A coupled SPH-DEM model for micro-scale structural deformations of plant cells during drying

A single plant cell was modeled with smoothed particle hydrodynamics (SPH) and a discrete element method (DEM) to study the basic micromechanics that govern the cellular structural deformations during drying. This two-dimensional particle-based model consists of two components: a cell fluid model and a cell wall model. The cell fluid was approximated to a highly viscous Newtonian fluid and modeled with SPH. The cell wall was treated as a stiff semi-permeable solid membrane with visco-elastic properties and modeled as a neo-Hookean solid material using a DEM. Compared to existing meshfree particle-based plant cell models, we have specifically introduced cell wall–fluid attraction forces and cell wall bending stiffness effects to address the critical shrinkage characteristics of the plant cells during drying. Also, a moisture domain-based novel approach was used to simulate drying mechanisms within the particle scheme. The model performance was found to be mainly influenced by the particle resolution, initial gap between the outermost fluid particles and wall particles and number of particles in the SPH influence domain. A higher order smoothing kernel was used with adaptive smoothing length to improve the stability and accuracy of the model. Cell deformations at different states of cell dryness were qualitatively and quantitatively compared with microscopic experimental findings on apple cells and a fairly good agreement was observed with some exceptions. The wall–fluid attraction forces and cell wall bending stiffness were found to be significantly improving the model predictions. A detailed sensitivity analysis was also done to further investigate the influence of wall–fluid attraction forces, cell wall bending stiffness, cell wall stiffness and the particle resolution. This novel meshfree based modeling approach is highly applicable for cellular level deformation studies of plant food materials during drying, which characterize large deformations.     

Introduction of an Adaptive Smoothed Particles Hydrodynamics Formulation

In this work an adaptive Smoothed Particles Hydrodynamics (SPH) formulation is presented which is capable of adjusting the discretization level of a simulation at runtime. In order to increase and decrease the local resolution, the adaptive refinement and coarsening approach introduced in literature was extended to merge a userdefined number of particles at each simulation step. Depending on the simulation different coarsening strategies may be advantageous. Considering for example an SPH formulation for elastic solids, the particles discretizing the continuum experience considerably less disordering than in fluid simulations allowing for an advanced coarsening algorithm which takes each particles refinement history under consideration and preferably merges particles originating from one and the same particle, whereas in SPH for fluids such a strategy would not be reasonable since fluid particles usually experience great relative displacement. Hence different coarsening strategies may be recommended for different simulation scenarios. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling of van der Waals force with smoothed particle hydrodynamics: Application to the rupture of thin liquid films

The rupture of thin liquid films driven by the van der Waals force is of significance in many engineering processes, and most previous studies have relied on the lubrication approximation. In this paper, we develop a smoothed particle hydrodynamics (SPH) representation for the van der Waals force and simulate the rupture of thin liquid films without resort to lubrication theory. The van der Waals force in SPH is only imposed on one layer, i.e., the outermost layer of fluid particles, where a weighting function is deployed to evaluate the contributions of particles on or near the interface. However, to obtain an accurate hydrostatic pressure in reaction to the van der Waals force, a smaller smoothing length is used for the calculation of the weighting function than that used for SPH discretizations of the bulk fluid. The same surface particles are also used to model the surface tension. To deal with the rupture of a thin liquid film with a very small aspect ratio ε (ε = thickness/length), a coordinate transformation is introduced to shrink the length of the liquid film to achieve accurate numerical resolution with a manageable number of particles. As verifications of our physical model and numerical algorithm, we simulate the hydrostatic pressure in a stationary film and the relaxation of an initially square droplet and compare the SPH results with the analytical solutions. The method is then applied to simulate the rupture of thin liquid films with moderate and small aspect ratios (ε = 0.5 and 0.005). The convergence of the method is verified by refining particle spacing to four different levels. The effect of the capillary number on the rupture process is analyzed.     

A coupled NMM-SPH method for fluid-structure interaction problems

The main challenges in the numerical simulation of fluid–structure interaction (FSI) problems include the solid fracture, the free surface fluid flow, and the interactions between the solid and the fluid. Aiming to improve the treatment of these issues, a new coupled scheme is developed in this paper. For the solid structure, the Numerical Manifold Method (NMM) is adopted, in which the solid is allowed to change from continuum to discontinuum. The Smoothed Particle Hydrodynamics (SPH) method, which is suitable for free interface flow problem, is used to model the motion of fluids. A contact algorithm is then developed to handle the interaction between NMM elements and SPH particles. Three numerical examples are tested to validate the coupled NMM-SPH method, including the hydrostatic pressure test, dam-break simulation and crack propagation of a gravity dam under hydraulic pressure. Numerical modeling results indicate that the coupled NMM-SPH method can not only simulate the interaction of the solid structure and the fluid as in conventional methods, but also can predict the failure of the solid structure.     

