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

Residual strength is an indispensable factor in evaluating rock fracture,yet the current Smoothed Particle Hydrodynamics(SPH)framework rarely considers its influence when simulating fracture.An improved cracking strategy considering residual stress in the base bond SPH method was proposed to simulate failures in layered rocks and slopes and verified by experimental results and other simulation methods(i.e.,the discrete element method).Modified Mohr–Coulomb failure criterion was applied to distinguish the mixed failure of tensile and shear.Bond fracture markψwas introduced to improve the kernel function after tensile damage,and the calculation of residual stress after the damage was derived after shear damage.Numerical simulations were carried out to evaluate its performance under different stress and scale conditions and to verify its effectiveness in realistically reproducing crack initiation and propagation and coalescence,even fracture and separation.The results indicate that the improved cracking strategy precisely captures the fracture and failure pattern in layered rocks and rock slopes.The residual stress of brittle tock is correctly captured by the improved SPH method.The improved SPH method that considers residual strength shows an approximately 13%improvement in accuracy for the safety factor of anti-dip layered slopes compared to the method that does not consider residual strength,as validated against analytical solutions.We infer that the improved SPH method is effective and shows promise for applications to continuous and discontinuous rock masses.

An Innovative Coupled Common-Node Discrete Element Method-Smoothed Particle Hydrodynamics Model Developed with LS-DYNA and Its Applications

In this study,a common-node DEM-SPH coupling model based on the shared node method is proposed,and a fluid–structure coupling method using the common-node discrete element method-smoothed particle hydrodynamics(DS-SPH)method is developed using LS-DYNA software.The DEM and SPH are established on the same node to create common-node DEM-SPH particles,allowing for fluid–structure interactions.Numerical simulations of various scenarios,including water entry of a rigid sphere,dam-break propagation over wet beds,impact on an ice plate floating on water and ice accumulation on offshore structures,are conducted.The interaction between DS particles and SPH fluid and the crack generation mechanism and expansion characteristics of the ice plate under the interaction of structure and fluid are also studied.The results are compared with available data to verify the proposed coupling method.Notably,the simulation results demonstrated that controlling the cutoff pressure of internal SPH particles could effectively control particle splashing during ice crushing failure.

Application of Smoothed Particle Hydrodynamics(SPH)for the Simulation of Flow-Like Landslides on 3D Terrains

Flow-type landslide is one type of landslide that generally exhibits characteristics of high flow velocities,long jump distances,and poor predictability.Simulation of its propagation process can provide solutions for risk assessment and mitigation design.The smoothed particle hydrodynamics(SPH)method has been successfully applied to the simulation of two-dimensional(2D)and three-dimensional(3D)flow-like landslides.However,the influence of boundary resistance on the whole process of landslide failure is rarely discussed.In this study,a boundary condition considering friction is proposed and integrated into the SPH method,and its accuracy is verified.Moreover,the Navier-Stokes equation combined with the non-Newtonian fluid rheologymodel was utilized to solve the dynamic behavior of the flow-like landslide.To verify its performance,the Shuicheng landslide event,which occurred in Guizhou,China,was taken as a case study.In the 2D simulation,a sensitivity analysis was conducted,and the results showed that the shearing strength parameters have more influence on the computation accuracy than the coefficient of viscosity.Afterwards,the dynamic characteristics of the landslide,such as the velocity and the impact area,were analyzed in the 3D simulation.The simulation results are in good agreement with the field investigations.The simulation results demonstrate that the SPH method performs well in reproducing the landslide process,and facilitates the analysis of landslide characteristics as well as the affected areas,which provides a scientific basis for conducting the risk assessment and disaster mitigation design.

