Narrow Results

We have developed a microscopic blood model based on the Smoothed Particle Hydrodynamics (SPH) method. In the model, plasma fluid is discretized by SPH particles, and a red blood cell (RBC) is expressed by internal SPH particles surrounded by elastic membrane particles. For verifying the model, we numerically analyzed two popular phenomena of blood flow. One is the tank-tread motion of an RBC under a constant shear field. The numerical results are agreed well with the experimental data and the tank-tread motion of RBC is well reproduced. The other is the axial migration or pinch effect of RBCs in Poiseuille flow. From the numerical results, we find that the axial migration effect becomes weaker as the viscosity of cell internal fluid becomes higher. The reason is because the RBC motion changes from tank-tread motion to rigid body rotation (from axial migration effect to pinch effect) as the cell contents become thick. From these results, it is confirmed that our blood model based on the SPH method can well express microscopic and rheological properties of RBCs.

This paper presents three-dimensional computational simulations of the hypervelocity impact (HVI) using standard smoothed particle hydrodynamics (SPH). The classic Taylor-Bar-Impact test is revisited with the focus on the variation of results corresponding to the different model parameters in the SPH implementation. The second example involves both normal and oblique HVIs of a sphere on the thin plate, producing large deformation of structures. Based on original experimental results and some numerical results reported previously, some comparisons are also made, in the hope of providing informative data on appropriate SPH implementation options for the software being developed. The results obtained show that the current SPH procedure is well suited for the HVI problems.

We study the dynamic fracture of thin-walled structure mainly due to impact and explosive loading. Therefore, we make use of a meshless smoothed particle hydrodynamics (SPH) shell formulation based on Mindlin–Reissner's theory. The formulation is an extension of the continuum-corrected and stabilized SPH method, so that thin structure can be modeled using only one particle characterizing mean position of shell surface. Fracture is based on separation of particles. We study tearing of pre-notched plates, fracture due to impact loading and dynamic fracture of cylindrical shells.

This paper presents an implementation of an improved smoothed particle hydrodynamics (SPH) method for numerical simulation of free-surface flow problems. The presented SPH method involves two major modifications on the traditional SPH method: (1) kernel gradient correction (KGC) and density correction to improve the computational accuracy in particle approximation and (2) RANS turbulence model to capture the inherent physics of flow turbulence. In the simulation, artificial compressibility for modeling incompressible fluid and ghost particles for treating solid boundaries are both applied. The presented SPH has been applied to two dam-breaking problems. We demonstrated that the presented SPH method has very good performance with more accurate flow patterns and pressure field distribution.

This paper presents an implementation of an improved smoothed particle hydrodynamics (SPH) method for simulating violent water impinging jet flow problems. The presented SPH method involves three major modifications on the traditional SPH method, (1) The kernel gradient correction (KGC) and density correction are used to improve the computational accuracy and obtain smoothed pressure field, (2) a coupled dynamic solid boundary treatment (SBT) is used to remove the numerical oscillation near the solid boundary and ensure no penetration condition, (3) a free surface condition, which is obtained from the summation of kernel function and volume, is used to describe the water jet accurately. Different cases about violent impinging jet flows are simulated. The influences of impact velocity and angles are investigated. It is demonstrated that the presented SPH method has very good performance with accurate impinging jet patterns and pressure field distribution. It is also found that the pressure time histories of observation points are greatly influenced by the rarefaction wave from surrounding air. Closer distance from free surface can lead to quicker decay of the pressure time history.

The low accuracy near the boundary or the interface in SPH method has been paid extensive attention. The Finite Particle Method (FPM) is a significant improvement to the traditional SPH method, which can greatly improve the computational accuracy for boundary particles. However, there are still some inherent defects for FPM, such as the long computing time and the potential numerical instability. By conducting matrix decomposition on the basic equations of FPM, an improved FPM method (IFPM) is proposed, which can not only maintain the high accuracy of FPM for boundary particles, but also keep the invertibility of the coefficient matrix in FPM. The numerical results show that the IFPM is really an effective improvement to traditional FPM, which could greatly reduce the computing time. Finally, the modified method is applied to two transient problems.

In the standard smoothed particle hydrodynamics (SPH) method, the interaction between two particles might be not pairwise when the support domain varies, which can result in a reduction of accuracy. To deal with this problem, a modified SPH approach is presented in this paper. First of all, a Lagrangian kernel is introduced to eliminate spurious distortions of the domain of material stability, and the gradient is corrected by a linear transformation so that linear completeness is satisfied. Then, concepts of support and dual-support are defined to deal with the unbalanced interactions between the particles with different support domains. Several benchmark problems in one, two and three dimensions are tested to verify the accuracy of the modified SPH model and highlight its advantages over the standard SPH method through comparisons.

