On the harmonic response of plates with the shear deformation effect using the elastodynamic solution in the boundary element method

The harmonic response of plates is studied by using the frequency domain solution in conjunction with the direct boundary integral equation (DBIE) for Mindlin's model. The shear deformation and rotatory inertia effects in that model can be switched off in the presented formulation and a DBIE for the classical bending model is then obtained, which includes an additional degree of freedom for the tangential boundary rotation. The frequency responses were obtained to map the plate behavior and they were calculated both with and without the effects of the shear deformation and the rotatory inertia. The analyses were finished when the first natural frequency was identified. The results were compared to available solutions in the literature, employing three-dimensional elasticity theory, the Mindlin and the classical bending models.     

On some similarity solutions to shear flows of non-Newtonian power law fluids

Summary The nonlinear rheological effects of non-Newtonian power law fluids on some shear flows are addressed. Exact similarity solutions to Stokes' first problem for unsteady flow generated by the vertical motion of a slender cylinder in an unbounded fluid are presented. The nonlinear effects on the velocity and shear stress distributions are shown and discussed. These reveal the existence of traveling wave characteristics for a shear thickening fluid, which determine a moving shear front for which the shear disturbances propagate with a finite velocity.     

Equivalent inclusion method-based simulation of particle sedimentation toward functionally graded material manufacturing

A novel numerical approach based on Eshelby’s equivalent inclusion method is presented to simulate the Stokes’ flow of many spherical particles moving in a viscous fluid at a small Reynolds number. Many particles fall toward the bottom of the fluid at different velocities and thus form a graded microstructure in terms of the material phase and the particle size. For each particle, an eigenstrain rate, which is given in a polynomial form, is introduced to represent the mismatch between the particle and the rest of the fluid. Rongved’s fundamental solution of a point force in a semi-infinite domain with a fixed boundary (Rongved in J. Appl. Mech. 22, 545–546, 1955) is used to calculate the velocity field caused by the body force and eigenstrain rate. Based on Eshelby’s stress equivalent condition, the eigenstrain rate of each particle can be solved and the sedimentation process of a many-particle system can be simulated as a quasi-equilibrium process. If only one or two particles are considered, the results agree with the finite element results very well. Using a suspension of aluminum and high-density polyethylene (HDPE) powders mixed in ethanol, the microstructural evolution is illustrated along with the sedimentation process, which produces a graded mix collected at the fixed boundary for functionally graded material manufacturing.     

3D numerical simulation of the behaviour of a spherical particle suspended in a Newtonian fluid and submitted to a simple shear

The 3D flow around a rigid spherical particle suspended in a Newtonian fluid and submitted to simple shear is numerically studied using Rem3D^® finite element code. The sphere motion is imposed by a sticking contact between the sphere and the fluid. The effect of the particle size as compared with the finite dimension of the shear cell was investigated. The direct calculations show that 3D modelling is necessary to correctly predict the sphere behaviour. The proximity of the particle and the cell walls strongly affects the flow velocities, the sphere motion (increase of the rotation period of the sphere) and the stress field (change of orientation angle and increase of maximal local stresses).     

The movement law and orientation control of rectangular particles in the viscous fluid domain based on IS-FEM

Understanding the movement law and orientation control mechanism of non-spherical particles are significant for industrial applications. In this work, the flow characteristics of rectangular particles, in the uniform and wedge viscous fluid domain, are simulated by the immersed smoothed finite element method (IS-FEM). The influences of mesh resolution and time-step on particle velocity are analyzed, and the numerical procedure is validated by the published model and sedimentation experiments. The operating parameters that affect the particle flow are systematically studied, including Reynolds number, initial angle, channel offset distance, and aspect ratio. Moreover, the particle angles are adjusted by the velocity gradient of fluid domains. The result indicates that the velocities, angle, and drag of rectangular particles are closely related to the working conditions. The long axis of rectangular particles is consistent with the flow direction in shrinking fluid domains and is perpendicular to the flow direction in expanding fluid domains. The angle distribution law of rectangular particles in moving wedge fluid domains is determined. These findings provide a theoretical foundation for particle sedimentation and suspension flow, which is helpful for the further separation and orientation control of mixed particles.     

