A GPU-based SPH Algorithm

The stress intensity factors or strain energy release rate are typically used to characterise the stress field in the vicinity of a crack in fracture mechanics. One way to obtain the strain energy release rate in elastic–plastic fracture mechanics is from the stress and deformation field around the crack tip through the calculation of the J integral. The J-integral is contour independent, although the contour must start and end from a traction-free surface, such as the crack surface. Using Green’s theorem, the J-integral can be formulated as a surface or area integral, which makes it convenient for implementation in finite element method (FEM). More importantly, the J-integral calculation is insensitive to uncertainty of the exact crack tip location, can be applied for linear elastic analysis with small scale yielding and in an improved formulation for elastic plastic fracture. In short, the J-integral is an indispensable tool in the study of fracture mechanics. Despite the J-integral being widely used in FEM, including availability in most commercial FEM codes, there is currently no algorithm to calculate the J-integral in the Smoothed Particle Hydrodynamics (SPH) method. This is somewhat surprising since the SPH method, due to its meshless nature, has inherent advantages in dealing with cracks compared to mesh based methods such as FEM. In this paper we will therefore address this deficiency and develop an algorithm for calculation of the J integral in the SPH method. The implementation of his new alghorithm is based on a new definition of the weighting function q 1 , as appropriately normalised kernel function, which inherently satisfies all the specific requirements on q 1 : The function is sufficiently smooth in the J-integral area, it is equal to unit inside contour path of the integral and zero outside of the path. A further element of novelty is that in the current implementation, the gradient of this function is evaluated analytically rather than through a numerical approximation. The verification and validation of developed algorithm is based on simulation of the standard single edge notch tension test (SENT) under the plain strain conditions. The SPH results are compared to the FEM results for stress and displacement fields in the vicinity of the crack tip, as well as the J integral solutions. The SPH results demonstrated convergence and were within 2% of the converged FEM solutions. The validation also allows for the definition of simple guidelines for the definition of the J-integral area to achieve accurate results. The implementation is currently developed for linear elastic fracture mechanics applications, but its generalisation and application to elastic plastic fracture mechanics, including the combination with elastic plastic constitutive models is straightforward. • New algorithm to calculate J-Integral developed in Smoothed Particle Hydrodynamics (SPH). • New approach for calculating gradient of J-Integral weighting function q 1 analytically. • Confirmed accuracy of J-integral results from SPH compared to FEM results.

In this paper, a new bird model which combined the visco-elastic material properties and Smooth Particle Hydrodynamics (SPH) method has been proposed to simulate the bird features in high-speed conditions. A rigid plate impact test was adopted to compare the reaction of SPH and Lagrangian bird model. Compared with the results of Lagrangian bird model, new SPH model was more in line with the experimental data, and has better computational efficiency. The SPH bird model was further used to bird impacting with the wing leading edge by using finite element program LS-DYNA. Two kinds of leading edge structural enhancement programs have been proposed and carried out simulation of bird impact. Basis of calculation, the design parameters of experimental structure was determined and was produced to wait for final testing.

An improved Riemann SPH-Hamiltonian SPH coupled solver for hydroelastic fluid-structure interactions

An overview of smoothed particle hydrodynamics for simulating multiphase flow

Purpose – The purpose of this paper is to present an efficient smoothed particle hydrodynamics (SPH) method particularly adapted for the geometrically nonlinear analysis of structures. Design/methodology/approach – In order to resolve the inconsistency phenomenon which systematically occurs in the standard SPH method at the domain’s boundaries of the studied structure, the classical kernel function and its spatial derivatives were modified by the use of Taylor series expansion. The well-known tensile instabilities inherent to the Eulerian SPH formulation were attenuated by the use of the Total Lagrangian Formulation (TLF). Findings – In order to demonstrate the effectiveness of the present improved SPH method, several numerical applications involving geometrically nonlinear behaviors were carried out using the explicit dynamics scheme for the time integration of the PDEs. Comparisons of the obtained results using the present SPH model with analytical reference solutions and with those obtained using ABAQUS finite element (FE) commercial software, show its good accuracy and robustness. Practical implications – An additional application including a multilayered composite structure and involving buckling and delamination was investigated using the present improved SPH model and the results are compared to the FE results, they confirmed both the efficiency and the accuracy of the proposed method. Originality/value – An efficient 2D-continuum SPH model for the geometrically nonlinear analysis of thin and thick structures is proposed. Contrarily to the classical SPH approaches, here the constitutive material relations are used to link naturally the stresses and strains. The Total Lagrangian approach is investigated to alleviate the tensile instabilities problem, allowing at the same time to avoid the updating procedure of the neighboring particles search and therefore reducing CPU usage. The proposed approach is valid for isotropic and multilayered composites structures undergoing large transformations. CPU time savings and better results with the new 2D-continuum SPH formulation compared to the classical continuum SPH. The explicit dynamic scheme was used for time integration allowing a fast resolution algorithm even for highly nonlinear problems.

Helmholtz decomposition-based SPH

We present our benchmark results for a newly developed multi-phase chemodynamic code by using the raceSPH library on different hardware accelerators. A maximum speedup of 24x is reached for the SPH part in the serial run when the Smoothed Particle Hydrodynamics (SPH) calculation is accelerated by an NVIDIA GeForce 8800 GTS 512 graphics card (128 cores, 1.8GHz). This code is developed for the simulation of physical processes in dwarf galaxies, in which the SPH method is used to describe the behavior of warm gas. The raceSPH library implements the SPH calculation on different hardware. It provides a set of general interfaces to help integrate hardware accelerators into existing astrophysical programs. In this paper we show that after both gravity and SPH calculation are accelerated by GPU, the neighbour list construction consumes most of the time and becomes the bottleneck of the current program.

