Arbitrary Lagrangian Eulerian Approach Research Articles

Numerical Study of Paramagnetic Elliptical Microparticles in Curved Channels and Uniform Magnetic Fields.

We numerically investigated the dynamics of a paramagnetic elliptical particle immersed in a low Reynolds number Poiseuille flow in a curved channel and under a uniform magnetic field by direct numerical simulation. A finite element method, based on an arbitrary Lagrangian-Eulerian approach, analyzed how the channel geometry, the strength and direction of the magnetic field, and the particle shape affected the rotation and radial migration of the particle. The net radial migration of the particle was analyzed after executing a rotation and at the exit of the curved channel with and without a magnetic field. In the absence of a magnetic field, the rotation is symmetric, but the particle-wall distance remains the same. When a magnetic field is applied, the rotation of symmetry is broken, and the particle-wall distance increases as the magnetic field strength increases. The causation of the radial migration is due to the magnetic angular velocity caused by the magnetic torque that constantly changes directions during particle transportation. This research provides a method of magnetically manipulating non-spherical particles on lab-on-a-chip devices for industrial and biological applications.

Numerical modeling based on moving mesh method to simulate fast crack propagation

An analysis to show the capability of moving mesh strategy to predict dynamic crack growth phenomena in 2D continuum media is proposed. The numerical method is implemented in the framework of the finite element method, which is coupled with moving mesh strategy to simulate the geometry variation produced by the crack tip motion. In particular, a computational procedure based on the combination of Fracture Mechanics concepts and Arbitrary Lagrangian-Eulerian approach (ALE) is developed. This represents a generalization of previous authors’ works in a dynamic framework to propose a unified approach for predicting crack propagation in both static and dynamic frameworks. The crack speed is explicitly evaluated at each time step by using a proper crack tip speed criterion, which can be expressed as a function of energy release rate or stress intensity factor. Experimental and numerical results are proposed to validate the proposed approach. Mesh dependence problem, computational efficiency and numerical complexity are verified by comparative results

Dynamics of a pair of ellipsoidal microparticles under a uniform magnetic field

Under a uniform magnetic field, magnetic particles tend to form chains, clusters or columns due to particle–particle interactions. Non-spherical magnetic particles dispersed in a liquid medium show different rheological properties. However, there is a lack of knowledge about the fundamental mechanism of particle–particle interactions of non-spherical particles under a uniform magnetic field. In this work, we numerically investigate the particle–particle interactions and relative motions of a pair of paramagnetic elliptical particles by using direct numerical simulations to create two-dimensional models that resolve the magnetic and flow fields around the finite-sized particles. The modeling is based on the finite element method and arbitrary Lagrangian–Eulerian approach with full consideration of particle–fluid–magnetic field interaction. The effects of initial position and aspect ratio of the particles are investigated. The results show that the particles spend much more time under global reorientation than local magneto-orientation. Larger initial relative angles and distances, and larger aspect ratios, tend to require more time to form a stable chain. The particle–particle interactions and relative motion of a pair of elliptical particles in this study provide insights into the particle alignment and chaining processes under uniform magnetic fields, which are closely related to the response of magneto-rheological fluids to magnetic fields.

Three-dimensional fluid-structure interaction simulations of a yarn subjected to the main nozzle flow of an air-jet weaving loom using a Chimera technique

In air-jet weaving looms, the main nozzle pulls the yarn from the prewinder by means of a high velocity air flow. The flexible yarn is excited by the flow and exhibits high amplitude oscillations. The motion of the yarn is important for the reliability and the attainable speed of the insertion. Fluid-structure interaction simulations calculate the interaction between the air flow and the yarn motion and could provide additional insight into yarn behavior. However, the use of an arbitrary Lagrangian–Eulerian approach for the deforming fluid domain around a flexible yarn typically results in severe mesh degradation, vastly reducing the accuracy of the calculations or limiting the physical time that can be simulated. In this research, the feasibility of using a Chimera technique to simulate the motion of a yarn interacting with the air flow from a main nozzle was investigated. This methodology combines a fixed background grid with a moving component grid deforming along with the yarn. The component grid is, however, not constrained by the boundaries of the flow domain allowing for large deformations with limited mesh degradation. Two separate cases were investigated. In the first case, the yarn was considered to be clamped at the main nozzle inlet. For the second case, the yarn was allowed to move axially as the main nozzle pulled it from a drum storage system.

