Arbitrary Lagrangian-Eulerian Model Research Articles

High fidelity nonlinear finite element tire modeling for dynamic analysis: Total Lagrangian formulation in rolling contact

Tire design with respect to vibrational behavior and noise emission is a challenging task due to the large number of parameters and their coupling. Therefore, accurate high fidelity nonlinear Finite Element (FE) models are needed to aid in the design process. The widely used Arbitrary Lagrangian Eulerian (ALE) models, despite their computational efficiency, are limited to rib-slicked tires and require significant effort to consider inelastic material behavior and frictional phenomena. To overcome these limitations a novel nonlinear FE tire model is presented based on the Total Lagrangian (TL) formulation. The TL model is compared to the reference ALE model for the case of stationary rolling on a smooth and a rough road surface. The observed match of the TL model with respect to the hub and contact forces proves the feasibility of using the TL formulation in the context of rolling contact tire simulations. Therefore, the TL model can be seen as a valid alternative to the frequently used ALE models.

Comprehensive thermo-mechanical simulation of friction surfacing of aluminum alloys using smoothed particle hydrodynamics method

Using the Smoothed Particle Hydrodynamics (SPH) model, this article has studied the thermomechanical and microstructural aspects of AA6061 aluminum coating applied by friction surfacing. The predicted results were compared and validated with the experimental results. A comparison was also performed between the results predicted by the SPH and Arbitrary Lagrangian-Eulerian (ALE) models. The results showed that using the SPH model, the un-bonding zone and coating profile were simulated with high accuracy without any need to determine the plastic strain criterion required for the ALE model. The maximum percentage errors in estimating the effective thickness and width of the coating by the SPH model were 6% and 8%, respectively. According to the predicted and experimental results, the minimum temperature at the interface between the consumable rod and substrate required to create an effective coating was higher than 0.54 Tm of the AA6061 consumable rod. Compared to the SPH model, the ALE model was less accurate in predicting the microstructure and estimating the thermal cycle of the coating, especially in the heating/cooling stage and at the maximum temperature of the thermal cycle.

Modeling of Drag Finishing—Influence of Abrasive Media Shape

Drag finishing is a widely used superfinishing technique in the industry to polish parts under the action of abrasive media combined with an active surrounding liquid. However, the understanding of this process is not complete. It is known that pyramidal abrasive media are more prone to rapidly improving the surface roughness compared to spherical ones. Thus, this paper aims to model how the shape of abrasive media (spherical vs. pyramidal) influences the material removal mechanisms at the interface. An Arbitrary Lagrangian–Eulerian model of drag finishing is proposed with the purpose of estimating the mechanical loadings (normal stress, shear stress) induced by both abrasive media at the interface. The rheological behavior of both abrasive slurries (media and liquid) has been characterized by means of a Casagrande direct shear test. In parallel, experimental drag finishing tests were carried out with both media to quantify the drag forces. The correlation between the numerical and experimental drag forces highlights that the abrasive media with a pyramidal shape exhibits a higher shear resistance, and this is responsible for inducing higher mechanical loadings on the surfaces and, through this, for a faster decrease of the surface roughness.

Probabilistic blast load model for domes under external surface burst explosions

The increasing threat of terrorist attacks and the risk of accidental explosions has raised the alarm on structural design, and consequently, the dome structure as the classical building configuration model for public buildings requires safe and reliable defence capabilities against blast loads for the duration of its lifespan. Some deterministic blast load models for specific blast loading scenarios are unable to take the risk of damage into consideration. Therefore, the variability and uncertainty of blast loads need to be studied and quantified. In this study, a probabilistic blast load model is proposed based on a series of repeated field trials. The repeatability of explosive mass and size, detonator type and location, stand-off distance, field condition, data acquisition device and the structure were ensured to realise consistency and standardisation. The experimental results reveal a high degree of variability and uncertainty in the impulse, reflected overpressure and decay coefficient distributed on the studied dome under the effect of external surface explosions. The decay coefficient of a blast wave on the dome has a large variability with a coefficient of variation of 55% when the impulse is less than 8%, which demonstrates that the impulse distributed on the dome has higher precision than other blast load parameters. Furthermore, statistical analysis shows that the normal distribution is the best-fit probability blast load model in an anti-explosion protection design. Furthermore, the accuracy of some blast load predictive methods was also assessed. It was found that the semi-empirical CONWEP air blast code is not an appropriate blast load model for the dome. However, the Arbitrary Lagrangian-Eulerian model is a safer and relatively more accurate method for describing the distribution and variation characteristics of a blast wave distributed on the dome, which can serve as an approximate mean blast load.