A novel approach to determine residual stress field during FSW of AZ91 Mg alloy using combined smoothed particle hydrodynamics/neuro-fuzzy computations and ultrasonic testing

The faults in welding design and process every so often yield defective parts during friction stir welding(FSW).The development of numerical approaches including the finite element method(FEM)provides a way to draw a process paradigm before any physical implementation.It is not practical to simulate all possible designs to identify the optimal FSW practice due to the inefficiency associated with concurrent modeling of material flow and heat dissipation throughout the FSW.This study intends to develop a computational workflow based on the mesh-free FEM framework named smoothed particle hydrodynamics(SPH)which was integrated with adaptive neuro-fiizzy inference system(ANFIS)to evaluate the residual stress in the FSW process.An integrated SPH and ANFIS methodology was established and the well-trained ANIS was then used to predict how the FSW process depends on its parameters.To verify the SPH calculation,an itemized FSW case was performed on AZ91 Mg alloy and the induced residual stress was measured by ultrasonic testing.The suggested methodology can efficiently predict the residual stress distribution throughout friction stir welding of AZ91 alloy.

Coupling of discrete-element method and smoothed particle hydrodynamics for liquid-solid flows

Particle based methods can be used for both the simulations of solid and fluid phases in multiphase medium, such as the discrete-element method for solid phase and the smoothed particle hydrodynamics for fluid phase. This paper presents a computational method combining these two methods for solid-liquid medium. The two phases are coupled by using an improved model from a reported Lagrangian-Eulerian method. The technique is verified by simulating liquid-solid flows in a two-dimensional lid-driven cavity.

Numerical analysis of submarine landslides using a smoothed particle hydrodynamics depth integral model

Submarine landslides can cause severe damage to marine engineering structures. Their sliding velocity and runout distance are two major parameters for quantifying and analyzing the risk of submarine landslides.Currently, commercial calculation programs such as BING have limitations in simulating underwater soil movements. All of these processes can be consistently simulated through a smoothed particle hydrodynamics（SPH） depth integrated model. The basis of the model is a control equation that was developed to take into account the effects of soil consolidation and erosion. In this work, the frictional rheological mode has been used to perform a simulation study of submarine landslides. Time-history curves of the sliding body＇s velocity, height,and length under various conditions of water depth, slope gradient, contact friction coefficient, and erosion rate are compared; the maximum sliding distance and velocity are calculated; and patterns of variation are discussed.The findings of this study can provide a reference for disaster warnings and pipeline route selection.

An approach for the coupled simulation of machining processes using multibody system and smoothed particle hydrodynamics algorithms

The prediction accuracy of a simulation method is limited by its theoretical background. This fact can lead to disadvantages regarding the simulation quality when investigating systems of high complexity, e.g. containing components showing a fairly different behavior. To overcome this limitation, co-simulation approaches are used more and more, combining the advantages of different simulation disciplines. That is why we propose a new strategy for the dynamic simulation of cutting processes. The method couples Lagrangian particle methods, such as the smoothed particle hydrodynamics （SPH） method, and multibody system （MBS） tools using co-simulations. We demonstrate the capability of the new approach by providing simulation results of an orthogonal cutting process and comparing them with experimental data. @ 2013 The Chinese Society of Theoretical and Applied Mechanics. [doi：10.1063/2.1301305]

A Simplified Approach of Open Boundary Conditions for the Smoothed Particle Hydrodynamics Method

In this paper,we propose a simplified approach of open boundary conditions for particle-based fluid simulations using the weakly compressible smoothed-particle hydrodynamics(SPH)method.In this scheme,the values of the inflow/outflow particles are calculated as fluid particles or imposed desired values to ensure the appropriate evolution of the flow field instead of using a renormalization process involving the fluid particles.We concentrate on handling the generation of new inflow particles using several simple approaches that contribute to the flow field stability.The advantages of theδ^(+).-SPH scheme,specifically the particle shifting technique,were successfully applied to correct the position,velocity,and pressure terms of the particles.Therefore,unexpected errors were removed and tensile instabilities of the particles were prevented.The proposed technique is validated for several benchmark test cases,and the tests show that the results match the reference solutions well.A viscous open-channel flow is used to demonstrate the stability of the flow field during the computational time.Based on this stability,we compress the computational domain to a lower resolution in a second test case while preserving the accuracy of the simulation.Flow over a backward-facing step is used to highlight the challenges of inflow boundary conditions with prescribed or non-prescribed values.The developed technique is well suited to the wall boundaries and the evolution of the flow field.The results demonstrate the robustness and versatility of the proposed technique for a variety of simulations.

