Arbitrary Lagrangian Eulerian Formulation Research Articles

Prediction of rolling resistance and wheel force for a passenger car tire: A comparative study on the use of different material models and numerical approaches

In this research, the characteristics of tire-road interaction of a 185/65R14 88H passenger car tire are investigated using the Finite Element Method in Abaqus commercial software. Moreover, the effect of various material models on tire performance is studied by implementing Visco-Hyperelastic, Parallel Rheological Framework, and Mullins effect. The novelty of this research is devoted to the development of the complex material models particularly considering the Mullins effect of the rubber compounds in the tire structure for the load-displacement criteria. For this purpose, a tire finite element model was generated using Abaqus/Standard command line in two different methods including an Arbitrary Lagrangian-Eulerian formulation for steady state rolling and implementing a pure Lagrangian approach for the transient dynamic analysis carried out implicit and explicit process respectively. Rolling resistance force was computed according to ISO 28580 with 210 kPa inflation pressure and 4155 N vertical load. The footprint test results were extracted in both static and transient dynamic analyses. Additionally, the wheel reaction force was predicted using an indirect method by extracting the tire-terrain contact patch reaction force in Abaqus/Explicit to observe the effect of the material convection along with stress softening phenomena of the rubber compounds of tire structure. In the post-processing analysis, the wheel reaction was filtered by implementing SAE60 filter to reduce the numerical noise in the final response.

Aeroacoustic simulation of human phonation based on the flow-induced vocal fold vibrations including their contact

This paper deals with the numerical simulation of the flow induced sound as generated in the human phonation process including vocal folds (VF) contact. The hybrid approach is used allowing to separate the acoustic and the biomechanical description of the considered problem. The two-dimensional fluid–structure interaction (FSI) problem is modelled by a simplified linear elastic model coupled to the incompressible Navier–Stokes equations in the arbitrary Lagrangian–Eulerian form and special attention is paid to the treatment of the contact problem in the FSI context. Following approach of [Sváček and Horáček, 2021] the incompressible flow model is modified by an addition of fictitious porosity term and the penalization inlet boundary condition is used. Further, the Lighthill acoustic analogy is applied for calculation of sound sources and their propagation through a vocal tract model. All partial differential equations, describing the elastic body vibration, the fluid flow and the acoustics, are approximated by finite element method. Numerical results of one-sided vocal fold paralysis are presented.

Sedimentation of a spheroidal particle in an elastoviscoplastic fluid

The sedimentation dynamics of a prolate spheroidal particle in an unbounded elastoviscoplastic (EVP) fluid is studied by direct finite element simulations under inertialess flow conditions. The Saramito–Giesekus constitutive equation is employed to model the suspending liquid. The arbitrary Lagrangian–Eulerian formulation is used to handle the particle motion. The sedimentation, lift, and angular velocities of spheroids with aspect ratio between 1 and 8 are computed as the initial orientation, Bingham, and Weissenberg numbers are varied. Similar to the purely viscoelastic case, a spheroid in an EVP fluid rotates up to align its major axis with the applied force. As the Bingham number increases, the settling rate monotonically reduces, while the angular velocity first increases and then decreases. The initial orientation has a relevant effect on the particle stoppage because of the different drag experienced by the spheroid as its orientation is varied. The yielded and unyielded regions around the spheroid reveal that, for particle oriented transversely to the force, the yielded envelope shrinks near the tips due to the fast spatial decay of the stresses, and unyielded regions appear along the surface of the particle, similar to the solid caps observed at the front and back of a sphere. Fluid plasticity enhances the negative wake phenomenon that is observed at Weissenberg numbers significantly lower than the purely viscoelastic case. The results of the drag correction coefficient for particles aligned with longest axis along the force are presented.