Finite element modeling of macrosegregation coupled with shrinkage cavity in steel ingots using arbitrary Lagrangian-Eulerian model

Shrinkage cavity has significant influence on macrosegregation in steel ingots. An arbitrary Lagrangian-Eulerian (ALE) model based on volume averaging method is developed to predict the coupled formation progress of macrosegregation and shrinkage cavity during solidification of steel ingots. The combined effect of thermal-solutal convection and solidification shrinkage on macrosegregation is considered in the model. A specially designed mesh update algorithm is proposed to consider the formation of shrinkage cavity. The streamline-upwind/Petrov-Galerkin (SUPG) stabilized finite element algorithm is adopted to solve the conservation equations. Two solution methods for the energy conservation equation are proposed, i.e. the temperature-based solver and enthalpy-based solver. A Pb-48wt.%Sn solidification benchmark is used for validation. Then, the ALE model is applied to a Fe-3.6wt.%C industrial steel ingot. The formation progress of macrosegregation coupled with shrinkage cavity is predicted. By comparison with the predictions of the finite element model and finite volume model, the effect of shrinkage cavity formation on macrosegregation is investigated. Results show that the formation of shrinkage cavity can significantly change the segregation region and segregation degree at the hot top. It is demonstrated that the ALE model can predict the coupled formation of macrosegregation and shrinkage cavity in steel ingots.

Numerical Simulation of Macrosegregation Caused by Thermal–Solutal Convection and Solidification Shrinkage Using ALE Model

Solidification shrinkage has been recognized as an important factor for macrosegregation formation. An arbitrary Lagrangian–Eulerian (ALE) model is constructed to predict the macrosegregation caused by thermal–solutal convection and solidification shrinkage. A novel mesh update algorithm is developed to account for the domain change induced by solidification shrinkage. The velocity–pressure coupling between the non-homogenous mass conservation equation and momentum equation is addressed by a modified pressure correction method. The governing equations are solved by the streamline-upwind/Petrov–Galerkin-stabilized finite element algorithm. The application of the model to the Pb-19.2 wt%Sn alloy solidification problem is considered. The inverse segregation is successfully predicted, and reasonable agreement with the literature results is obtained. Thus, the ALE model is established to be a highly effective tool for predicting the macrosegregation caused by solidification shrinkage and thermal–solutal convection. Finally, the effect of solidification shrinkage is analyzed. The results demonstrate that solidification shrinkage delays the advance of the solidification front and intensifies the segregation.

Numerical study of heat transfer from a synthetic impinging jet with a detailed model of the actuator membrane

Synthetic jets are produced by the oscillatory movement of a membrane inside a cavity, causing the fluid to enter and leave through a small orifice. The present study is focused on investigating the cooling capabilities of a synthetic jet enclosed between two parallel isothermal plates with an imposed temperature difference. The unsteady three-dimensional Navier-Stokes equations have been solved for a range of Reynolds numbers from 50 to 1000 using time-accurate numerical simulations. A detailed model based on an Arbitrary Lagrangian-Eulerian (ALE) formulation is used to account for the movement of the actuator membrane. All the resulting flows are inherently three-dimensional and dominated by two major vortices, which find their counterparts inside the actuator cavity. A new structure, which is not found in open cavities, appears as an interaction of the synthetic jet flow with the bottom wall and results in a change on the jet's heat transfer mechanisms. Analysis of the outlet temperature has shown that assuming a uniform profile is reasonable if the Reynolds number is high enough, however, the outlet jet temperature is significantly higher than the cold plate temperature. Finally, this study proposes correlations for the heat transfer at the hot wall and the outlet temperature with the Reynolds number, which can be used to account for the cavity effects without the computationally expensive ALE model.

Modelling of guillotine cutting of multi-layered aluminum sheets

The paper presents a numerical modelling of the guillotine cutting process of sheet aluminum bundles. A finite element method with a smoothed particle hydrodynamics approach were coupled to simulate the cutting process. Moreover, arbitrary Lagrangian–Eulerian formulation was also proposed and applied to model the process. Experimental results of the cutting were presented for the validation purposes. The measured force characteristics in all numerical simulations and experiment were compared. The computational costs of the implemented methods were also analyzed. Additionally, a mesh (particles) sensitivity study was performed, and the influence of the mesh on the obtained results was assessed. Based on the outcomes the arbitrary Lagrangian–Eulerian model was selected as more suitable method of modelling the guillotine cutting process and it was validated in different cutting conditions and the influence of technological parameters such as knife velocity and cutting-edge angle was investigated.