Second-invariant-preserving Remap of the 2D deviatoric stress tensor in ALE methods

For numerical simulations of impact problems or fluid–solid interactions, the ALE (Arbitrary Lagrangian–Eulerian) approach is a useful tool due to its ability to keep the computational mesh smooth and moving with the fluid. The elastic–plastic extension of the compressible fluid model requires tensor variables for the description of non-volumetric (deviatoric) mechanical stress. While Lagrangian numerical schemes based on the evolution equation of the stress tensor are well developed, tensor remap is still a relatively unexplored territory.We propose a new approach to deviatoric stress remapping, where the second invariant J2 (a conservative scalar quantity related to the strain energy) is remapped independently of the tensor components. These are re-scaled to match the remapped invariant value, effectively using only the principal directions and eigenvalue ratio from the component-wise remap. This approach is frame invariant, preserves J2 invariant bounds and conserves the total invariant. We compare our method with component-based remapping using a simple synchronized limiter or a specialized stress tensor limiter described in the literature.

Adaptive time-step control for nonlinear fluid–structure interaction

In this work, we consider time step control for variational-monolithic fluid–structure interaction. The fluid–structure interaction (FSI) system is based on the arbitrary Lagrangian–Eulerian approach and couples the incompressible Navier–Stokes equations with geometrically nonlinear elasticity resulting in a nonlinear PDE system. Based on the monolithic setting, we develop algorithms for temporal adaptivity that are based on a rigorous derivation of dual-weighted sensitivity measures and heuristic truncation-based time step control. The Fractional-Step-theta scheme is the underlying time-stepping method. In order to apply the dual-weighted residual method to our setting, a Galerkin interpretation of the Fractional-Step-theta scheme must be employed. All developments are substantiated with several numerical tests, namely FSI-benchmarks, including appropriate extensions, and a flapping membrane example.

Effects of friction conditions on the formation of dead metal zone in orthogonal cutting – a finite element study

A numerical study of the effects of friction conditions on the formation of dead metal zone (DMZ) is presented. The friction conditions are classified as three different cases in the form of coefficient: (1) constant coefficient of friction, (2) “smooth” and “sharp” change of the friction coefficient and (3) time-dependent friction coefficient. These friction cases are numerically investigated using the finite element (FE) code ABAQUS/Explicit. A FE model based on the arbitrary-Lagrangian–Eulerian approach is developed to simulate the cutting process and investigate the influences of the friction conditions. The simulated results, for a wide range of friction conditions, are obtained, analyzed and compared with previously published experimental/numerical data. It has been found that the friction coefficient has a direct effect on the amount and shape of DMZ, the sharp change of coefficient has a larger effect on the DMZ formation than the smooth one and the formation of DMZ is more determined by the value of the friction coefficient than its duration.

Flexible multibody modeling of reeving systems including transverse vibrations

This paper presents a discretization procedure for the flexible multibody modeling of reeving systems. Reeving systems are assumed to include a set of rigid bodies connected by wire ropes using a set of sheaves and reels. The method is capable to model the deformation of the varying-length wire-rope spans. Wire ropes are assumed to deform axially, transversally and in torsion. This paper shows the capability of the presented method to model transverse vibrations. The discretization procedure uses a combination of absolute position coordinates, relative-transverse deformation coordinates and longitudinal material coordinates. Each wire-rope span is modeled using a single two-noded element under an arbitrary Lagrangian–Eulerian approach. The discretization method is validated using analytical and numerical reference solutions found in the literature that describe the dynamics of varying-length strings. In addition, the dynamics of a three-dimensional tower crane is simulated.

A numerical study of the effect of fluid-structure interaction on transient natural convection in an air-filled square cavity

The present study aims to investigate the transient natural convection in an air-filled square cavity based on the effects of fluid-structure interaction (FSI). The Prandtl number of air is assumed to be 0.71. A thin deformable baffle is horizontally located in the center of the cavity and the top wall of the cavity is also elastic. The horizontal walls are completely insulated. Initially, the cavity is set at Tc temperature, then the left side wall temperature is raised to Th. The arbitrary Lagrangian-Eulerian approach is implemented to study the flow field in the presented model. The fluid field equations are discretized by Galerkin finite element method. Further, the dimensionless equations of flexible parts of the cavity are solved using the Newton-Raphson method. The study examines the effects of Rayleigh number and baffle length on flow and temperature fields, heat transfer rate and deformation of elastic parts of the cavity. The results show that an increase in the Rayleigh number enhances the natural convection and increases the elastic parts deformations. Finally, the increase of baffle length has different effects on thermal performance of cavity depending on the Rayleigh number and rigidness or flexibility of the system.

