Lagrangian-Eulerian Finite Element Research Articles

Ground response during of EPB shield shutdown in gravel ground based on coupled CEL-FEM analysis

The shutdown of earth pressure balance (EPB) shield tunneling in gravel stratum can easily lead to significant unexpected ground deformation. In order to study the response of gravel strata during shield shutdown and the characteristic change of soil state in the chamber, this paper establishes a coupled Eulerian-Lagrangian finite element method (CEL-FEM) coupling analysis model that reflects the interaction between the spoiled soil and gravel strata. The plastic flow parameters of CEL spoiled soil are calibrated using the slump method, and a quantitative relationship between the slump value, plastic flow parameters, equivalent coefficient of loosening, and excavation face support pressure is established. The reliability and applicability of CEL method in the simulation of shield shutdown are verified by the field measurements. Results show that: (1) The chamber’s soil equivalent loose coefficient is inversely proportional to the soil slump value which is related to soil’s plastic flow parameters. (2) The shield shutdown in gravel strata has a more significant impact on the deep strata displacement than on the surface. (3) During the shield shutdown stage, the chamber pressure should be dynamically adjusted based on the soil deformation characteristics, and an increase of 16% could result in a stable rebalance.

Data-driven parameter identification of an equivalent mechanical model for large amplitude liquid sloshing

The accurate extraction of model parameters is vital to ensure that the equivalent mechanical model can precisely describe the dynamic behavior of large amplitude liquid sloshing. In this paper, the parameters of the moving pulsating ball model (MPBM), which is an equivalent mechanical model used to represent the large amplitude liquid sloshing, are extracted using a combination of computational fluid dynamics (CFD), experimental data, and data-driven algorithms. The arbitrary Lagrangian-Eulerian finite element method (ALE-FEM) is adopted to simulate three-dimension large amplitude liquid sloshing in the tank with high precision. The calculated results from the presented algorithm are compared with the experimental data to verify the reliability and validity. The typical parameters required by the MPBM mainly include equivalent sloshing mass, equivalent ball radius, and damping coefficient. These parameters are extracted by using a data-driven parameter optimization algorithm, which is based on the numerical calculation results of ALE-FEM. The accuracy of the MPBM with the equivalent model parameters extracted by using data-driven parameter optimization algorithm is investigated under two types of excitations: harmonic excitation and step excitation. The results show that the MPBM with equivalent model parameters extracted by a data-driven parameter optimization algorithm can precisely imitate the large amplitude liquid sloshing behavior and the method presented can provide significant reference for the overall design of spacecraft dynamics system.

Arbitrary Lagrangian-Eulerian finite element method for liquid sloshing with contact angle hysteresis in microgravity

Liquid sloshing in microgravity environment remains a focus of attention in space engineering. In this paper, an arbitrary Lagrangian-Eulerian finite element method is proposed to simulate the liquid sloshing dynamics with contact angle hysteresis, in which an infinitely small contact free-surface mesh method is used to implement the contact angle boundary condition. The contact angle hysteresis is accounted for by the relation between the contact angle and the advancing contact angle or the receding contact angle. This method not only guarantees the conformity between the numerical treatment and the actual liquid sloshing behavior, but also improves the accuracy of the numerical method. The numerical results of the free surface configurations, including the height of the contact line along the tank wall and the height of the free surface along the centerline, which are obtained by simulating the partially wetted liquid reorientation show good agreements with the correspongding experimental results. Then, the liquid sloshing in a spherical tank under microgravity is simulated, and the influences of the contact angle hysteresis on the free surface evolution are analyzed. The results show that it is of great significance to consider the contact angle hysteresis in microgravity environment.