In this paper, perforations of 12mm thick Weldox 460E steel plates by 20mm diameter blunt projectiles are simulated based on Two-dimensional Smoothed Particle Hydrodynamics method (SPH), and the modified Johnson–Cook (MJC) material model is adopted. To describe the shear plugging process, the particle approximation between different materials is canceled, and only the particle contact model based on the principle of conservation of momentum is applied. Then the separation of projectile and plug is simulated successfully, which is consistent with the experimental observations. Furthermore, it can be found that the particle size has a great influence on the calculation by comparing the effects of the different SPH particle sizes on plugging calculations. In general, the smaller the particle size is, the greater the residual velocity of projectile is. The residual velocities are tending towards stability as the decrease of particle size. Taking computational efficiency and accuracy into consideration, 0.033 (size$=$0.4mm) is the most appropriate dimensionless particle size. Then, the effect of target thickness on perforation is conducted, which shows that the target thickness has certain influence on the global deformation of target. Moreover, the sensitivity of MJC material constants on the residual velocity of projectile is also analyzed and discussed using orthogonal experimental design method and the range analysis method. The results indicate that the most sensitivity parameter is yield strength $A$, followed by strain hardening modulus $n$ and strain hardening exponent $B$.

In order to improve the computational efficiency and spatial resolution of smoothed particle hydrodynamics (SPH) method, a SPH method with space-based variable smoothing length has been developed. In addition, since linked-list search algorithm cannot handle the variable smoothing length problems, an improved linked-list search algorithm and a balanced alternating digital tree (B-ADT) search algorithm have been proposed. The performance of the two improved search algorithms has been evaluated in detail. These methods have been used to simulate two cases of water entry impact and two cases of gas–liquid two-phase flow. The results show that, by using space-based variable smoothing length algorithm, computational cost can be greatly reduced and the numerical accuracy is maintained.

In mesh-free methods, discrete equations are built according to physics information of micro-bodies arbitrarily spread in vicinal space. As the requirements about topology of micro-bodies are reduced, simulations with Lagrangian approach may be easier even with large distortions. Owing to the insufficiency of topological information, there is a challenge for mesh-free method to reflect physics especially as discontinuities exist. Based on the physical laws and developing trend of numerical simulation, a new mesh-free systematic method PECM (physics evoked cloud method) with excellent applicability has been developed. High fidelity to physics of the method is demonstrated through five one-dimensional challenging problems in which strong discontinuities exist.

In the present study, for the first time, the flow and mass transfer in the rotary micropump-micromixers were investigated by the SPH method. In fact, the present work shows the ability of the SPH method to model the mixing process due to pumping action. The incompressible SPH method applied for modeling is improved by the kernel gradient corrective tensor, a particle shifting algorithm, and an improved periodic boundary condition. SPH is a proper method for modeling the mixing process because there is no modeling for the convective terms and so, the false diffusion is not observed in the SPH modeling. In the present study, first, a viscous micropump comprising a microchannel in which a circular cylinder rotates with special eccentricity is modeled and validated. Then, the geometry is manipulated in order to achieve a desirable micromixer.

In this study, a novel asymmetric adaptive particle refinement algorithm in smoothed particle hydrodynamics (SPH) is developed for soil cutting problems. Each candidate particle that located at the cutting blade of the structure is split into two “children” particles to minimize the oscillation of the contact force. And thus reduce the local instability. To minimize the density refinement error, a numerical method to determine the optimal smoothing lengths for “children” particles is given. To verify the accuracy of proposed algorithm, the adaptive refinement procedure are implemented into two models: one for soil cutting test on plane strain condition and the other for sample drilling test on axisymmetric condition. The observed flow pattern of the soil and contact forces are compared with laboratory experimental data available in the literature. Results indicate that the proposed asymmetric adaptive refinement algorithm could significantly avoid severe local instability and contributes to high-accuracy simulation.

In order to solve partial differential equations (PDEs) numerically, one first needs to approximate the field functions (such as the displacement functions), and then obtain the derivatives of the field functions (such as the strains), by directly differentiating the field functions. Using such direct-derivatives in formulating a numerical method is common and is used in the standard finite element method (FEM), but such models are often found to be “stiff”. In the weakened weak (W2) formulations, it is found that the use of properly re-constructed derivatives can be beneficial in ways because the model can become “softer”. This paper presents a novel “pick-out” theory and technique for re-constructing the derivatives (such as the strains) of functions defined in a local domain, using smoothing operations. The local domain can be a smoothing domain used in the smoothed finite element methods (S-FEMs), smoothed point interpolation methods (S-PIMs), and smoothed particle hydrodynamics (SPH). It is discovered that through the use of a set of linearly independent smoothing functions that are continuous in the local domain, one can simply pick out various orders of smoothed derivatives (at the center of a domain) from any given function that may discontinuous (strictly) inside the local domain. As long as the smoothing function is continuous in the smoothing domain, the picked out “smoothed derivatives” are equivalent (in a local integral sense) to the compatible direct-derivatives, which ensures the convergence of the smoothed model (such as the S-FEM) when the smoothing domains shrinking to zero. The pick-out technique can be used in strong, weak, local weak, weak-strong, or weakened weak formulations to create stable and convergent numerical models. It may offer a new window of opportunity to develop new effective numerical models using smoothed derivatives (strains) that are “softer” and can produce accurate solutions also in the derivatives (strains and stresses) of the field functions (displacements).