FE temperature- and residual stress prediction in milling inserts and correlation with experimentally observed damage mechanisms

In milling applications thermal and mechanical loadings are affecting the damage behavior of milling inserts. There are several open questions regarding the influence of loading and tool temperature on inelastic deformations and damage mechanisms. The aim of the current work is to simulate industrial milling processes with the finite element method and generate knowledge about the acting damage mechanisms. The validation of the results is made by two recently reported experimental milling setups. The focus of the simulations is set on investigations of the evolution of tensile residual stresses orientated parallel to the cutting edge of a milling insert. These tensile residual stresses foster the formation and growth of so-called comb cracks growing in planes perpendicular to the cutting edge which are detrimental to the performance of the tool. The insert is made of WC-Co hard metal with 8 wt.% Co-binder and an average WC grain size of 1 μm. It is coated with a 7 μm thick TiAlN layer acting as a thermal shield. The workpiece material is 42CrMo4, described by a Johnson-Cook constitutive material model. The milling process is modeled with a 2D Arbitrary Lagrangian-Eulerian (ALE) approach. Results of the 2D simulations are used to generate the temperature and contact load imposed on a 3D solid-model of the milling insert that is in turn used to predict the evolution of stress and temperature over 50 milling cycles. The simulations reproduce a shift of residual stresses toward tension in the milling insert at the same location as observed in experiments from which one failed due to comb cracks and one due to wear.

A Higher-Order Discontinuous Galerkin/Arbitrary Lagrangian Eulerian Partitioned Approach to Solving Fluid–Structure Interaction Problems with Incompressible, Viscous Fluids and Elastic Structures

This manuscript presents a discontinuous Galerkin-based numerical method for solving fluid–structure interaction problems involving incompressible, viscous fluids. The fluid and structure are fully coupled via two sets of coupling conditions. The numerical approach is based on a high-order discontinuous Galerkin (with Interior Penalty) method, which is combined with the Arbitrary Lagrangian–Eulerian approach to deal with the motion of the fluid domain, which is not known a priori. Two strongly coupled partitioned schemes are considered to resolve the interaction between fluid and structure: the Dirichlet–Neumann and the Robin–Neumann schemes. The proposed numerical method is tested on a series of benchmark problems, and is applied to a fluid–structure interaction problem describing the flow of blood in a patient-specific aortic abdominal aneurysm before and after the insertion of a prosthesis known as stent graft. The proposed numerical approach provides sharp resolution of jump discontinuities in the pressure and normal stress across fluid–structure and structure–structure interfaces. It also provides a unified framework for solving fluid–structure interaction problems involving nonlinear structures, which may develop shock wave solutions that can be resolved using a unified discontinuous Galerkin-based approach.

A Comparison of Different Finite Element Methods in the Thermal Analysis of Friction Stir Welding (FSW)

Friction Stir Welding (FSW) is a novel kind of welding for joining metals that are impossible or difficult to weld by conventional methods. Three-dimensional nature of FSW makes the experimental investigation more complex. Moreover, experimental observations are often costly and time consuming, and usually there is an inaccuracy in measuring the data during experimental tests. Thus, Finite Element Methods (FEMs) has been employed to overcome the complexity, to increase the accuracy and also to reduce costs. It should be noted that, due to the presence of large deformations of the material during FSW, strong distortions of mesh might be happened in the numerical simulation. Therefore, one of the most significant considerations during the process simulation is the selection of the best numerical approach. It must be mentioned that; the numerical approach selection determines the relationship between the finite grid (mesh) and deforming continuum of computing zones. Also, numerical approach determines the ability of the model to overcome large distortions of mesh and provides an accurate resolution of boundaries and interfaces. There are different descriptions for the algorithms of continuum mechanics include Lagrangian and Eulerian. Moreover, by combining the above-mentioned methods, an Arbitrary Lagrangian–Eulerian (ALE) approach is proposed. In this paper, a comparison between different numerical approaches for thermal analysis of FSW at both local and global scales is reviewed and the applications of each method in the FSW process is discussed in detail. Observations showed that, Lagrangian method is usually used for modelling thermal behavior in the whole structure area, while Eulerian approach is seldom employed for modelling of the thermal behavior, and it is usually employed for modelling the material flow. Additionally, for modelling of the heat affected zone, ALE approach is found to be as an appropriate approach. Finally, several significant challenges and subjects remain to be addressed about FSW thermal analysis and opportunities for the future work are proposed.