Modelling Dam Break Evolution over a Wet Bed with Smoothed Particle Hydrodynamics: A Parameter Study

When investigating water flow in spillways and energy dissipation, it is important to know the behavior of the free surfaces. To capture the real dynamic behavior of the free surfaces is therefore crucial when performing simulations. Today, there is a lack in the possibility to model such phenomenon with traditional methods. Hence, this work focuses on a parameter study for one alternative simulation tool available, namely the meshfree, Lagrangian particle method Smoothed Particle Hydrodynamics (SPH). The parameter study includes the choice of equation-of-state (EOS), the artificial viscosity constants, using a dynamic versus a static smoothing length, SPH particle spatial resolution and the finite element method (FEM) mesh scaling of the boundaries. The two dimensional SPHERIC Benchmark test case of dam break evolution over a wet bed was used for comparison and validation. The numerical results generally showed a tendency of the wave front to be ahead of the experimental results, i.e. to have a greater wave front velocity. The choice of EOS, FEM mesh scaling as well as using a dynamic or a static smoothing length showed little or no significant effect on the outcome, though the SPH particle resolution and the choice of artificial viscosity constants had a major impact. A high particle resolution increased the number of flow features resolved for both choices of artificial viscosity constants, but at the expense of increasing the mean error. Furthermore, setting the artificial viscosity constants equal to unity for the coarser cases resulted in a highly viscous and unphysical solution, and thus the relation between the artificial viscosity constants and the particle resolution and its impact on the behavior of the fluid needed to be further investigated.

Real-time Simulation of Gas Based on Smoothed Particle Hydrodynamics

This paper extends the SPH method to gas simulation. The SPH （Smoothed Particles Hydrodynamics） method is the most popular method of flow simulation, which is widely used in large-scale liquid simulation. However, it is not found to apply to gas simulation, since those methods based on SPH can＇t be used in real-time simulation due to their enormous particles and huge computation. This paper proposes a method for gas simulation based on SPH with a small number of particles. Firstly, the method computes the position and density of each particle in each point-in-time, and outlines the shape of the simulated gas based on those particles. Secondly the method uses the grid technique to refine the shape with the diffusion of particle＇s density under the control of grid, and get more lifelike simulation result. Each grid will be assigned density according to the particles in it. The density determines the final appearance of the grid. For ensuring the natural transition of the color between adjacent grids, we give a diffuse process of density between these grids and assign appropriate values to vertexes of these grids. The experimental results show that the proposed method can give better gas simulation and meet the request of real-time.

Smoothed-Particle Hydrodynamics Simulation of Ship Motion and Tank Sloshing under the Effect of Regular Waves

Predicting the response of liquefied natural gas(LNG)contained in vessels subjected to external waves is extremely important to ensure the safety of the transportation process.In this study,the coupled behavior due to ship motion and liquid tank sloshing has been simulated by the Smoothed-Particle Hydrodynamics(SPH)method.Firstly,the sloshing flow in a rectangular tank was simulated and the related loads were analyzed to verify and validate the accuracy of the present SPH solver.Then,a three-dimensional simplified LNG carrier model,including two prismatic liquid tanks and a wave tank,was introduced.Different conditions were examined corresponding to different wave lengths,wave heights,wave heading angles,and tank loading rates.Finally,the effects of liquid tank loading rate on LNG ship motions and sloshing loading were analyzed,thereby showing that the SPH method can effectively provide useful indications for the design of liquid cargo ships.

