenarios for the entry of carbon dioxide into the aqueous solution are modeled and discussed. The results reveal that as the number of carbon dioxide inputs increases, the instabilities of the two-phase flow along the microchannel also increase. These instabilities significantly enhance the rate of carbon dioxide absorption. Overall, this study highlights the importance of considering Lagrangian methods, specifically the SPH method, in simulating multiphase and complex flows in carbon capture technology. The findings contribute to a better understanding of the carbon dioxide absorption process and can potentially aid in the development of more efficient carbon capture systems.

New design of materials, order and thicknesses of an aircraft windshield behaviour layers to increase its resistance against repeated bird impacts

Abstract There are instances when an aircraft encounters a bird’s flock or faces a heavy hailstorm, causing the windshield to sustain consecutive impacts. Therefore, the investigation of windshield resistance against repeated impacts is crucial. In this research, various tests such as tensile, split Hopkinson pressure bar (SHPB), and three-point bending are conducted to extract the mechanical properties of the materials used in a five-layers windshield under high strain rates. Using this information, the bird impact on the windshield is simulated using the smooth particle hydrodynamics (SPH) method, and the results are compared with real bird impact test outcomes, and the validation of this simulation is confirmed. The simulation of two consecutive bird strikes indicates the current windshield lacks sufficient resistance against successive dual impacts; in such scenarios, the second bird penetrates the windshield after breaking it and tearing the interlayer. Considering new materials and thicknesses for each windshield layer, a Taguchi experimental design method is employed to examine various layer arrangements with different materials and thicknesses. The configurations in which the windshield can withstand a maximum of three bird impacts in succession are identified. Subsequently, using the “the smaller, the better” criterion in the Taguchi optimisation approach, the configuration that not only prevents bird penetration but also minimises the maximum strain in the inner layer is selected as the desired outcome. Thus, a new five-layer windshield with new materials and thicknesses is presented, which is resistant to the repeated collision of up to three birds, tearing in the interlayer and bird penetration does not happen.

Fragment dispersion characteristics of uncoupled charge structures with internal explosive loading

The demand for uncoupled charge structures has risen alongside advancements in warheads and protective design technologies in defense and public security sectors. Consequently, this work investigates the fragment dispersion characteristics of uncoupled charge structures and the impact of different structural parameters through numerical simulations. A modified equation derived from the Gurney formula is proposed using numerical simulation and the smoothed particle hydrodynamics method, tailored to the uncoupled charge concept and the foundational theory of the Gurney formula. To validate the fragment velocity prediction model for uncoupled charge structures, explosion experiments and other testing methods were utilized. By examining the theoretical underpinnings and the application of numerical simulation methods, this paper provides a robust foundation for the uncoupled charge structure, offering a crucial reference for designing protective measures against improvised explosive devices.

Simulation study on the damage behavior of tantalum target plates under high-velocity projectile impact

This study aims to explore the damage behavior of tantalum target plates under high-velocity projectile impact, addressing the threats of damage in the aerospace field due to debris and other factors. With the advent of low-cost space launches and large satellite projects, spacecraft such as space stations are facing increasingly severe collision risks. The research utilizes numerical simulation techniques, based on ANSYS/AUTODYN software and the Smoothed Particle Hydrodynamics (SPH) method, to simulate the impact process of projectiles of different velocities (1 ∼ 10 km/s) and materials (aluminum and steel) on tantalum target plates. The results are intended to provide theoretical support for the design of spacecraft protection structures and contribute data support for establishing a millimeter-level space debris impact database.

A modified smoothed particle hydrodynamics method considering residual stress for simulating failure and its application in layered rock mass

A modified smoothed particle hydrodynamics method considering residual stress for simulating failure and its application in layered rock mass

Fallback Rates in Partial Tidal Disruptions of White Dwarfs by Intermediate-mass Black Holes

The fallback rate of debris after the partial tidal disruption of a star by an intermediate-mass black hole (IMBH) might provide important signatures of such black holes rather than supermassive ones. Here using smoothed particle hydrodynamics methods, we provide a comprehensive numerical analysis of this phenomenon. We perform numerical simulations of single partial tidal disruptions of solar-mass white dwarfs in parabolic orbits, with a nonspinning 103 M ⊙ IMBH for various values of the impact parameter, and determine the core mass fractions and fallback rates of debris into the IMBH. For supermassive black holes, in full disruption processes, it is known that the late-time fallback rate follows a power law t −5/3, whereas for partial disruptions, such a rate has recently been conjectured to saturate at a steeper power law t −9/4, independent of the mass of the remnant core. We show here that for IMBHs, partial disruptions significantly alter this conclusion. That is, the fallback rate at late times does not asymptote to a t −9/4 power law, and this rate is also a strong function of the core mass. We derive a robust formula for the late-time fallback rate as a function of the core mass fraction, which is independent of the mass of the white dwarf, as we verify numerically by varying it.