Descriptions of contacts in the presence of wear debris

The mechanism of abrasive wear involves formation and circulation of debris particles detached from rubbing solids. The loose wear particles form a more or less continuous intermediate layer which separates the sliding surfaces. The layer is treated as a single continuum with own kinematics and constitutive relations. The removal of material from rubbing solids, continuum based models and granular models of wear debris are discussed in the contribution. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Lagrangian-based SPH-DEM model for fluid–solid interaction with free surface flow in two dimensions

A Lagrangian-based SPH-DEM coupling model is proposed to study fluid–solid interaction (FSI) problems with free-surface flow. In this model, SPH uses an incompressible divergence-free scheme for simulating complex flow problems. Based on the Mohr–Coulomb criterion with tension cut, the DEM describes the characteristics of solid deformation and failure by means of contact models between particles. The coupling mechanism between SPH and DEM is realised by the decoupling of the force field during the process of fluid–solid interaction. That is, the motions of fluid and solid particles are reflected by the Navier–Stokes equations and interactions among solid particles are determined by Newton's second law in the DEM. To demonstrate the applicability of the SPH-DEM model, three case studies are used to verify the different fluid interaction situations with rigid bodies, deformable objects, and granular assemblies, respectively. The results of the proposed model shows good agreement with experimental data and indicates that it is capable of capturing the features of solid movement, deformation and failure under complex flow conditions with convincing accuracy and high efficiency.     

Coupled SPH and Phase Field method for hydraulic fracturing

Simulation of fracture initiation and propagation using classical mesh-based methods involves computationally expensive operations for pre-processing and (adaptive) remeshing of complex geometries. To overcome the difficulties we propose to use a Smoothed Particle Hydrodynamics (SPH) method to model hydraulic fracturing. SPH is a meshless Lagrangian method highly suitable for large deformations [1]. The present contribution discusses a numerical approach to model fractures initiation and propagation, by coupling SPH with the Phase Field method [2]. The proposed hybrid method overcomes the instability problems that can present SPH due to kernel incompleteness. We first validate the proposed model with a stationary elastic fracture and compare the results with the classical SPH to the SPH-Phase Field approach. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A corrected smoothed particle hydrodynamics method for solving transient viscoelastic fluid flows

In this work, a corrected smoothed particle hydrodynamics (CSPH) method is proposed and extended to the numerical simulation of transient viscoelastic fluid flows due to that its approximation accuracy in solving the Navier–Stokes equations is higher than that of the smoothed particle hydrodynamics (SPH) method, especially near the boundary of the domain. The CSPH approach comes with the idea of combining the SPH approximation for the interior particles with the modified smoothed particle hydrodynamics (MSPH) method for the exterior particles, this is because that the later method has higher accuracy than the SPH method although it also needs more computational cost. In order to show the validity of CSPH method to simulate unsteady viscoelastic flows problems, the planar shear flow problems, including transient Poiseuille, Couette flow and transient combined Poiseuille and Couette flow for the Oldroyd-B fluid are solved and compared with the analytical and SPH results. Subsequently, the general viscoelastic fluid based on the eXtended Pom–Pom (XPP) model is numerically investigated and the viscoelastic free surface phenomena of impacting drop are simulated by the CSPH for its extended application and the purpose of illustrating the ability of the proposed method. The numerical results are presented and compared with available solutions, which shows a very good agreement. All the numerical results show the higher accuracy and better stability of the CSPH than the SPH, especially for larger Weissenberg numbers.     

A model to estimate the size of aggregates formed in a Dissolved Air Flotation unit

In Dissolved Air Flotation (DAF) a solid phase is separated from a liquid phase with the aid of air bubbles. The solid phase is usually coagulated into larger particles termed flocs. The air bubbles and flocs form aggregates, which rise to the surface of the flotation unit where they are removed. In this paper we propose a model that estimates the size of the formed aggregates. The estimation is based on the local balance of forces describing the approach and attachment of flocs to air bubbles. The interaction of flocs and bubbles is described by surface forces, hydrodynamic forces and the buoyancy force. The model is validated with available experimental results and the obtained aggregate sizes agree reasonable with those obtained by the experiments. The approach proposed here is intended for water treatment applications, but can be modified for other flotation processes.     