Smoothed particle hydrodynamics and its applications in fluid-structure interactions

In ocean engineering, the applications are usually related to a free surface which brings so many interesting physical phenomena （e.g. water waves, impacts, splashing jets, etc.）. To model these complex free surface flows is a tough and challenging task for most computational fluid dynamics （CFD） solvers which work in the Eulerian framework. As a Lagrangian and meshless method, smoothed particle hydrodynamics （SPH） offers a convenient tracking for different complex boundaries and a straightforward satisfaction for different boundary conditions. Therefore SPH is robust in modeling complex hydrodynamic problems characterized by free surface boundaries, multiphase interfaces or material discontinuities. Along with the rapid development of the SPH theory, related numerical techniques and high-performance computing technologies, SPH has not only attracted much attention in the academic community, but also gradually gained wide applications in industrial circles. This paper is dedicated to a review of the recent developments of SPH method and its typical applications in fluid-structure interactions in ocean engineering. Different numerical techniques for improving numerical accuracy, satisfying different boundary conditions, improving computational efficie- ncy, suppressing pressure fluctuations and preventing the tensile instability, etc., are introduced. In the numerical results, various typical fluid-structure interaction problems or multiphase problems in ocean engineering are described, modeled and validated. The prospective developments of SPH in ocean engineering are also discussed.

On the modeling of viscous incompressible flows with smoothed particle hydrodynamics

Smoothed particle hydrodynamics （SPH） is a Lagrangian, meshfree particle method and has been widely applied to diffe- rent areas in engineering and science. Since its original extension to modeling free surface flows by Monaghan in 1994, SPH has been gradually developed into an attractive approach for modeling viscous incompressible fluid flows. This paper presents an overview on the recent progresses of SPH in modeling viscous incompressible flows in four major aspects which are closely related to the computational accuracy of SPH simulations. The advantages and disadvantages of different SPH particle approximation sche- mes, pressure field solution approaches, solid boundary treatment algorithms and particle adapting algorithms are described and analyzed. Some new perspectives and fuRtre trends in SPH modeling of viscous incompressible flows are discussed.

Numerical simulation of hydro-elastic problems with smoothed particle hydrodynamics method

Violent free surface flows with strong fluid-solid interactions can produce a tremendous pressure load on structures, resu- lting in elastic and even plastic deformations. Modeling hydro-elastic problems with structure deformations and a free surfaee breakup is difficult by using routine numerical methods. This paper presents an improved Smoothed Particle Hydrodynamics （SPH） method for modeling hydro-elastic problems. The fluid particles are used to model the free surface flows governed by Navier-Stokes equations, and the solid particles are used to model the dynamic movement and deformation of the elastic solid objects. The improved SPH method employs a Kernel Gradient Correction （KGC） technique to improve the computational accuracy and a Fluid-Solid Interface Treatment （FSIT） algorithm with the interface fluid and solid particles being treated as the virtual particles against their counterparts and a soft repulsive force to prevent the penetration and a corrective density approximation scheme to remove the numerical oscillations. Three typical numerical examples are simulated, including a head-on collision of two rubber rings, the dam break with an elastic gate and the water impact onto a forefront elastic plate. The obtained SPH results agree well with experimental observations and numerical results from other sources.

NUMERICAL WAVE FLUME WITH IMPROVED SMOOTHED PARTICLE HYDRODYNAMICS

This paper presents an improved Nearest Neighboring Particle Searching （NNPS） technique for numerical modeling of water waves with the Smoothed Particle Hydrodynamics （SPH） method. The proposed technique differs from others by introducing the concept of Inner and Outer Particle Searching （lOPS） and shifting most of advanced CPU operations into simple addition operations. The IOPS method is shown to significantly improve the computational efficiency and reduce the CPU time especially for large number of particles, based on comparisons with other two NNPS methods. This method is implemented in a 2DV numerical wave flume conducted by the SPH method. Three test cases are examined, including generations and propagations of dam-breaking induced waves, solitary wave and irregular wave. Calculated results are in good agreements with experimental data and theoretical solutions with fairly satisfactory CPU time-consuming. The wave motions observed in physical facilities are successfully reproduced by the SPH numerical wave flume, revealing its robust capability of modeling realistic wave propagation and substantial potential for a wide variety of hydrodynamic problems.