Comparison investigations of numerical simulations of incompressible viscous flows by the SPH (smoothed particle hydrodynamics) and the MPS (moving particle semi-implicit) are presented. A dam-break problem is chosen as the test case. In the calculation with the SPH method, weakly compressible model is used, i.e. WCSPH, which describes water as a nearly incompressible fluid, while in MPS method, the pressure Poisson equation is introduced to keep the density of fluid to be constant. The numerical results show that the two particle methods are robust and flexible, numerical results qualitatively agree with the experimental data. It can be seen that both the SPH method and the MPS method can be easily applied to the complex free surface flow problems.

SUMMARYThis paper presents the development, calibration, and validation of a smoothed particle hydrodynamics (SPH) model for the simulation of seismically induced slope deformation under undrained condition. A constitutive model that combines the isotropic strain softening viscoplasticity and the modified Kondner and Zelasko rule is developed and implemented into SPH formulations. The developed SPH model accounts for the effects of wave propagation in the sliding mass, cyclic nonlinear behavior of soil, and progressive reduction in shear strength during sliding, which are not explicitly considered in various Newmark‐type analyses widely used in the current research and practice in geotechnical earthquake engineering. Soil parameters needed for the developed model can be calibrated using typical laboratory shear strength tests, and experimental or empirical shear modulus reduction curve and damping curve. The strain‐rate effects on soil strength are considered. The developed SPH model is validated against a readily available and well‐documented model slope test on a shaking table. The model simulated slope failure mode, acceleration response spectra, and slope deformations are in excellent agreement with the experimental data. It is thus suggested that the developed SPH model may be utilized to reliably simulate earthquake‐induced slope deformations. This paper also indicates that if implemented with appropriate constitutive models, SPH method can be used to model large‐deformation problems with high fidelity. Copyright © 2013 John Wiley & Sons, Ltd.

This paper discusses alternative Lagrangian formulations for smooth particle hydrodynamics method. These Lagrangian formulations are here employed in solving large strain problems that involve elasto-plastic and hyperelastic materials. It has previously been shown in the literature that the Lagrangian formulation for continuum eliminates the problem of tension instability which is generally coupled with Eulerian continuum formulation of smooth particle hydrodynamics and other meshless methods. This paper presents the details of the methodologies used in formulating Lagrangian smooth particle hydrodynamics method and their characteristics.

Ultrasonic-assisted grinding, a promising processing technique for machining hard and brittle materials, is already quite extensively employed in manufacturing industries. However, the material removal mechanism in ultrasonic-assisted grinding is not yet fully understood, which hinders its further application. This study investigates the material removal process in ultrasonic-assisted scratching (UAS) of SiC ceramics using both simulation and experiment method, in order to detail the material removal mechanism in ultrasonic-assisted grinding. A conventional scratching (CS) test was also carried out, but without ultrasonic vibration for comparison. The simulated workpiece is modeled by smooth particle hydrodynamic (SPH) particles. Results show the following: (1) the SPH method is suitable to investigate the material removal mechanism during ultrasonic-assisted grinding of hard and brittle materials. (2) The profile of scratching trace in ultrasonic vibration (UV) is a sinusoidal path. UV vibrating in the direction vertical to the workpiece results in material removed in either a continuous or a discontinuous mode. UV vibrating in the direction parallel to the workpiece expands the cutting area. (3) The groove depth in UAS is much bigger than that in CS. (4) UV results in the impact of the abrasive grain on the workpiece, causing the deformation field to spread from the impact site and leading to deeper scratching depths and larger radial and lateral cracks.

Comparison of MPS and SPH methods for solving forced motion ship flooding problems

Numerical wave flume with improved smoothed particle hydrodynamics

A smooth particle hydrodynamic (SPH) method combined with the Herschel–Bulkley-Papanastasiou (HBP) model is proposed to simulate 3D concrete printing (3DCP). HBP model can better resolve the divergence of equivalent viscosity coefficient under small deformation and extend the compatibility of simulation to dilatant and pseudoplastic fluids, so it possesses natural superiority in modelling the 3D printing of cement-based material with visco-plastic rheology behaviour. The HBP-based SPH method considers the influence of the printing parameters including nozzle characteristics and printing-to-extrusion velocity ratio on the cross-sectional geometry of the deposited filament, and its outcomes agree qualitatively well with the experiment results. Furthermore, by utilising process parameters furnished by simulation cases, it is possible to determine the critical conditions under which filaments printed by different nozzle shapes are vulnerable to tearing, and the corresponding critical intervals when tearing occurs are also defined. 3DPC experiments verify these findings and confirm that SPH simulation provides additional information on the geometric characteristics of single-layer structures, as well as physical quantities that cannot be straightforwardly measured.

We have developed a microscopic blood model, that can express the deformation of an erythrocyte in micro-circulation, based on the Smoothed Particle Hydrodynamics (SPH) method. In the method, plasma fluid is discretized by SPH particles and an erythrocyte is modeled by internal SPH particles wrapped in elastic membrane particles. For verifying the model, in two dimensions, we numerically analyzed a popular phenomenon of erythrocyte; the tank tread motion of an erythrocyte under a constant shear field. The numerical results agreed well with the experimental data and the tank tread motion of erythrocyte was well realized by the model. From these results, it is confirmed that our blood model based on the SPH method can well express microscopic and rheological properties of erythrocytes.