A study of truly incompressible and weakly compressible Smoothed Particle Hydrodynamics methods to model incompressible flows with free surfaces

The Smoothed Particle Hydrodynamics (SPH) method is a meshless discretization method for solving, e.g., the Navier-Stokes equations. By now, it is used for hydraulic problems as well as for solid bodies. In general, there are two distinguishable approaches for incompressible fluid flows. One is called weakly compressible SPH (WCSPH) and the other is called truly incompressible SPH (ISPH). The main difference between these two approaches is the way of pressure evaluation. In WCSPH, a state equation is used, while in ISPH the pressure Poisson equation is solved. Each approach has its advantages as well as its disadvantages, for example the complexity of the numerical algorithm for WCSPH is smaller than for ISPH, but the pressure field is more accurate for ISPH. In this work, two representative examples are studied. The simulations were performed with two different codes, one developed at the Institute of Engineering and Computational Mechanics and one at the Institute of Chemical Process Engineering. It is the aim of this work to show some properties of WCSPH and ISPH as well as to compare two different implementations that, in detail, are very complex. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Model based optimization of a statistical simulation model for single diamond grinding

We present a model for simulating normal forces arising during a grinding process in cement for single diamond grinding. Assuming the diamond to have the shape of a pyramid, a very fast calculation of force and removed volume can be achieved. The basic approach is the simulation of the scratch track. Its triangle profile is determined by the shape of the diamond. The approximation of the scratch track is realized by stringing together polyhedra. Their sizes depend on both the actual cutting depth and an error implicitly describing the material brittleness. Each scratch track part can be subdivided into three three-dimensional simplices for a straightforward calculation of the removed volume. Since the scratched mineral subsoil is generally inhomogeneous, the forces at different positions of the workpiece are expected to vary. This heterogeneous nature is considered by sampling from a Gaussian random field. To achieve a realistic outcome the model parameters are adjusted applying model based optimization methods. A noisy Kriging model is chosen as surrogate to approximate the deviation between modelled and observed forces. This deviation is minimized and the results of the modelled forces and the actual forces from conducted experiments are rather similar.     

SPH method applied to compression of solid materials for a variety of loading conditions

Smoothed Particle Hydrodynamics (SPH) is a numerical method that does not use a mesh or grid when solving a set of partial differential equations. This makes it particularly useful in application to solid mechanics problems where the sample undergoes large deformation. Whereas mesh-based methods have difficulty when the sample becomes severely distorted, SPH naturally deals with this important engineering scenario. We implement the SPH method for compressional deformation of solid samples and focus on uniaxial, biaxial and triaxial loading. We develop numerical procedures that naturally deal with these three different sets of boundary conditions and apply it to both small and larger strains in elastic and more complex materials. The method is shown to be robust up to large strains of 30%. Under uniaxial loading, a cylindrical sample tends to deform by bulging while under triaxial loading the cylindrical sample will remain cylindrical, but the diameter of the sample increases accordingly.     

Smoothed Particle ElectroMagnetics: A mesh-free solver for transients

In this paper an advanced mesh-free particle method for electromagnetic transient analysis, is presented. The aim is to obtain efficient simulations by avoiding the use of a mesh such as in the most popular grid-based numerical methods. The basic idea is to obtain numerical solutions for partial differential equations describing the electromagnetic problem by using a set of particles arbitrarily placed in the problem domain. The mesh-free smoothed particle hydrodynamics method has been adopted to obtain numerical solution of time domain Maxwell's curl equations. An explicit finite difference scheme has been employed for time integration. Details about the numerical treatment of electromagnetic vector fields components are discussed. Two case studies in one and in two dimensions are reported. In order to validate the new proposed methodology, named as Smoothed Particle ElectroMagnetics, a comparison with the standard finite difference time domain method results is performed. The intrinsic adaptive capability of the proposed method, has been exploited by introducing irregular particles distribution.     

单轴拉伸条件下细观非均匀性岩石损伤局部化和应力应变关系分析

岩石在拉应力状态下的力学特性不同于压应力状态下的力学特性．利用细观力学理论研究了细观非均匀性岩石拉伸应力应变关系包括:线弹性阶段、非线性强化阶段、应力降阶段、应变软化阶段.模型考虑了微裂纹方位角为Weibull分布和微裂纹长度的分布密度函数为Rayleigh函数时对损伤局部化和应力应变关系的影响,分析了产生应力降和应变软化的主要原因是损伤和变形局部化.通过和实验成果对比分析验证了模型的正确性和有效性．     

A three-dimensional discrete element model for heterogeneous solids under mechanical loading