Fluid‐structure interaction study of an oscillating heat source effect on the natural convection flow

AbstractThe objective of this paper is to investigate fluid‐structure interaction (FSI) within conjugate natural convection. An oscillating fin, featuring a heat source placed at different locations, is examined using the Arbitrary Lagrangian–Eulerian formulation. The Galerkin finite element method is utilized to solve nonlinear dimensionless equations. Verification of grid independence is conducted and the model undergoes validation. Simulation outcomes for three fin positions (left, center, and right) and three heat source locations (bottom, middle, and top) are presented, illustrating streamlines, isotherms, and the average Nusselt number. The governing equations and boundary conditions are addressed using the finite element method. Temperature profiles in four scenarios are analyzed, along with horizontal velocities at different levels (0, D/2, D from the bottom wall). Dimensionless time (10−5 ≤ t ≤ 3), Ra = 106, Kr = 10, E = 1011 are used as parameters. The impact of the heat source position on vibratory motion is evaluated through Nusselt number variation, affecting heat exchange in different cases. The results show that heat transfer is minimal for a source location at the center of the fin (c). These findings also offer insights into FSI applications in economics and industry, guiding practical design considerations. Additionally, coupling the vibratory motion of the heat source with the flexible oscillating fin at the same frequency enhances understanding of the system.

Numerical investigation of liquid sloshing in 2D flexible tanks subjected to complex external loading

Due to the complexity of fluid–structure interactions (FSI), the majority of studies in the literature dealing with the sloshing problem are restricted to rigid tanks. This paper is devoted to a numerical investigation of the liquid sloshing behavior in a flexible tank subjected to external loading. A numerical methodology is proposed, taking into account the FSI problem by coupling two open-source codes: OpenFOAM for the fluid and FEniCS for the solid, using the preCICE library, a free library for fluid–structure interaction. The Arbitrary Lagrangian–Eulerian formulation is used for the two-phase flow system to solve the Navier–Stokes equations in the fluid domain using the finite volume method. Simultaneously, the linear-elastic equation of the structure is solved using the finite element method. An implicit coupling scheme is considered at the fluid–structure interface. The numerical methodology is validated by the results given in literature for harmonic excitation at different frequencies. Subsequently, an analysis of complex external loading, such as Gabor wavelets and earthquake ground motion, is conducted to highlight the significant impact of the wall flexibility on sloshing, as well as the influence of hydrodynamic forces on the structure’s deformation. The proposed coupling methodology is robust and effective, it can be applied to all types of liquids and materials. A dataset of one of the studied cases is given as a supplement to the paper (Kha et al., 2024).

Experimental and numerical investigation of badarpur sand subjected to air-blast loading

In the present study, the results of experimental and numerical investigation of Badarpur sand subjected to air-blast loading generated from a laboratory-scale blast simulator are presented. The air-blast loading on the sand specimen is simulated experimentally using a vertical shock tube test facility to investigate the stress wave attenuation and vibrational characteristics of the Badarpur sand. The peak stress wave pressure and peak particle acceleration are recorded using the synchronized pressure transducers and triaxial accelerometers embedded inside the sand specimen. A stress enhancement of about 1.25-2.69 times the peak over-pressure is observed at the top one-third layer of the sand due to its compaction by the stress wave generated upon the blast wave impact. The stress wave intensity first increases and then rapidly decreases with the depth of the sand specimen. The amplitude of the peak particle acceleration is also observed to attenuate with the depth of the sand specimen. Further, based on the experimental results, the empirical equations are developed to predict peak particle velocity against the scaled distance with a power law index of 3.9, 2.5, and 3.0 for dense-coarse, dense-fine, and medium-dense fine sand, respectively. The numerical model of the vertical shock tube and sand specimens are also developed based on the Arbitrary Lagrangian-Eulerian formulation, commercially available in finite element simulation package LS DYNA and the results are validated with the experimental data.

Load history estimation for ballistic impacts with bullet-splash

The paper validates two simplified approaches to simulate the interactions between impactor and target during the so-called bullet splash phenomenon, i.e., the full fragmentation of the impactor without any penetration of the target. The approaches are based on treating the interactions between impactor and target as the deflection of a fluid flow; in one case the load history is estimated by the mass distribution of the bullet and its impact velocity; in the second case the interaction is simulated by means of an arbitrary Lagrangian Eulerian formulation. The two methods are applied and experimentally validated to simulate a monolithic .308 rifle bullet impacting on a high strength steel plate. The results demonstrate the suitability of the load history method for large scale finite element explicit simulations for the assessment of ballistic protection systems.