An immersed multi-material arbitrary Lagrangian–Eulerian finite element method for fluid–structure-interaction problems

Fluid–structure-interaction (FSI) phenomena are widely concerned in engineering practice and challenge current numerical methods. In this article, the finite element method is strongly coupled with the multi-material arbitrary Lagrangian–Eulerian (MMALE) method to develop a monolithic FSI method named the immersed multi-material arbitrary Lagrangian–Eulerian finite element method (IALEFEM). By immersing the finite elements in the MMALE computational grid, the fluid–solid interface is directly tracked by the element boundary with accurate normal directions. The fluid–structure-interaction is implicitly implemented by assembling the nodal variables and updating the Lagrangian momentum equation on the MMALE grid. Combining the advantages of both MMALE and FEM with the immersed boundary method, the IALEFEM is effective for solving complicated FSI problems with multi-material fluid flow. A slip fluid–structure-interaction method is also proposed to enhance the computational accuracy in simulating FSI problems with significantly different velocity fields. The accuracy and effectiveness of the IALEFEM are verified and validated by several benchmark numerical examples including the shock-cylinder obstacle interaction, flexible panel deformation induced by shock wave, dam break problem with large structural deformation, water entry of a wedge, fragmentation of a cylinder shell induced by blast, response of elastic plate subjected to spherical near-field explosion and structural damage of open-frame building under blast loading.

A method for estimating coefficient of lateral earth pressure based on cone penetration tests

The coefficient of lateral earth pressure at rest (K0) is a key state soil variable for the design of foundations and underground structures, characterizes in-situ stress state and soil condition. In this study, a method for the in-situ estimation of K0 using the cone penetration test (CPT) is proposed considering vertical and inclined cone resistances (qc). For this purpose, a series of laboratory CPTs in a soil chamber were conducted to obtain and characterize vertical and inclined qc values at various inclination angles (θ) and relative densities (DR). It was observed that the values of qc increased as θ increased, which was more pronounced at higher DR. Coupled Eulerian-Lagrangian (CEL) finite element analyses were performed to quantify the values of inclined qc at various cone penetration and soil conditions. Based on results from laboratory CPTs and CEL analyses, a CPT-based K0 correlation model was established, which was given as a function of vertical and inclined qc values. The model parameter for the proposed method was evaluated and quantified. The validity of the proposed method was confirmed from the comparison with case examples.

Spatial energy evolution of focused waves generated in numerical wave tank

This paper numerically investigates the energy evolution of the focused wave and its correlation with input parameters for the wave generation. The focused wave is numerically generated based on the fully nonlinear potential wave theory which is solved by the Quasi Arbitrary Lagrangian Eulerian-Finite Element Method. The investigation is performed by dividing the generated wave energy into three categories according to their frequency intervals, i.e., the initially assigned frequency interval [f1fN], the frequencies lower (f < f1) and higher (f > fN) than the initial interval. The amount of the generated energy falling into three energy categories and the energy distribution in the initial frequency interval are analysed against amplitude parameters and frequency bands under three amplitude spectra. Four indicators are proposed to indicate the actual energy variations comparing to the initial design. It is found that for all the three frequency intervals the energies increase when the amplitude parameters increases or the given frequency shifts towards the lower frequency domain. The choice of wave amplitude spectrum plays a significant role to maintain the distribution of the energy in the design frequency range and to minimise the energies out of the design frequency range. The results from the second-order wave group theory are used to assist analyses of the mechanism of the energy evolution alongside the focused wave generation. It is found that the lower-frequency energy in the vicinity of the focusing point is dominated by the second-order difference waves, whereas the higher-frequency energy is mainly produced by the wave flap. The waves which are higher than the second-order and the complex interactions not considered by the second-order wave theory are found significantly disturbing the energy distribution in the originally assigned wave-frequency interval.