Application of mesh-free and finite element methods in modelling nano-scale material removal from copper substrates: A computational approach

This study explores the modelling methodology using mesh-free smoothed particle hydrodynamics (SPH) and finite element modelling (FE) techniques to simulate the AFM-based nano-scratching processes for advancing precision engineering in nanotechnology. Tip wear in nano machining substantially increases the tip radius, thereby influencing the material removal mechanism and subsequently affecting the quality of machined nanostructures. In this context, this study examines the effects of rake angle (the inclination of the main cutting edge to the plane perpendicular to the scratched surface), tip radius and scratching depth on cutting forces, groove dimensions, and deformed thickness. This was achieved by implementing an in-house SPH method based particle code employing a Lagrangian algorithm, and an FE model incorporating the dynamic explicit algorithm implemented (in ABAQUS) to carry out nano-scratching simulations. The investigation revealed that the cutting mechanism transitioned to ploughing when the scratching depth decreased to 30% of the tip radius for OFHC-Cu workpiece material machined with a diamond tip. The dominance of normal forces over cutting forces during scratching indicated the side flow of material in the vicinity of the tip radius under intense contact pressure. The ploughing mechanism exhibited more sensitivity at a higher negative rake angle of 60°. Increased scratching depth and tip radius led to more significant material deformation owing to the induction of higher cutting forces, with the maximum deformation thickness 3.6 times the tip radius. The simulated results demonstrated favourable concordance with the experimental data.

Analysis of fluid force and flow fields during gliding in swimming using smoothed particle hydrodynamics method

Gliding is a crucial phase in swimming, yet the understanding of fluid force and flow fields during gliding remains incomplete. This study analyzes gliding through Computational Fluid Dynamics simulations. Specifically, a numerical model based on the Smoothed Particle Hydrodynamics (SPH) method for flow-object interactions is established. Fluid motion is governed by continuity, Navier-Stokes, state, and displacement equations. Modified dynamic boundary particles are used to implement solid boundaries, and steady and uniform flows are generated with inflow and outflow conditions. The reliability of the SPH model is validated by replicating a documented laboratory experiment on a circular cylinder advancing steadily beneath a free surface. Reasonable agreement is observed between the numerical and experimental drag force and lift force. After the validation, the SPH model is employed to analyze the passive drag, vertical force, and pitching moment acting on a streamlined gliding 2D swimmer model as well as the surrounding velocity and vorticity fields, spanning gliding velocities from 1 m/s to 2.5 m/s, submergence depths from 0.2 m to 1 m, and attack angles from −10° to 10°. The results indicate that with the increasing gliding velocity, passive drag and pitching moment increase whereas vertical force decreases. The wake flow and free surface demonstrate signs of instability. Conversely, as the submergence depth increases, there is a decrease in passive drag and pitching moment, accompanied by an increase in vertical force. The undulation of the free surface and its interference in flow fields diminish. With the increase in the attack angle, passive drag and vertical force decrease whereas pitching moment increases, along with the alteration in wake direction and the increasing complexity of the free surface. These outcomes offer valuable insights into gliding dynamics, furnishing swimmers with a scientific basis for selecting appropriate submergence depth and attack angle.

Study on Water Entry of a 3D Torpedo Based on the Improved Smoothed Particle Hydrodynamics Method

The water entry of a torpedo is a complex nonlinear problem, involving transient impact, free surface deformation, droplet splashing, and fluid–structure coupling, which poses severe challenges to traditional mesh methods. The meshless smoothed particle hydrodynamics (SPH) method shows unique advantages in capturing the complex features of the water entry of the torpedo at different entry angles. However, it still suffers from some inherent shortcomings, such as low surface discretization accuracy, poor discretization flexibility, and low calculation efficiency. In this study, an improved adaptive SPH algorithm is proposed to investigate the water entry of the torpedo accurately and efficiently. This method integrates meshless point generation and adaptive techniques simultaneously. The numerical results demonstrate that when the torpedo vertically enters the water at different velocities, the induced impact loads acting on the head of the torpedo fluctuate significantly with two peak values in the initial stage and thereafter stabilize in a later stage. The impact load acting on the torpedo, the entry depth of the torpedo, the splash height of the droplets, and the size of the cavity generated around the torpedo increase with the increment in the entry velocity. When the torpedo enters the water at different entry angles under the same initial entry velocity, both the vertical and the horizontal movements of the torpedo are observed, which results in more complex variations in parameters along the x- and y-axes. The findings and the corresponding numerical method in this study can provide a certain basis for the future designs of the entry trajectory and the structural bearing capacity of torpedoes.