A three-dimensional finite element formulation coupling electrochemistry and solid mechanics on resolved microstructures of all-solid-state lithium-ion batteries

In this paper we present an all-solid-state lithium-ion battery (ASSB) model that considers electrochemistry and solid mechanics in a fully coupled manner. The model spatially resolves the three-dimensional microstructure of an ASSB cell and is based on non-linear continuum mechanics. The coupling of electrochemistry and solid mechanics is incorporated via lithiation-dependent volumetric changes of the active materials and the consistent formulation of the electrochemical governing equations on deformed geometries resulting in changed percolation paths. As the volumetric changes due to (de-)lithiation are reported to be large for several active materials, we introduce this effect using a multiplicative split of the deformation gradient. To also allow for large deformations in the mass conservation equation, an Arbitrary Lagrangian–Eulerian formulation is employed. Furthermore, we show the central steps to deduce the finite element formulation of our model as well as the adopted monolithic solution procedure to solve this strongly coupled non-linear problem. The linear solver used for large problem setups is adjusted from the advanced, physics-oriented preconditioning technique published in our previous work. In the numerical examples, we investigate three different geometries with up to about 1.3 million degrees of freedom and thereby prove that our approach is applicable to geometrically large and complex scenarios. Moreover, we show that our approach consistently introduces the mass and charge conservation on deformed meshes. Furthermore, the numerical examples demonstrate the high relevance to incorporate current collectors into the ASSB cell simulations. Finally, we show that solid mechanics and the coupling effects have indeed a large impact on the ASSB cell performance and their incorporation is therefore vital for precise results and predictions.

An arbitrary Lagrangian–Eulerian formulation for the Reynolds equation considering the JFO boundary condition

AbstractIn the realm of lubrication theory, the hydrodynamics of the fluid lubricant are commonly elucidated through the Reynolds equation. Its establishment stems from using the Eulerian description method, restricting the fluid domain to a fixed spatial configuration. However, certain scenarios necessitate coupling the Reynolds equation with solid deformation, wherein the fluid boundary undergoes alterations concurrent with the displacement or deformation of the solid. In such cases, the employment of a movable fluid domain becomes imperative. To address this requirement, this contribution introduces the arbitrary Lagrangian–Eulerian method, which effectively transforms the reference system of the Reynolds equation into a fluid domain amenable to arbitrary movement. Subsequently, the weak formulation associated with the movable fluid domain is derived and synergistically combined with a preexisting cavitation formulation. This integration facilitates an efficient solution of the Reynolds equation utilizing the finite element method while duly accounting for the mass‐conserving cavitation effects. Ultimately, a transient hydrodynamic lubrication example is presented to demonstrate the feasibility of the newly developed formulations.

Addressing geometric and material nonlinearities in fluid-structure interaction with the ALE-SSM framework

A novel methodology was introduced for integrating skeleton-based structural models (SSMs) with an Arbitrary Lagrangian-Eulerian (ALE) formulation to perform fluid–structure interaction (FSI) simulations (i.e., ALE-SSM). In ALE-SSM, the structural domain consists of force-based line elements, which are favored in modeling solid structures because of their computational efficiency. This paper enhances ALE-SSM to account for geometrically nonlinear and inelastic material responses of the structural domain. Geometric nonlinearity is introduced in two stages: (1) at the basic coordinate system of the force-based elements, where second-order effects stemming from the transverse element deformations are accounted for in the element flexibility matrix; and (2) at the global coordinate system, where a corotational formulation is used to perform the geometric transformation from the basic to the global coordinate system. The proposed approach for modeling geometric nonlinearity in ALE-SSM is evaluated with benchmark problems involving large deformations of beam structures positioned parallel and perpendicular to one-phase flows. Next, ALE-SSM is employed to define a new benchmark study that evaluates the effects of geometric and material nonlinearities in FSI simulations with force-based elements.