Determination of pullout capacity for an inclined single-plate helical pile under combined loading in clay

Although helical piles are frequently installed at an angle to the vertical, there has been limited investigation into how this inclination affects the pile’s ability to resist pullout forces. This paper utilizes numerical analysis to examine the pullout capacities and failure envelopes of inclined helical piles under combined loading. Through the application of the coupled Eulerian-Lagrangian finite element analysis, the impact of load inclination and azimuth angle of the pullout plane on the ultimate holding capacity of inclined helical piles was assessed. It was found that the pullout plane that is in the opposite direction to the helical pile inclination is the most crucial. The parametric study showed that the crucial failure envelope is primarily influenced by the helical pile inclination angle, embedment depth ratio, helix diameter ratio, and normalized soil strength ratio. Several tables were provided, which contain fitting constants suitable for a range of helical pile inclination angles, embedment depth, helix diameter ratio, and normalized soil strength ratios. Based on these results, a straightforward design procedure was established to evaluate the holding capacity of an inclined installed helical pile. The research results are expected to assist engineers in accounting for helical pile inclination during the design phase.

Arbitrary Lagrangian-Eulerian finite element approximations for axisymmetric two-phase flow

We analyze numerical approximations for axisymmetric two-phase flow in the arbitrary Lagrangian-Eulerian (ALE) framework. We consider a parametric formulation for the evolving fluid interface in terms of a one-dimensional generating curve. For the two-phase Navier-Stokes equations, we introduce both conservative and nonconservative ALE weak formulations in the 2d meridian half-plane. Piecewise linear parametric elements are employed for discretizing the moving interface, which is then coupled to a moving finite element approximation of the bulk equations. This leads to a variety of ALE methods, which enjoy either an equidistribution property or unconditional stability. Furthermore, we adapt these introduced methods with the help of suitable time-weighted discrete normals, so that the volume of the two phases is exactly preserved on the discrete level. Numerical results for rising bubbles and oscillating droplets are presented to show the efficiency and accuracy of these introduced methods.

An enhanced stress resultant plasticity model for shell structures with application in sheet metal roll forming

AbstractThe proposed Kirchhoff-Love shell stress resultant plasticity model extends a previously reported model for plates by complementing the constitutive law of elastoplasticity with membrane effects. This enhanced model is designed for bending dominant settings with small to moderate membrane forces. It is thus implemented in a purpose-built nonlinear mixed Eulerian–Lagrangian finite element scheme for the simulation of sheet metal roll forming. Numerical experiments by imposing artificial strain histories on a through-the-thickness element are conducted to test the model against previously reported stress resultant plasticity models and to validate it against the traditional continuum plasticity approach that features an integration of relations of elastoplasticity in a set of grid points distributed over the thickness. Results of actual roll forming simulations demonstrate the practicality in comparison to the computationally more expensive continuum plasticity approach.

Numerical simulations of the dynamics of a deformable particle in a viscoelastic liquid subjected to Poiseuille flow in a cylindrical microcapillary at non-negligible inertia

The manipulation and control of particles in microfluidic devices through non-intrusive methods is pivotal in many application fields, e.g., cell focusing and sorting. Inertial microfluidics is rapidly gaining attention in the scientific community because of the considerable advantages in terms of throughput. In addition to inertia, other factors can trigger the cross-stream migration of particles in liquids undergoing pressure-driven channel flows, such as the deformability of the particles themselves and/or the viscoelasticity of the carrier fluid. For this reason, the dynamics of an initially spherical elastic particle suspended in a viscoelastic liquid subjected to pressure-driven flow in a cylindrical channel at non-negligible inertia is studied through three-dimensional arbitrary Lagrangian–Eulerian finite-element numerical simulations. The mechanical behavior of the particle is described through the neo-Hookean hyper-elastic constitutive equation, whereas the rheological behavior of the carrier liquid is described through the Giesekus model. The Reynolds number Re, measuring the relative importance of inertial and viscous forces in the tube, the elastic capillary number Cae, measuring the relative importance of liquid viscous stress and solid elastic stress, and the Deborah number De, measuring the ratio of the liquid relaxation time and the flow characteristic time, are varied. The particle migrates transversally to the flow direction until reaching a radial equilibrium position depending on Re, Cae, and De. Different dynamics are observed depending on the interplay among inertia and elasticity of both the liquid and the solid phase: one, two, or even three stable equilibrium positions can be found along the tube radius.