A hierarchical sequential ALE poromechanics model for tire‐soil‐water interaction on fluid‐infiltrated roads

SummaryThis paper introduces a hierarchical sequential arbitrary Lagrangian‐Eulerian (ALE) model for predicting the tire‐soil‐water interaction at finite deformations. Using the ALE framework, the interaction between a rolling pneumatic tire and the fluid‐infiltrated soil underneath will be captured numerically. The road is assumed to be a fully saturated two‐phase porous medium. The constitutive response of the tire and the solid skeleton of the porous medium is idealized as hyperelastic. Meanwhile, the interaction between tire, soil, and water will be simulated via a hierarchical operator‐split algorithm. A salient feature of the proposed framework is the steady state rolling framework. While the finite element mesh of the soil is fixed to a reference frame and moves with the tire, the solid and fluid constituents of the soil are flowing through the mesh in the ALE model according to the rolling speed of the tire. This treatment leads to an elegant and computationally efficient formulation to investigate the tire‐soil‐water interaction both close to the contact and in the far field. The presented ALE model for tire‐soil‐water interaction provides the essential basis for future applications, for example, to a path‐dependent frictional‐cohesive response of the consolidating soil and unsaturated soil, respectively. Copyright © 2017 John Wiley & Sons, Ltd.

An unstructured mesh arbitrary Lagrangian-Eulerian unsteady incompressible flow solver and its application to insect flight aerodynamics

In this paper, an unstructured mesh Arbitrary Lagrangian-Eulerian (ALE) incompressible flow solver is developed to investigate the aerodynamics of insect hovering flight. The proposed finite-volume ALE Navier-Stokes solver is based on the artificial compressibility method (ACM) with a high-resolution method of characteristics-based scheme on unstructured grids. The present ALE model is validated and assessed through flow passing over an oscillating cylinder. Good agreements with experimental results and other numerical solutions are obtained, which demonstrates the accuracy and the capability of the present model. The lift generation mechanisms of 2D wing in hovering motion, including wake capture, delayed stall, rapid pitch, as well as clap and fling are then studied and illustrated using the current ALE model. Moreover, the optimized angular amplitude in symmetry model, 45°, is firstly reported in details using averaged lift and the energy power method. Besides, the lift generation of complete cyclic clap and fling motion, which is simulated by few researchers using the ALE method due to large deformation, is studied and clarified for the first time. The present ALE model is found to be a useful tool to investigate lift force generation mechanism for insect wing flight.

Application of the Coupled Eulerian-Lagrangian (CEL) method to the modeling of orthogonal cutting

Abstract Numerical modeling of metal cutting is a complex problem involving many nonlinear and coupled phenomena (high speed, large strains, large strain-rates, heat generation, etc.). Due to the large deformations, the mesh of the workpiece is often highly distorted. When it does not ends prematurely the computing, it slows it down and decreases the confidence in the results. Many formalisms are encountered in the literature to model the orthogonal cutting process, each with their pros and cons, more or less significant. This paper introduces the Coupled Eulerian-Lagrangian (CEL) formulation, in which the workpiece is described by the Eulerian formulation and the tool by the Lagrangian one. The comparison with experimental results and an Arbitrary Lagrangian-Eulerian (ALE) model with pure Lagrangian boundaries shows that the chip morphology and the cutting forces are well predicted by that new model. The absence of mesh deformation in the part does not decrease the stable time increment and therefore does not slow down the computing, which is competitive compared to the reference ALE model. This also increases confidence in the results given by the CEL model and opens new possibilities in the modeling of metal cutting.