On a local predictor of shear instability and the initiation of local turbulence

The stability of a local laminar shear flow and its transition into turbulent flow is considered as a local phenomenon. This transition may remain local, in which case the flow field is partially laminar and partially turbulent, or it may spread and make the whole field turbulent. One of the applications of this analysis is the prediction of local heat-convection rates, which are enhanced by local turbulence. Another application is in heart-lung blood pumps, where excessive shear rates are detrimental to red blood cells.The analysis is Lagrangian, which concentrates on the stability of a fluid particle in maintaining its position in a laminar shear flow. This stability is shown to depend on the magnitude of a non-dimensional parameter, namely the local Reynolds numberRe _L =ha ²/v whereh is the local shear rate,a is the particle radius andv is the fluid's kinematic viscosity. It is shown that when, locally,Re _L > 530, the flow is, locally, unstable. The application of this criterion is simple and direct, and in certain cases it can be shown that the resulting unstable flow is indeed turbulent.Because the analysis relies on an experimental coefficient which has been obtained for a rigid sphere, rather than for a fluid particle, the criterion is introduced at this stage as a conjecture. Several examples are presented which demonstrate the criterion's ability to yield correct predictions for instability.     

An improved immersed moving boundary for hydrodynamic force calculation in lattice Boltzmann method

Particles suspension is considerably prevalent in petroleum industry and chemical engineering. The efficient and accurate simulation of such a process is always a challenge for both the traditional computational fluid dynamics and lattice Boltzmann method. Immersed moving boundary (IMB) method is promising to resolve this issue by introducing a particle-fluid interaction term in the standard lattice Boltzmann equation, which allows for the smooth hydrodynamic force calculation even for a large grid size relative to the solid particle. Although the IMB method was proved good for stationary particles, the deviation of hydrodynamic force on moving particles exists. In this work, we reveal the physical origin of this problem first and figure out that the internal fluid effect on the hydrodynamic force calculation is not counted in the previous IMB. An improved immersed moving boundary method is therefore proposed by considering the internal fluid correction, which is easy to implement with the little extra computation cost. A 2D single elliptical particle and a 3D sphere sedimentation in Newtonian fluid is simulated directly for the validation of the corrected model by excellent agreements with the standard data.     

Moving Particles Through a Finite Element Mesh

We present a new numerical technique for modeling the flow around multiple objects moving in a fluid. The method tracks the dynamic interaction between each particle and the fluid. The movements of the fluid and the object are directly coupled. A background mesh is designed to fit the geometry of the overall domain. The mesh is designed independently of the presence of the particles except in terms of how fine it must be to track particles of a given size. Each particle is represented by a geometric figure that describes its boundary. This figure overlies the mesh. Nodes are added to the mesh where the particle boundaries intersect the background mesh, increasing the number of nodes contained in each element whose boundary is intersected. These additional nodes are then used to describe and track the particle in the numerical scheme. Appropriate element shape functions are defined to approximate the solution on the elements with extra nodes. The particles are moved through the mesh by moving only the overlying nodes defining the particles. The regular finite element grid remains unchanged. In this method, the mesh does not distort as the particles move. Instead, only the placement of particle-defining nodes changes as the particles move. Element shape functions are updated as the nodes move through the elements. This method is especially suited for models of moderate numbers of moderate-size particles, where the details of the fluid-particle coupling are important. Both the complications of creating finite element meshes around appreciable numbers of particles, and extensive remeshing upon movement of the particles are simplified in this method.     

Fabric rates of elliptical particle assembly in monotonic and cyclic simple shear tests: a numerical study

This paper aims to investigate the evolutions of microscopic structures of elliptical particle assemblies in both monotonic and cyclic constant volume simple shear tests using the discrete element method. Microscopic structures, such as particle orientations, contact normals and contact forces, were obtained from the simulations. Elliptical particles with the same aspect ratio (1.4 and 1.7 respectively for the two specimens) were generated with random particle directions, compacted in layers, and then precompressed to a low pressure one-dimensionally to produce an inherently anisotropic specimen. The specimens were sheared in two perpendicular directions (shear mode I and II) in a strain-rate controlled way so that the effects of inherent anisotropy can be examined. The anisotropy of particle orientation increases and the principal direction of particle orientation rotates with the shearing of the specimen in the monotonic tests. The shear mode can affect the way fabric anisotropy rate of particle orientation responds to shear strain as a result of the initial anisotropy. The particle aspect ratio exhibits quantitative influence on some fabric rates, including particle orientation, contact normal and sliding contact normal. The fabric rates of contact normal, sliding contact normal, contact force, strong and weak contact forces fluctuate dramatically around zero after the shear strain exceeds 4 % in the monotonic tests and throughout the cyclic tests. Fabric rates of contact normals and forces are much larger than that of particle orientation. The particle orientation based fabric tensor is harder to evolve than the contact normal or contact force based because the reorientation of particles is more difficult than that of contacts.     