A 3D frequency domain finite element formulation for solving the wave equation in the presence of rotating obstacles

A frequency domain numerical method aimed at solving the propagation of sound waves in a three-dimensional domain enclosing rotating obstacles is presented. It relies on a domain decomposition whereby rotating parts are all embedded in a cylindrically-shaped domain. Following the classical Arbitrary Lagrangian Eulerian formalism, the governing equation, which is written in the local rotating frame, takes the form of a convected wave equation. The transmission conditions at the interface between the fixed and rotating domains is accomplished via the Frequency Scattering Boundary Conditions which, after classical FEM discretization, give rise to a series of coupled problems associated with a discrete set of frequencies. The performances of the method are demonstrated through several test cases involving rotating sources and/or obstacles inserted in circular and rectangular ducts.

Finite Element Modeling and Verification of the Plunge Stage in Friction Stir Welding

In the present work, a finite element model of the first stage, plunge, of friction stir welding is considered. The welded parts are flat aluminum 1050 plates. The arbitrary Lagrangian-Eulerian formulation implemented in ABAQUS/Explicit is used. The material model of the welded parts is the Johnson-Cook law, and Coulomb’s law describes the friction between the tool and the weldment. Temperature field during the process is obtained, and the influence of the parameters concerning the algorithmic implementation of the finite element method is established. The simulation results are compared with experimental results obtained for this purpose.

From the material behaviour to the thermo-mechanical long-term response of asphalt pavements and the alteration of surface drainage due to rutting: a sensitivity study

ABSTRACT In this contribution, a simulation chain for the thermo-mechanical and hydromechanical analysis (surface drainage) of a pavement structure during its whole service life is applied to a typical asphalt pavement (Bk100) used for motorways in Germany. Transient load signals for each tyre position of a truck-trailer combination (vehicle) are generated from a multibody analysis of the vehicle driving on a motorway with rough pavement surface. Material model parameters are derived from experimental identification tests of asphalt materials. The model parameters are used together with a continuum-mechanical description of the asphalt material representing the thermo-mechanical material behaviour at the material scale. The material response of the pavement layers is integrated on the structural scale by using the finite element method (FEM) in combination with an arbitrary Lagrangian-Eulerian (ALE) formulation and equivalent tyre loads of a representative, finite element (FE) discretised truck tyre rolling on an FE discretised pavement section. Different scenarios of rut formation are computed by varying different influence factors (climate temperature, vertical tyre force, type of asphalt material of the surface layers etc.). During the subsequent hydromechanical analysis of the pavement, the simulated deformed geometry of the pavement surface is used to numerically compute surface drainage characteristics.

A 2D elastic wall model to analyze the hyper‐viscous effects on blood flow across abdominal aortic aneurysm in COVID patients by fluid–structure interaction technique with ALE formulation

The worldwide dissemination of the coronavirus, as well as its dependencies, is being aided by detrimental urbanization. The impact of the viral infection upon an infected person is also thought to be influenced by any pre‐existing medical issues. Recent investigations have demonstrated that COVID‐19 patients have a higher degree of blood viscosity as a result of alterations in morphology in blood cells. Examining the importance of hyper‐viscosity in patients with COVID is crucial in determining the diseases of the arteries since viscosity is a key flow characteristic that affects the flow across a stenosis as well as an aneurysm. In the current study, a patient‐specific instance with an aneurysm across the abdominal aortal walls was taken into consideration. Given that abdominal aneurysms occur frequently in people, the high viscosity values are taken into account while examining the hyper‐viscous impact of fluid on its passage through the affected aorta. The current study is the initial endeavor to use the Arbitrary Lagrangian–Eulerian (ALE) Technique to study the impact of fluid–structure interaction (FSI) on the movement of fluid across an aneurysmal aortal section in conjunction with hyper‐viscous anomalous blood characteristics. The investigation backs up the different medical results that described the negative consequences of blood hyper‐viscosity. The computational findings from employing a finite element method (FEM) solver to resolve the fluid mechanical computations complemented alongside the solid mechanical principles indicate a possibility that the increased stress imposed by the hyper‐viscous propagates on the interior walls of the aneurysmal aorta may prompt the aneurysmal pouch to grow or breakdown. Also, the hyper‐viscous blood in COVID patients destroys the smooth muscle cells of the media layer endangering its normal structure and functions and leading to the development of new aneurysms.

