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.

A flexible multiscale algorithm based on an improved smoothed particle hydrodynamics method for complex viscoelastic flows

Viscoelastic flows play an important role in numerous engineering fields,and the multiscale algorithms for simulating viscoelastic flows have received significant attention in order to deepen our understanding of the nonlinear dynamic behaviors of viscoelastic fluids.However,traditional grid-based multiscale methods are confined to simple viscoelastic flows with short relaxation time,and there is a lack of uniform multiscale scheme available for coupling different solvers in the simulations of viscoelastic fluids.In this paper,a universal multiscale method coupling an improved smoothed particle hydrodynamics(SPH)and multiscale universal interface(MUI)library is presented for viscoelastic flows.The proposed multiscale method builds on an improved SPH method and leverages the MUI library to facilitate the exchange of information among different solvers in the overlapping domain.We test the capability and flexibility of the presented multiscale method to deal with complex viscoelastic flows by solving different multiscale problems of viscoelastic flows.In the first example,the simulation of a viscoelastic Poiseuille flow is carried out by two coupled improved SPH methods with different spatial resolutions.The effects of exchanging different physical quantities on the numerical results in both the upper and lower domains are also investigated as well as the absolute errors in the overlapping domain.In the second example,the complex Wannier flow with different Weissenberg numbers is further simulated by two improved SPH methods and coupling the improved SPH method and the dissipative particle dynamics(DPD)method.The numerical results show that the physical quantities for viscoelastic flows obtained by the presented multiscale method are in consistence with those obtained by a single solver in the overlapping domain.Moreover,transferring different physical quantities has an important effect on the numerical results.

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.

An efficient non-iterative smoothed particle hydrodynamics fluid simulation method with variable smoothing length

In classical smoothed particle hydrodynamics(SPH)fluid simulation approaches,the smoothing length of Lagrangian particles is typically constant.One major disadvantage is the lack of adaptiveness,which may compromise accuracy in fluid regions such as splashes and surfaces.Attempts to address this problem used variable smoothing lengths.Yet the existing methods are computationally complex and non-efficient,because the smoothing length is typically calculated using iterative optimization.Here,we propose an efficient non-iterative SPH fluid simulation method with variable smoothing length(VSLSPH).VSLSPH correlates the smoothing length to the density change,and adaptively adjusts the smoothing length of particles with high accuracy and low computational cost,enabling large time steps.Our experimental results demonstrate the advantages of the VSLSPH approach in terms of its simulation accuracy and efficiency.

Simulation of mould filling process using smoothed particle hydrodynamics

The implementation of high pressure die casting （HPDC） filling process modeling based on smoothed particle hydrodynamics （SPH） was discussed. A new treatment of inlet boundary was established by discriminating fluid particles from inlet particles. The roles of artificial viscosity and moving least squares method in the present model were compared in the handling pressure oscillation. The final model was substantiated by simulating filling process in HPDC in both two and three dimensions. The simulated results from SPH and finite difference method （FDM） were compared with the experiments. The results show the former is in a better agreement with experiments. It demonstrates the efficiency and precision of this SPH model in describing flow pattern in filling process.

Smoothed particle hydrodynamics modeling and simulation of foundry filling process

A numerical model of foundry filling process was established based on the smoothed particle hydrodynamics（SPH）method.To mimic the constraints that the solid mold prescribes on the filling fluid,a composite treatment to the solid boundaries is elaborately designed.On solid boundary surfaces,boundary particles were set,which exert Lennard-Jones force on approaching fluid particles;inside the solid mold,ghost particles were arranged to complete the compact domain of near-boundary fluid particles.Water analog experiments were conducted in parallel with the model simulations.Very good agreement between experimental and simulation results demonstrates the success of model development.

Numerical Simulation of Dam Breaking Using Smoothed Particle Hydrodynamics and Viscosity Behavior

Smoothed particle hydrodynamics (SPH) is a Lagrangian meshless particle method. It is one of the best method for simulating violent free surface flows in fluids and solving large fluid deformations. Dam breaking is a typical example of these problems. The basis of SPH was reviewed, including some techniques for governing equation resolution, such as the stepping method and the boundary handling method. Then numerical results of a dam breaking simulation were discussed, and the benefits of concepts like artificial viscosity and position correction were analyzed in detail. When compared with dam breaking simulated by the volume of fluid (VOF) method, the wave profile generated by SPH had good agreement, but the pressure had only reasonable agreement. Improving pressure results is clearly an important next step for research.

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 Method to Improve First Order Approximation of Smoothed Particle Hydrodynamics

Smoothed particle hydrodynamics (SPH) is a useful meshless method.The first and second orders are the most popular derivatives of the field function in the mechanical governing equations.New methods were proposed to improve accuracy of SPH approximation by the lemma proved.The lemma describes the relationship of functions and their SPH approximation.Finally,the error comparison of SPH method with or without our improvement was carried out.

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 treatment of solid boundary in smoothed particle hydrodynamics

As a popular meshfree particle method,the smoothed particle hydrodynamics(SPH) has suffered from not being able to di-rectly implement the solid boundary conditions.This influences the SPH approximation accuracy and hinders its further de-velopment and application to engineering and scientific problems.In this paper,a coupled dynamic solid boundary treatment(SBT) algorithm has been proposed,after investigating the features of existing SPH SBT algorithms.The novelty of the cou-pled dynamic SBT algorithm includes a new repulsive force between approaching fluid and solid particles,and a new numeri-cal approximation scheme for estimating field functions of virtual solid particles.The new SBT algorithm has been examined with three numerical examples including a typical dam-break flow,a dam-break flow with a sharp-edged obstacle,and a water entry problem.It is demonstrated that SPH with this coupled dynamic boundary algorithm can lead to accurate results with smooth pressure field,and that the new SBT algorithm is also suitable for complex and even moving solid boundaries.

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.