Dielectrophoretic behavior of a single cell when manipulated by optoelectronic tweezers: A study based on COMSOL ALE simulations

Abstract Optoelectronic tweezers uses optically induced dielectrophoretic (DEP) force for manipulating cells in aqueous solution, which has shown potential applications in biology and tissue engineering among other possibilities. To effectively design the optoelectronic tweezers (OETs) chip, detailed knowledge about the behavior of cells in response to DEP force in an aqueous layer is needed. In this paper, the trajectories of an SMMC-77721 cell, simulated as a rigid dielectric sphere, in the induced electric field of optical trapping are studied using both an Arbitrary Lagrangian-Eulerian (ALE) method and a particle-tracing method (PTM) available within the COMSOL multiphysics software platform. Because the ALE method involves solving the distorted electric field around the cell and taking a full account of the Maxwell stress tensor (MST), it is expected to provide more accurate predictions about the spherical cell velocity than PTM that involves dipole moment approximation. Our ALE results show noticeably greater cell velocity than that predicted by the classical DEP expression based on dipole moment approximation. The ALE model can help gain new insights for analyzing cell motions in aqueous solution under sophisticated optical spot patterns.

A Study of Granular Flow in a Conical Hopper Discharge Using Discrete and Continuum Approach

Discrete and continuum modelling of granular flow in a conical hopper discharge is presented. The Discrete Element Method (DEM) is used for discrete modelling and Finite Element Method based on an Arbitrary Lagrangian-Eulerian (ALE) formulation for continuum modelling. The ALE model has shown its capability to model granular flow and macroscopic behaviour in silos in the authors’ previous work (Wang et al., 2013). The use of ALE overcomes mesh distortion problem due to material large deformation which is often encountered in standard finite element modelling of silo discharge. However, there is still limitation when a continuum method is used to model silo discharge, in particular, to pursue particle-scale features in such granular flow. In this study, wall pressure, flow pattern and flow rate during silo discharge are investigated using both ALE and DEM simulation. Classical theories are used as a comparison, to verify the two numerical models. By comparison, it is indicated that both FE model using ALE formulation and DEM model have the capacity to model the granular behaviour and wall pressure for granular process in silos. The conclusion that ALE has advantages over DEM in wall pressure prediction giving stable pressure profile with smooth trend; while DEM has the ability to evaluate the role of particle-scale parameters on macro-scale response in such granular flow after carefully smoothing out the results has been drawn in the present study.

Head and brain response to blast using sagittal and transverse finite element models

Mild traumatic brain injury caused by blast exposure from Improvised Explosive Devices has become increasingly prevalent in modern conflicts. To investigate head kinematics and brain tissue response in blast scenarios, two solid hexahedral blast-head models were developed in the sagittal and transverse planes. The models were coupled to an Arbitrary Lagrangian-Eulerian model of the surrounding air to model blast-head interaction, for three blast load cases (5 kg C4 at 3, 3.5 and 4 m). The models were validated using experimental kinematic data, where predicted accelerations were in good agreement with experimental tests, and intracranial pressure traces at four locations in the brain, where the models provided good predictions for frontal, temporal and parietal, but underpredicted pressures at the occipital location. Brain tissue response was investigated for the wide range of constitutive properties available. The models predicted relatively low peak principal brain tissue strains from 0.035 to 0.087; however, strain rates ranged from 225 to 571 s-1. Importantly, these models have allowed us to quantify expected strains and strain rates experienced in brain tissue, which can be used to guide future material characterization. These computationally efficient and predictive models can be used to evaluate protection and mitigation strategies in future analysis.

Numerical simulation of a bird impact on a composite aerodynamic brake wing of a high-speed train

Experimental bird strike tests were conducted in which a 2.6-kg dead chicken was projected at a speed of 500 km/h to hit a raised aerodynamic brake wing. The brake wing was fabricated with a sandwich of composite material as its skin and polymethacrylimide foam as its core. Pre-test numerical analyses of bird strikes were performed using the LS-Dyna solver code, an Arbitrary Lagrangian Eulerian model of the bird, and a Lagrangian model of the brake wing. The numerical and experimental results were well correlated, confirming the validity of the finite element model and calculation approach. Finally, bird strikes were conducted on a brake wing extended to 75° and 90° to determine the difference between the two conditions on the basis of effective wind-drag area. Impact, failure after impact and high strength at impact properties were investigated for a composite of carbon and glass fibre laminate.

An arbitrary Lagrangian–Eulerian model for modelling the time-dependent evolution of crevice corrosion

An arbitrary Lagrangian–Eulerian (ALE) model is proposed to model the time-dependent evolution of a crevice corrosion that can achieve the simulation of the transient potential distribution, the dynamic concentration profiles and the time-dependent geometry deformation for a corroding crevice. The time-dependent deformation of the crevice geometry, which is caused by metal dissolution and corrosion product precipitation, is implemented via the ALE method. The model reasonably predicted the dynamic pH distribution inside the crevice. It is also predicted that the deposition of corrosion product accelerates crevice corrosion. The current model would be helpful in elucidating the mechanism of crevice corrosion and other forms of related localised corrosion.