A unified formulation of laminated composite, shear deformable, five-degrees-of-freedom cylindrical shell theories

The main objective of this paper is a theoretical unification of most of the variationally consistent classical and shear deformable cylindrical shell theories available in the literature. This is achieved by introducing into the shell displacement approximation certain general functions of the transverse coordinate which account for the incorporation of the transverse shear deformation effects. Avoiding having to provide a single choice of the forms of these ‘shear deformation shape functions’ befor or during the variational formulation of the general theory, the present formulation leaves open possibilities for a multiple, a-posteriori specification of particular shear deformable shell theories. As a result, the classical Donnell-, Love- and Sanders-type shell theories as well as their well known uniform and parabolic shear deformable analogues are obtained as particular cases. Moreover, a generalized ‘zig-zag’ displacement model is presented which gives further multiple freedom in achieving continuous distributions of interlaminar stresses through the thickness of an unsymmetric cross-ply laminated cylindrical shell.     

Shear controllable synthesis of barium sulfate particles using lobed inner cylinder Taylor-Couette flow reactor

A novel lobed inner cylinder assembled in Taylor-Couette flow reactor (LTC) has been adopted to synthesize barium sulfate particles. The fluid dynamics that affects synthesis of particles using both the LTC and the classical Taylor-Couette flow reactor (CTC) was investigated through CFD modelling and experiments. The results have demonstrated that the Taylor vortices and turbulence induced shear rate distribution in the reactors have a significant influence on the final particle size distribution. The narrower shear rate distribution in the LTC is beneficial to the synthesis of particles with smaller size. The local turbulence intensification in the intra-Taylor vortices in the LTC effectively reduces the low shear strain regions. A strong correlation between the synthesized particle size and the local turbulent dissipation rate is existing. Shear induced by small turbulent eddies can inhibit particle growth. The LTC can be used for effectively shear controllable synthesis of particles.     

Geometric correction factors for center cracked specimens subjected to nonlinear bridging stresses in the shear lag model

Fiber bridging plays an important role in the fracture mechanism of fiber-reinforced composites. The determination of the geometric correction factors for finite-width specimens subjected to complex bridging stresses is vital for the practical application of various bridging models. An approximate approach named the force balance method (FBM) was recently reported in the literature to evaluate such geometric factors. The main purpose of this study is to assess the effectiveness of the FBM by using the well-established boundary element method. The case of a center cracked specimen subjected to a nonlinear fiber bridging stress in the shear lag model in fiber-reinforced composites is considered. The geometric correction factors computed by the boundary element method are compared with those deduced by the FBM.     

Influence of inelastic collision on the dynamic behavior of particle sedimentation in high-viscosity fluids

To further understand the characteristics of particle–fluid flow, the particle sedimentation process in a high-viscosity fluid is conducted with both experimental and numerical methods. In this work, inelastic collisions between particles during the sedimentation process are observed. Different from the sedimentation in a low-viscosity fluid, the increase of particle sedimentation velocity can be found due to the inelastic collisions in a high-viscosity fluid. This phenomenon is more obvious with the increase of the particle volume fractions and the viscosity of the fluid. The necessary conditions for the inelastic collision phenomenon are determined based on the viscous dissipative dynamics of particle collisions. According to the experimental and numerical results, the interactions between particles in high-viscosity liquids are mainly the inelastic collisions which caused the particle aggregation. The correction coefficient of particle sedimentation velocity equation is obtained, and the applicability of the equation for the sedimentation in a high-viscosity fluid is improved.     

Investigating the Applicability of Combined Lattice Boltzmann-Smoothed Profile Methods in Particulate Systems

In this article, a combination of Lattice-Boltzmann method (LBM) and smoothed profile method (SPM) are used in simulation of one, two, and many particles’ motion in fluid flow. SPM is used as the simulation method for particles motion. A shear flow is produced using a) solid walls for which standard bounce-back (SBB) boundary condition is applied and b) Lees-Edwards boundary conditions (LEBC). Simulation of Couette flow problem of fluid-only system reveals the accuracy of both methods. LBM-SPM coupled with LEBC is applied for flow geometries of one and two particles in a shear flow. Comparison of results obtained from simulation of one and two interacting particles using moving walls with SBB with those in the literature shows good correspondence. In addition, for the case of many particles, the effective viscosity of a suspension of circular particles which are placed randomly between two parallel walls is investigated from dilute to dense regimes. Relative bulk viscosity is compared with theoretical and semi-empirical results of other investigators and satisfactory agreement is found. Finally, a combination of SPM-LBM is examined for sedimentation of one, two and many particles. Numerical results show suitability of LBM-SPM with LEBC for simulation of particles suspended in flow.     