A dynamic ALE formulation for structures under moving loads

This work describes the implementation of a novel dynamic Arbitrary LagrangianEulerian (ALE) formulation for the simulation of pavement structures loaded by rolling tires in a finite element framework. The proposed formulation enables the simulation of dynamic effects like acceleration, deceleration and variation of the wheel load on the pavement. The ALE scheme is described for a hyperelastic St. Venant-Kirchhoff material capable of finite deformations. With the adoption of this dynamic ALE formulation, a significant improvement in terms of speed and efficiency of the simulation is achieved in comparison to a classical transient Lagrangian formulation. This is primarily because only the relevant portion of the mesh around the applied load needs to be discretized and simulated. Another benefit is that a cumbersome moving load formulation does not need to be implemented. The results show satisfactory agreement with a conventional Lagrangian simulation with a moving load.

A computational framework for crack propagation along contact interfaces and surfaces under load

We present the first implicit computational framework for simulating crack propagation along contact interfaces and surfaces under load in three-dimensional bodies, which is distinct from modelling the contact interaction associated with crack closure. We restrict ourselves to brittle fracture and frictionless contact and focus on numerical challenges associated with the coupling of unilateral constraints emerging from the Griffith’s criterion and the contact conditions. The formulation is based on the configurational mechanics framework and is solved using the finite element method. The approach utilises a monolithic Arbitrary Lagrangian–Eulerian formulation permitting simultaneous resolution of crack propagation and unilateral contact constraints. Contact is embedded in the model using the well-known mortar contact formulation. Evolving cracks are explicitly modelled as displacement discontinuities within the mesh. Heterogeneous approximation of arbitrary order is used to discretise spatial displacements, enabling hp-adaptive refinement around the crack front and the contact interfaces traversed by the crack. The result is a holistic approach which handles issues associated with thermodynamic consistency, numerical accuracy and robustness of the computational scheme. Several numerical examples are presented to verify the model formulation and implementation; they also highlight how contact pressure and load applied on surfaces traversed by cracks influence their propagation. The robustness of the approach is validated by comparison of our simulations with existing numerical results and an industrial experiment involving cracks of complex morphologies propagating along contact interfaces between multiple deformable bodies.

Transport phenomena and dynamics of an evaporating water meniscus at low heat fluxes

It is known that evaporation efficiency of novel solar thermal vapor generation/desalination systems can potentially increase by incorporating interfacial heat localization techniques utilizing porous wicks. The ensuing efficiency is a strong function of the geometric and thermal properties of the wicks and the ambient operating parameters. We investigate the role of these critical process parameters on the evaporation dynamics of pure and saline water from a single-layered wire mesh operating at low heat fluxes (1 kW/m2, 5 kW/m2and 10 kW/m2), which are typical for devices working on solar energy. Evaporation rates of water from stainless steel and nylon meshes are determined using non-invasive infra-red thermography and digital microscopy. A finite element based computational model is developed to understand local transient evaporation phenomenon at the microscale. Arbitrary Lagrangian-Eulerian (ALE) formulation is used to solve the coupled transport equations on a deforming computational grid, incorporating the Fick's law of diffusion at the evaporating water-air interface. With increasing heat fluxes, there is a deviation from purely diffusion-based transport. Higher evaporation rates are observed in meshes with smaller wire diameter and higher thermal diffusivity. In addition, the decisive role of local thin capillary films is exemplified. Simulations also indicate the diminutive role of thermocapillary convection during evaporation at such low input heat fluxes. Finally, we also investigate the effect of mesh size on the nature of salt crystallization. The evolution of salt concentration gradient at the microscale is computed that complements the experimental observations. Optimal exploitation of heat localization technique for enhanced evaporation necessitates understanding of microscale mesh level local transport effects.