A fluid-structure interaction solver for the fluid flow through reed type valves

Suction and discharge processes with self actuated valves have a major influence in efficiency and reliability of hermetic reciprocating compressors. Understanding the operation completely in order to enhance compressor’s design needs precise prediction of the fluid-structure interaction complexities involved in these processes. This paper presents a comprehensive description of a numerical methodology to account for the coupled behaviour of a reed valve and a turbulent flow. The method is based on a partitioned semi-implicit scheme that only strongly couples the fluid pressure term to the structural solver. A three-dimensional CFD analysis with LES turbulence modelling is used for the flow while a combination of plate theory and mode summation method is used for the solid. The dynamically changing domains are tackled by means of lagrangian and arbitrary lagrangian-eulerian approaches for the solid and the fluid, respectively. The whole model is compared with experimental data at Reynolds number 10, 000, showing good agreement in lift amplitude and deformation fluctuations. Finally, as an illustrative case, results regarding lift, pressures, force and effective areas are compared with those of a valve with wider gland.

Dynamic debonding in layered structures: a coupled ALE-cohesive approach

A computational formulation able to simulate crack initiation and growth in layered structural systems is proposed. In order to identify the position of the onset interfacial defects and their dynamic debonding mechanisms, a moving mesh strategy, based on Arbitrary Lagrangian-Eulerian (ALE) approach, is combined with a cohesive interface methodology, in which weak based moving connections are implemented by using a finite element formulation. The numerical formulation has been implemented by means of separate steps, concerned, at first, to identify the correct position of the crack onset and, subsequently, the growth by changing the computational geometry of the interfaces. In order to verify the accuracy and to validate the proposed methodology, comparisons with experimental and numerical results are developed. In particular, results, in terms of location and speed of the debonding front, obtained by the proposed model, are compared with the ones arising from the literature. Moreover, a parametric study in terms of geometrical characteristics of the layered structure are developed. The investigation reveals the impact of the stiffening of the reinforced strip and of adhesive thickness on the dynamic debonding mechanisms.

An ALE approach for the chip formation process in high speed machining with transient cutting conditions: Modeling and experimental validation

The Arbitrary Lagrangian Eulerian approach (ALE) presents a lot of advantages. However, its use is limited to the cutting with a constant uncut chip thickness h. On the one hand, the previous numerical studies were focused on the prediction of the quasi-stationary response for cutting forces and heat transfer along the tool rake face. But on the other hand, in the industrial machining processes, as milling operations, the removal of the material from the workpiece varies with time. The aim of the present work is to extend the use of the ALE approach to the milling processes where the cutting conditions are transient: h varies with time. A new strategy combining the ALE approach and the tool translation is presented. In the present model, the out flow surface of the chip is assimilated to an Eulerian surface with a vertical moving direction of the mesh. This strategy allows to consider the increase of the tool-chip contact length with h as in up milling. The limitations of the conventional use of the ALE were also discussed in this study. The experimental study was focused on dry machining of the aluminum alloy AA2024–T351 at very high speed 51.5 and 66.2 m/s. The predicted cutting forces have been compared with the experimental results. The cutting forces are not proportional to h especially for the feed force. This tendency, reproduced by the model, is directly related to the thermal softening of the work material in the secondary shear zone. At the tool rake face, the variation of the local parameters in function of time is also discussed: tool-chip contact length, sticking zone and temperature.

Regularized immersed boundary-type formulation for fast transient dynamics with fluid-structure interaction

The present article deals with fast transient phenomena involving fluids and structures undergoing large displacements and rotations, associated with non-linear local behavior, such as plasticity, damage and failure. In this context, classical Arbitrary Lagrangian Eulerian approaches reach a limit where it is not possible to update the fluid grid to follow the structural motion without encountering entangled fluid cells forcing the simulations to stop. So-called immersed boundary approaches are thus frequently preferred in this situation, since they allow breaking the topological connection between the fluid and structural meshes and retrieve the expected level of robustness to handle complex structural motions. Their potential for efficient, robust and accurate simulations at the industrial level has been proven. However, it appears that the classical implementation of such approaches still imposes some constraints over the fluid mesh with respect to the structural mesh in terms of cell sizes, due to the expression of the kinematic links between fluid and structural velocities, which must be improved. It is demonstrated in the present article that an extended regularized framework can be designed to overcome the current drawbacks, but it comes with a significant increase of computational complexity and requires an extension of the classical software features encountered in fast transient dynamics simulation programs.