The Discrete Element Method (DEM) is used to model solids under quasi-static and dynamic loading. In order to model elastic bodies, a microscopic model must be able to represent the macroscopic properties of the material. An energy-based approach to determine the model parameters is presented for an unit cell assemblage of 13 particles in the hexagonal close packing of spheres. The stored strain energy in the unit cell is added up and the specific strain energy expression is derived with respect to the macroscopic strains. The resulting stress-strain relations can be compared to the constitutive equations of the elastic continuum. To avoid cubic anisotropy for Poisson's ratios above zero, an advanced octahedrongap-filled hexagonal close packing of spheres is presented and validated. This approach for regular lattices can be transferred to heterogeneous materials with the goal of describing porous media such as cement stone. Therefore it is possible to use the presented regular lattices with statistically distributed properties or to investigate irregular distributions of particles. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

压应力状态下细观非均匀性岩石的损伤局部化和应力应变关系分析

利用摩擦弯折裂纹模型研究了受压条件下细观非均匀性岩石的损伤局部化问题和全过程应力应变关系．模型考虑了裂纹相互作用对损伤局部化和全过程应力应变关系的影响,确定了损伤局部化发生的条件,分析了产生损伤局部化的原因．研究表明全过程应力应变关系包括线弹性阶段、非线性强化阶段、应力降和应变软化阶段．通过和实验对比分析验证了模型的正确性和有效性．     

Wear resistance of polyethylene

The effect of the molecular weight and branching of polyethylene on its wear resistance in direct contact with abrasive particles has been investigated. The abrasive wear resistance of the polyethylene increases with its molecular weight. Copolymers have better wear resistance than homopolymers."Plastolimer" Research and Production Association, Leningrad. Translated from Mekhanika Polimerov, No. 3, pp. 542–544, May–June, 1971.     

Application of Smoothed Particle Hydrodynamics for modelling gated spillway flows

Computational models of spillways are important for evaluating and improving dam safety, optimising spillway design and updating operating conditions. Traditionally, scaled down physical models have been used for validation and to collect hydraulic data. Computational fluid dynamics (CFD) models however provide advantages in time, cost and resource reduction. CFD models also provide greater efficiency when evaluating a range of spillway designs or operating conditions. Within the present literature, most studies of computational spillway models utilise a mesh-based method. In this work we use the particle based method of Smoothed Particle Hydrodynamics (SPH) to model weir flow through a four bay, gated, spillway system. Advantages of SPH for such modelling include automatic representation of the free surface flow behaviour due to the Lagrangian nature of the method, and the ability to incorporate complex and dynamic boundary objects such as gate structures or debris. To validate the SPH model, the reservoir water depth simulated is compared with a related physical study. The effect of SPH resolution on the predicted water depth is evaluated. The change in reservoir water level with discharge rates for weir flow conditions is also investigated, with the difference in simulated and experimental water depths found to range from 0.16% to 11.48%. These results are the first quantitative validation of the SPH method to capture spillway flow in three dimensions. The agreement achieved demonstrates the capability of the SPH method for modelling spillway flows.     

三维PTT黏弹性液滴撞击固壁面问题的改进SPH模拟

基于光滑粒子动力学(smoothed particle hydrodynamics, SPH)方法,对三维Phan-Thien Tanner(PTT)黏弹性液滴撞击固壁面问题进行了数值模拟.为了有效地防止粒子穿透固壁,且缩减三维数值模拟所消耗的计算时间,提出了一种适合三维数值模拟的改进固壁边界处理方法.为了消除张力不稳定性问题,采用一种简化的人工应力技术.应用改进SPH方法对三维PTT黏弹性液滴撞击固壁面问题进行了数值模拟,精细地捕捉了液滴在不同时刻的自由面,讨论了PTT黏弹性液滴不同于Newton(牛顿)液滴的流动特征,分析了PTT拉伸参数对液滴宽度、高度和弹性收缩比等的影响.模拟结果表明,改进SPH方法能够有效而准确地描述三维PTT黏弹性液滴撞击固壁面问题的复杂流变特性和自由面变化特征.     

Numerical simulation of fluid-structure interaction problems by a coupled SPH-FEM approach

In scientific computing there is a great interest in numerical simulation of fluid-structure interaction (FSI) problems. Within this work a numerical approach to simulate fluid-structure interactions between elastic structures and weakly incompressible fluids is developed. For the fluid part and the solid part the Smoothed Particle Hydrodynamics method (SPH) and the Finite Element Method (FEM) are used, respectively. To transfer the resulting reaction forces from the fluid particles onto the structure's surface two methods are implemented, investigated and compared. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)