Application of the Constrained Formulation to the Nonlinear Sloshing Problem Based on the Arbitrary Lagrangian–Eulerian Method

Abstract This study deals with an application of constrained formulation to a nonlinear sloshing problem based on the arbitrary Lagrangian–Eulerian finite element method (ALE). The ALE method incorporates a discretized form of equations of motion with mesh updating algorithms in order to prevent a problem of mesh distortion. This paper focuses on an analytical aspect of such treatments as constrained systems in the formulation of the ALE method. Since the mesh updating algorithms give algebraic relations for nodal coordinates, this study treats these relations as constraints. Then, we introduce formulation for constrained systems based on the method of Lagrange multipliers. As a result of this formulation, equations of motion are given by differential algebraic equations (DAEs) consisting of differential equations for time evolution of physical quantities and algebraic equations (constraints). The present method can be classified into a kind of augmented formulation. Moreover, we present a size-reduction technique used in the Newton–Raphson method in order to remove a part of the redundant degrees-of-freedom in the iterative procedures, because the resulting set of DAEs involves a larger number of unknowns than the minimal number of degrees-of-freedom due to the introduction of the constrained formulation. The derived reduced system still holds the physically essential part of equations of motion for the sloshing problem. Even though it is not reduced to the minimal degrees-of-freedom, it does not involve algebraically complicated and inefficient procedures in computation. In addition, this study presents a method to introduce damping effects defined in the modal space into the FEM models. The proposed approach is validated by comparisons with experimental data in the time domain analysis.

Finite Deformation of Scleral Tissue under Electrical Stimulation: An Arbitrary Lagrangian-Eulerian Finite Element Method.

The sclera is considered as the principal load-bearing tissue within the eye. The sclera is negatively charged; thus, it exhibits mechanical response to electrical stimulation. We recently demonstrated the electroactive behavior of sclera by performing experimental measurements that captured the deformation of the tip of scleral strips subjected to electric voltage. We also numerically analyzed the electromechanical response of the tissue using a chemo-electro-mechanical model. In the pre-sent study, we extended our previous work by experimentally characterizing the deformation profile of scleral strips along their length under electrical stimulation. In addition, we improved our previous mathematical model such that it could numerically capture the large deformation of samples. For this purpose, we considered the transient variability of the fixed charge density and the coupling between mechanical and chemo-electrical phenomena. These improvements in-creased the accuracy of the computational model, resulting in a better numerical representation of experimentally measured bending angles.

Bending moment response of batter piles in clay under spudcan-pile interaction

The bending moment response of straight pile foundations, as the dominant factor of spudcan-pile interaction, has received focused attention in the close joint operation between jacket platforms and jack-up drilling rigs. As the foundation for the same widely used in jacket platforms, the research on the batter pile is still a knowledge gap in this field. This paper presents a numerical study of the bending moment response of batter piles at different inclination angles and azimuthal angles during spudcan installation. Using a coupled Eulerian-Lagrangian finite element method, the effects of flexural rigidity, stiffness ratio, spudcan-pile clearance distance, and pile length on the pile head bending moment were sequentially evaluated. It was found that the pile bending moment response is related to the change in soil flow mechanism caused by spudcan penetration and becomes more significant with the increase of inclination angle; under the same inclination angle, the bending moment response is the most dangerous when the azimuthal angle is 0°. Based on the parameter study, a simple method is proposed to estimate the pile head bending moment during spudcan installation. The outcome may facilitate incorporating pile spatial inclination into spudcan-pile interaction research and contribute to related safety design.