Microstructural Modeling of Pitting Corrosion in Steels Using an Arbitrary Lagrangian–Eulerian Method

Two microscale numerical models are developed in this work using a moving-mesh approach to investigate the growth process of pitting in different iron phases and the corrosion prevention capability of polyaniline (PANi) on steels. The distributions of corrosion potential and current in the electrolyte-coating-steel system are computed to evaluate the anti-corrosion ability of PANi. The arbitrary Lagrangian–Eulerian approach was used to accomplish the continuous remesh process as was needed to simulate the dynamic growing forefront of the modeled pitting domain. Experimental validation of the numerical models was conducted using the technique of scanning kelvin probe force microscopy (SKPFM). The SKPFM-scanned surface topography and Volta potential difference exhibit comparable results to and thereby prove the numerical results. The potential distribution in the electrolyte phase of the validated models shows that the corrosion pit grows faster in the epoxy-only-coated steel than that in the PANi-primer-coated steel over the simulation time; also, the corrosion pit grows faster in the ferrite phase than in the cementite phase. The simulation results indicate that the epoxy-only coating lost its anti-corrosion capability as the coating was penetrated by electrolyte, while the PANi-based coating can still protect the steel from corrosion after the electrolyte penetration. The models developed in this work can be used to study the mechanisms of pitting corrosion as well as develop more effective corrosion prevention strategies for general metallic materials.

Dynamic computations of nonlinear beams in contact with rough surfaces

We present computations of a two-dimensional nonlinear ring in contact with a rough surface for the analysis of tire dynamic behaviour at low frequencies in both non-rolling and rolling conditions. For the ring, the assumptions of a Timoshenko beam and finite displacements are considered to build the model. The analytical formulation is established successfully in linear/nonlinear static and dynamic states in non-rolling and rolling conditions using an Arbitrary Lagrangian Eulerian approach. Then, the contact with a real road is introduced. In particular, the calculation of the contact is divided into a non-linear stationary analysis followed by a linear dynamic calculation. The validation of this model is successfully done by comparisons with test results like rolling on simple shapes or with Abaqus computations.

A coupled ALE-Cohesive formulation for layered structural systems

Abstract: A computational formulation able to simulate crack initiation and growth in layered structural systems is proposed. In order to identify the position of the onset interfacial defects and their dynamic debonding mechanisms, a moving mesh strategy, based on Arbitrary Lagrangian-Eulerian (ALE) approach, is combined with a cohesive interface methodology, in which weak based moving connections are implemented by using the finite element formulation. Contrarily to the existing models available from the literature, the proposed approach appears to be able to describe dynamic debonding processes with a relatively low number of computational elements also in specimens without a pre-existing interfacial crack. The numerical formulation has been implemented by means separate steps, concerned, at first, to identify the correct position of the onset cracks and, subsequently, their growth by changing the computational geometry of the interfaces. In order to verify the accuracy and to validate the proposed methodology, comparisons with experimental and numerical results are developed. In particular, the results, in terms of location and speed of the debonding front, obtained by the proposed model, are compared with the ones arising from the literature. Moreover, a parametric study in terms of geometrical characteristics of the layered structure are developed. The investigation reveals the impact of the stiffening of the reinforced strip and of adhesive thickness on the dynamic debonding mechanisms.

An ALE approach to mechano‐chemical processes in fluid–structure interactions

SummaryMathematical modeling and simulation of fluid–structure interaction problems are in the focus of research already for a longer period. However, taking into account also chemical reactions, leading to structural changes, including changes of mechanical properties of the solid phase, is rather new but for many applications is highly important area. This paper formulates a model system for reactive flow and transport in a vessel system, the penetration of chemical substances into the solid wall. Inside the wall, reactions take place that lead to changes of volume and of the mechanical properties of the wall. Numerical algorithms are developed and used to simulate the dynamics of such a mechano‐chemical fluid–structure interaction problem. As a proof of concept scenario, plaque formation in blood vessels is chosen. The arbitrary Lagrangian Eulerian approach (ALE) is chosen to solve the systems numerically. Temporal discretization of the fully coupled monolithic model is accomplished by backward Euler scheme and spatial discretization by stabilized finite elements. The numerical approach is verified by numerical tests, and effective methods to maintain mesh qualities under large deformations are described. For realistic system parameters, the simulations show that the plaque formation in blood vessel is a long‐time effect. The time scale of the formation is in the simulation of comparable order as in reality. Copyright © 2016 John Wiley & Sons, Ltd.