On the computation of compressible multiphase flows with heat and mass transfer in elastic pipelines

The present work is motivated by the engineering need to simulate the multiphase flows in the course of the start-up of a long-distance crude oil pipeline. We propose a model for compressible multiphase flows with heat and mass transfer and diffusion processes in elastic pipelines. The model is derived with two approaches, i.e., (a) the spatial averaging procedure of a single phase model and (b) the Arbitrary Lagrangian Eulerian (ALE) formulation of the Baer-Nunziato model with quasi-1D approximation. The diffusion processes include the viscous dissipation, wall friction, heat conduction, and heat exchange with external environment. In particular, the wall friction consists of steady friction term calculated by Darcy-Weisbach formula, and the unsteady friction determined by the instantaneous-acceleration-based (IAB) model. The unsteady friction modifies the characteristic structure of the hyperbolic part of the model. For the solution of the hyperbolic part, we propose a three-wave approximate Riemann solver incorporating the unsteady friction term. Mass and heat transfer are realized via instantaneous relaxations of the chemical potential and temperature, respectively. Efficient iterative relaxation procedures for N-phase flows have been proposed. We have validated the proposed model and numerical methods against some benchmark multiphase problems and applied the model to calculate the start-up of a realistic liquid pipeline with intermediate pump station boundary condition.

Configurational forces and ALE formulation for geometrically exact, sliding shells in non-material domains

The paper presents a novel Arbitrary Lagrangian–Eulerian formulation for dynamic problems of geometrically exact, sliding shells. In contrast to previous researches where the sliding motions are prescribed at sliding boundaries and the existence of configurational forces is not identified, the configurational momentum equation that governs the evolution of sliding motions is derived in a consistent variational framework in the present paper. To this end, the time-varying material domain due to the presence of sliding motion is mapped onto a time-invariant mesh domain, variations at fixed material and at fixed mesh coordinates are introduced, and their relationship with variation of material coordinates at fixed mesh coordinates are derived. Hamilton’s principle of variation of action is employed to derive the strong form of mechanical and configurational momentum equations together with natural boundary conditions at the sliding boundaries. In the finite element formulation, transfinite interpolation is employed to relate material coordinates of nodes inside the domain to the values at the sliding boundaries. The discrete form of Hamilton’s variational principle leads to discrete governing equations of the proposed ALE formulation. The generalized-α scheme is adjusted to integration the resulting mechanical and configurational momentum equations. Numerical examples are presented to validate correctness and efficiency of the proposed formulation.

Numerical simulation of wind-structure-soil interaction effects on the CAARC tall building model using hybrid CUDA-OpenMP parallelization

In the present work, the dynamic effects of the wind action over the Commonwealth Advisory Aeronautical Council (CAARC) tall building model are numerically evaluated considering the influence of soil-foundation interaction. A numerical model is developed considering a partitioned coupling scheme for fluid-structure-soil interaction, in which the fluid, structure and soil subsystems are solved sequentially using independent algorithms. The Finite Element Method (FEM) is adopted for spatial discretization, where linear hexahedral elements with underintegration techniques are used. The fundamental flow equations are kinematically described using an arbitrary lagrangian-eulerian (ALE) formulation and numerically solved using the explicit two-step Taylor-Galerkin scheme, while Large Scale Simulation (LES) is employed for the treatment of turbulent flows. Structure and soil are considered as deformable elastoplastic media, using a corotational approach to deal with physical and geometric nonlinearities. Dynamic equilibrium equation is solved using the generalized-α method and infinite elements are utilized in the soil domain to avoid elastic wave reflections. Load transfer between soil and structure is performed using a three-dimensional contact algorithm based on the penalty method that allows separation and sliding along soil-structure interfaces. A hybrid parallelization strategy based on CUDA-OpenMP techniques is proposed to accelerate the processing time associated with the present simulations. Numerical results obtained here are compared with numerical and experimental results reported by other authors, where one can observe that soil-structure interaction may significantly influence the building response due to wind loading and effects of aeroelastic instability may be considerably reduced in the presence of soil support.