A fully coupled soil–water-structure interaction algorithm was presented in the framework of smoothed particle hydrodynamics (SPH). In this algorithm, soil–water interaction was simulated based on the two-phase mixture theory. Each phase of the mixture occupies part of the macroscopic mixture and satisfies its own conservation equations of mass and momentum. The Drucker–Prager model with nonassociated plastic flow rule was used to describe the constitutive behavior of soil. The water was treated as Newtonian fluid. Interaction between soil and water was modeled by the pore water pressure and the viscous drag force. The structure was considered as rigid and the interaction with soil/water was modeled by the frictional sliding contact algorithm. With this algorithm, it is possible to investigate pore water pressure, the effective stress and deformation of the soil undergoing large deformation. Moreover, the effect of the temporal and spatial evolution of soil porosity was taken into consideration. This study first examined the proposed algorithm for a U-tube seepage problem and a two-dimensional consolidation problem. Afterwards, the continuous deep penetrating process of the spudcan, which involved large soil deformation and complex soil–water-structure interaction, was simulated under axisymmetric conditions. The comparison with previous research indicates the robustness and applicability of the proposed algorithm. Furthermore, the proposed approach could be a potentially efficient tool helping to reveal the mechanism of soil failure in geotechnical, costal and ocean engineering.

Smoothed particle hydrodynamics (SPH) has its unique advantages in simulating large deformation. However, in its calculation, it is easy for some regional particles to break off. This paper puts forward the concept of virtual crack boundary to solve crack propagating problems in the framework of SPH. The parameters of virtual crack boundary are determined by the projection method of descending dimension, which improves the support domains of crack tip particles. Based on the principle of minimum strain energy density factor in fracture mechanics, the initiation and extended directions of cracks in materials are estimated. By simulating the generation and expansion of three modes of cracks in materials, the SPH calculation results of the three types of support domain forms are compared with the ABAQUS simulation results and experiment results. It indicates that the method of virtual crack boundary method is more stable than the one based on discontinuous medium. And it can generate more reasonable results than the method based on continuous medium. This paper proves the effectiveness of strain energy density factor based on fracture mechanics theory in searching the direction of crack expansion using SPH, and explores the application of new support domain model in SPH crack solution.

An improved water–soil coupling algorithm was proposed based on the two-phase mixture theory within the framework of smoothed particle hydrodynamics (SPH). In this algorithm, the buoyant density was considered in saturated soil and the stress of two phases was completely exfoliated with the Terzaghi’s effective stress principle. Then the interaction between water and soil was only constituted by viscous drag force. The proposed algorithm was validated by several numerical tests to effectively solve a series of numerical problems caused by the truncation of the kernel approximation on the interface between submerged soil and water, and it can also be a feasible measure to simulate underwater soil excavation problems without drainage and underwater landside problems. Meanwhile, combined with frictional sliding contact algorithm, the interaction between water/soil and structure which was considered as rigid can be effectively modeled, and the calculated contact forces acting on the structure are more accurate. Furthermore, this improved algorithm can be applied to deal with large deformation problems involving complex water–soil–structure interaction in hydraulic and geotechnical engineering such as underwater excavation, shield dig, caisson sinking and other practical engineering problems. It is also significant to engineering design and the improvement of construction level.

Smoothing length plays a significant role in smoothed particle hydrodynamics (SPH). Inappropriate smoothing length will result in problems of stability, accuracy and efficiency. Updating smoothing length with time is very important for SPH modeling of large deformation problems. In this work, an effective smoothing length updating method is proposed. The method works in the framework of SPH with scalar smoothing length. It is quite simple in implementation and is computationally efficient. The method updates smoothing length according to maximum local particle spacing and inhomogeneity of material deformation. Numerical examples in both 2D and 3D which involve large deformation are calculated to validate the effectiveness of the proposed method. A comparison between the proposed method and several traditional methods is performed. Numerical results show that the present method can adapt to the simulation of severely inhomogeneous deformation and produce better stability and accuracy than the traditional methods for SPH modeling of large deformation problems.

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

The fatigue crack propagation analysis based on the SPH framework “SPH-Fatigue” is accelerated by using the single precision program on GPU. It is found that the single precision program slightly disorders the stress wave but doubles the computational speed. In addition, the computational results of the fatigue crack propagation by the single precision program show almost the same crack shapes as the experimental ones. Accordingly, it is concluded that the use of the single precision program is one of the choices to accelerate the SPH-Fatigue computation.