Particulate flow simulation using Lattice Boltzmann Method: A rheological study

This work deals with calculating rheological properties of a suspension of particles in a fluid. A suspension of mono- and poly-disperse circular particles in shear flow is studied using two different methods for application of shear force: (a) by placing parallel walls at the top and bottom of the domain which are moving in opposite directions with the same velocity, and (b) using the Lees–Edwards boundary condition. The system which starts moving from rest, is allowed to reach a statistically steady state. Rheological properties namely, bulks shear stress, effective viscosity and normal stress difference of the suspension at different particle-based Reynolds numbers and different mean particle area fractions are calculated. Furthermore, the effect of size distribution on the relative effective viscosity of the suspension is investigated. Comparison of the present results with empirical formulations found in the literature shows reasonable agreement.     

Coupled lattice Boltzmann method and discrete element modelling of particle transport in turbulent fluid flows: Computational issues

This paper presents essential numerical procedures in the context of the coupled lattice Boltzmann (LB) and discrete element (DE) solution strategy for the simulation of particle transport in turbulent fluid flows. Key computational issues involved are (1) the standard LB formulation for the solution of incompressible fluid flows, (2) the incorporation of large eddy simulation (LES)‐based turbulence models in the LB equations for turbulent flows, (3) the computation of hydrodynamic interaction forces of the fluid and moving particles; and (4) the DE modelling of the interaction between solid particles. A complete list is provided for the conversion of relevant physical variables to lattice units to facilitate the understanding and implementation of the coupled methodology. Additional contributions made in this work include the application of the Smagorinsky turbulence model to moving particles and the proposal of a subcycling time integration scheme for the DE modelling to ensure an overall stable solution. A particle transport problem comprising 70 large particles and high Reynolds number (around 56 000) is provided to demonstrate the capability of the presented coupling strategy. Copyright © 2007 John Wiley & Sons, Ltd.     

DEM modeling of shear bands in crushable and irregularly shaped granular materials

A method of modeling convex or concave polygonal particles is proposed. DEM simulations of shear banding in crushable and irregularly shaped granular materials are presented in this work. Numerical biaxial tests are conducted on an identical particle assembly with varied particle crushability. The particle crushing is synchronized with the development of macroscopic stress, and the evolution of particle size distribution can be characterized by fractal dimension. The shear banding pattern is sensitive to particle crushability, where one shear band is clearly visible in the uncrushable assembly and X-shaped shear bands are evident in the crushable assembly. There are fewer branches of strong force chains and weak confinement inside the shear bands, which cause the particles inside the shear bands to become vulnerable to breakage. The small fragments with larger rotation magnitudes inside the shear bands form ball-bearing to promote the formation of shear bands. While there are extensive particle breakages occurring, the ball-bearing mechanism will lubricate whole assembly. With the increase of particle crushability the shear band formation is suppressed and the shear resistance of the assembly is reduced. The porosity inside the shear bands are related to the particle crushability.     

Extension of MITC to higher‐order beam models and shear locking analysis for compact,thin‐walled,and composite structures

A class of mixed interpolated beam elements is introduced in this paper under the framework of the Carrera Unified Formulation to eliminate the detrimental effects due to shear locking. The Mixed Interpolation of Tensorial Components (MITC) method is adopted to generate locking‐free displacement‐based beam models using general 1D finite elements. An assumed distribution of the transverse shear strains is used for the derivation of the virtual work, and the full Gauss‐Legendre quadrature is used for the numerical computation of all the components of the stiffness matrix. Linear, quadratic, and cubic beam elements are developed using the unified formulation and applied to linear static problems including compact, laminated, and thin‐walled structures. A comprehensive study of how shear locking affects general beam elements when different classical integration schemes are used is presented, evidencing the outstanding capabilities of the MITC method to overcome this numerical issue. Refined beam theories based on the expansion of pure and generalized displacement variables are implemented making use of Lagrange and Legendre polynomials over the cross‐sectional domain, allowing one to capture complex states of stress with a 3D‐like accuracy. The numerical examples are compared to analytic, numerical solutions from the literature, and commercial software solutions, whenever it is possible. The efficiency and robustness of the proposed method demonstrated throughout all the assessments, illustrating that MITC elements are the natural choice to avoid shear locking and showing an unprecedent accuracy in the computation of transverse shear stresses for beam formulations.