An arbitrary Lagrangian–Eulerian model for studying the influences of corrosion product deposition on bimetallic corrosion

In this paper, a model is established to simulate the time-dependent deposition of corrosion product on the metal surface by considering mass transfer, electrochemical reactions and precipitation reaction. The model is also capable of tacking the movement of metal corrosion interface and the growing interface of the corrosion product deposits via arbitrary Lagrangian–Eulerian finite element method. The current model not only can be used to predict the time-dependent metal corrosion but also for investigating the influences of the deposits’ nature on metal corrosion. The numerical results of current density and corrosion rate are in good agreement with experiments. The presented model predicts that an exponential relationship exists between the maximum corrosion depth and the porosity of corrosion product deposits, and it is also predicted that the growth of the corrosion product layer is linear relative with the root of time, which is consistent with the existing theories.

Identification of a Friction Model at the Tool-Chip-Workpiece Interface in Dry Machining of a AISI 1045 Steel With a TiN Coated Carbide Tool

The characterization of frictional phenomena at the tool-chip-workpiece interface in metal cutting remains a challenge. This paper aims at identifying a friction model and a heat partition model at this interface during the dry cutting of an AISI1045 steel with TiN coated carbide tools. A new tribometer, based on a modified pin-on-ring system, has been used in order to reach relevant values of pressures, temperatures, and sliding velocities. Additionally a 3D Arbitrary Lagrangian Eulerian model (A.L.E.) numerical model simulating the frictional test has been developed in order to extract local parameters around the spherical pin, such as average contact pressure, average local sliding velocity, and average contact temperature, from experimental macroscopic measurements. A large range of sliding velocities [0.083–5 m/s] has been investigated. It has been shown that friction coefficient and heat partition coefficient are mainly dependant on local sliding velocity at the interface. Three friction regimes have been identified. These experimental and numerical results provide a better understanding of the tribological phenomena along the tool-chip-workpiece interfaces in dry machining of an AISI 1045 steel with a TiN coated carbide tool. Finally a new friction model and heat partition model has been developed for implementation in a numerical cutting model.

An operator‐split ALE model for large deformation analysis of geomaterials

AbstractAnalysis of large deformation of geomaterials subjected to time‐varying load poses a very difficult problem for the geotechnical profession. Conventional finite element schemes using the updated Lagrangian formulation may suffer from serious numerical difficulties when the deformation of geomaterials is significantly large such that the discretized elements are severely distorted. In this paper, an operator‐split arbitrary Lagrangian–Eulerian (ALE) finite element model is proposed for large deformation analysis of a soil mass subjected to either static or dynamic loading, where the soil is modelled as a saturated porous material with solid–fluid coupling and strong material non‐linearity. Each time step of the operator‐split ALE algorithm consists of a Lagrangian step and an Eulerian step. In the Lagrangian step, the equilibrium equation and continuity equation of the saturated soil are solved by the updated Lagrangian method. In the Eulerian step, mesh smoothing is performed for the deformed body and the state variables obtained in the updated Lagrangian step are then transferred to the new mesh system. The accuracy and efficiency of the proposed ALE method are verified by comparison of its results with the results produced by an analytical solution for one‐dimensional finite elastic consolidation of a soil column and with the results from the small strain finite element analysis and the updated Lagrangian analysis. Its performance is further illustrated by simulation of a complex problem involving the transient response of an embankment subjected to earthquake loading. Copyright © 2007 John Wiley & Sons, Ltd.

An extended arbitrary Lagrangian–Eulerian finite element modeling (X-ALE–FEM) in powder forming processes

Abstract In this paper, a new computational technique is presented based on the extended arbitrary Lagrangian–Eulerian finite element model (X-ALE–FEM) in plasticity forming of powder compaction. An arbitrary Lagrangian–Eulerian (ALE) technique is employed to capture the advantages of both Lagrangian and Eulerian methods and alleviate the drawbacks of the mesh distortion in Lagrangian formulation. In order to remove the limitation of the mesh conforming to the boundary conditions in this process, the extended finite element method (X-FEM) is implemented by incorporating discontinuous fields through a partition of unity method. The implementation of X-FEM technique in the framework of ALE model is finally presented in modeling of a shaped tablet component.