Surface Tension Model Based on Implicit Incompressible Smoothed Particle Hydrodynamics for Fluid Simulation

In order to capture stable and realistic microscopic features of fluid surface, a surface tension and adhesion method based on implicit incompressible SPH （smoothed particle hydrodynamics） is presented in this paper. It gives a steady and fast tension model and can solve the problem of not considering adhesion. Molecular cohesion and surface minimization are considered for surface tension, and adhesion is added to show the microscopic characteristics of the surface. To simulate surface tension and adhesion stably and efficiently, the surface tension and adhesion model is integrated to an implicit incompressible SPH method. The experimental results show that the method can better simulate surface features in a variety of scenarios compared with previous methods and meanwhile ensure stability and efficiency.

Numerical modeling of sediment transport based on unsteady and steady flows by incompressible smoothed particle hydrodynamics method

The purpose of the present paper is to introduce a simple two-part multi-phase model for the sediment transport problems based on the incompressible smoothed particle hydrodynamics（ISPH） method. The proposed model simulates the movement of sediment particles in two parts. The sediment particles are classified into three categories, including the motionless particles, moving particles behave like a rigid body, and moving particles with a pseudo fluid behavior. The criterion for the classification of sediment particles is the Bingham rheological model. Verification of the present model is performed by simulation of the dam break waves on movable beds with different conditions and the bed scouring under steady flow condition. Comparison of the present model results, the experimental data and available numerical results show that it has good ability to simulate flow pattern and sediment transport.

Simulations of helicopter ditching using smoothed particle hydrodynamics

The present work has been performed in the context of the European H2020 project increased SAfety and Robust certification for ditching of Aircrafts and Helicopters(SARAH)dedicated to improving the safety during aircraft ditching,together with a better understanding of the physics involved during those crucial events.Both numerical and experimental aspects are explored during this project.The present study focuses on the application of the smoothed particle hydrodynamics(SPH)method to the simulation of helicopter ditching,as this method has proved to be particularly adapted to free surface impact cases.Simulations are performed for three different impact configurations,for which the numerical solutions are compared with the experimental results(forces and kinematics)obtained at the wave basin of Ecole Centrale Nantes on a mock-up shape provided by Airbus Helicopters.Elements of sensitivity analysis are also provided when needed,to assess the role of some parameters involved in the helicopter behavior and the fluid pressure forces exerted during the impact.

Smoothed particle hydrodynamics for coarse-grained modeling of rapid granular flow

We simulated rapid flow in transient plane Couette flows of granular particles using the smoothed particle hydrodynamics （SPH） solutions of a set of continuum equations, This simulation was performed to test the viability of SPH in solving the equations for the solid phase of the two-fluid model associated with fluidization. We found that SPH requires the handling of fewer particles in simulating the collective behavior of rapid granular flow, thereby bolstering expectations of solving the equations for the solid phase in the two-fluid modeling of fluidization. Further work is needed to investigate the effect of terms describing pressure and viscous stress of solids on stability in simulations.

Numerical analysis of column collapse by smoothed particle hydrodynamics with an advanced critical state-based model

The complex behavior of granular material considering large deformation and post-failure is of great interest in the geotechnical field.Numerical prediction of these phenomena could provide useful insights for engineering design and practice.In this paper,we propose a novel numerical approach to study soil collapse involving large deformation.The approach combines a recently developed critical state-based sand model SIMSAND for describing complex sand mechanical behaviors,and the smoothed particle hydrodynamics(SPH)method for dealing with large deformation.To show the high efficiency and accuracy of the proposed approach,a series of column collapses using discrete element method(DEM)and considering the influence of particle shapes(i.e.spherical shape(SS),tetrahedral shape(TS),and elongated shape(ES))were adopted as benchmarks and simulated by the proposed method.The parameters of SIMSAND were calibrated from the results of DEM triaxial tests on the same samples.Compared with the results of DEM simulations and reference solutions derived by published collapse experiments,the runout distance and final height of specimens with different particle shapes simulated by SPH-SIMSAND were well characterized and incurred a lower computational cost.Comparisons showed that the novel SPH-SIMSAND approach is highly efficient and accurate for simulating collapse,and can be a useful numerical analytical tool for real scale engineering problems.