Investigation of the peak punch-through capacity of spudcan on sand overlying spatially variable clay

Accurately estimating peak penetration resistance in punch-through sensitive deposits is crucial for managing risks during jack-up rig installations. While offshore clays exhibit significant spatial variability, necessitating consideration of spatial variability in predicting peak penetration resistance. This study investigates the effects of spatial variability of underlying clay on the failure mechanism and magnitude of peak penetration resistance during punch-through incidents. The Modified Linear Estimation Method was used to generate three-dimensional random fields, incorporated into coupled Eulerian Lagrangian finite element analyses to simulate spudcan penetration from the ground surface. Results show that while spatial variability has an insignificant effect on the failure mechanism in the upper sand layer, it significantly alters soil flow in the underlying clay, leading to variations in peak penetration resistance. The peak penetration resistance follows a log-normal distribution, and a relationship was established between the probability of failure and the factor of safety. This study highlights the importance of considering soil spatial variability and demonstrates the significant impact of underlying clay on the failure mechanism and magnitude of peak penetration resistance during punch-through incidents, which might be helpful for the safety management of industry.

Estimation of spudcan penetration in variable sand deposits with the Arbitrary Lagrangian Eulerian Finite Element Method

Offshore jack-up rigs are most commonly founded on large-diameter conical “spudcan” foundations, which are frequently designed using traditional analytical methods for shallow footings. This paper presents the design of a spudcan installed off the coast of Tunisia. The maximum penetration depth of the footing under the available preload is predicted by a combination of analytical techniques, 2-dimensional axisymmetric modelling and 3-dimensional Finite Element Methods (FEM) using large strain arbitrary Lagrangian-Eulerian (ALE) techniques. Spudcan penetration based on FEM simulation of CPT soil profiles forms the basis of a comparison with results from the Society of Naval Architects and Marine Engineers (SNAME) guidelines. Particular attention is given to model calibration using the limited site investigation data available. Results are presented for the effect of penetrating footings on the behaviour of neighbouring footings, showing good agreement with conventional prediction methods.

Analysis of the drag anchor behaviour at shallow depths

Understanding the effects of shallow behaviour is necessary for accurate kinematic predictions of drag anchors since original methods are mostly based only on deep failure mechanisms. Therefore, shallow flow channel-soil interactions characterized by varying tangential and normal bearing factors are used in plasticity analysis (PA) to capture the distinct shallow behaviour of the anchor. To provide a comparison, using the coupled Eulerian-Lagrangian (CEL) finite element method combined with the VUAMP subroutine to incorporate the mooring chain effect, the embedment of the drag anchor under the tension of the mooring chain is simulated. With a constant soil strength profile, the CEL results on the variation of drag force, rotation angle, and anchor trajectory agree well with calculations of PA that are mature for deeply embedded anchors. However, for shallow depths, similar results to the CEL can only be gained from PA considering shallow fluke-soil interactions. The effects of soil strength flow during installation, soil stability, soil sensitivity and fluke width are also investigated.

Effects of welding physical fields on the microstructure evolution during dynamic-stationary shoulder friction stir welding

Studying the physical fields in the friction stir welding (FSW) can reveal how they impact the microstructure of the joint, allowing one to develop more reliable joints. In this study, the Al–Cu dynamic-stationary shoulder friction stir welding (DSSFSW) was simulated using a three dimensional (3D) coupled Eulerian-Lagrangian finite element model to elucidate weld physical characteristics. The results revealed that the materials were mainly deposited in the areas between the weld centerline and the RS in DSSFSW. Compared with the bottom of the joint, the material flow velocity and range at the top region were higher, which leads to greater strain. The high strain prevented the growth of IMCs at the interface, therefore, the tensile strengths of the top and middle regions of the joint were significantly higher than those of the bottom. The above results verified the accuracy of the simulation.

Comparative modeling of the mitral valve in normal and prolapse conditions.

Computational modeling is one of the best non-invasive approaches to predicting the functional behavior of the mitral valve (MV) in health and disease. Mitral valve prolapse (MVP) due to partial or complete chordae tendineae rapture is the most common valvular disease and results in mitral regurgitation (MR). In this study, Image-based fluid-structure interaction (FSI) models of the human MV are developed in the normal physiological and posterior leaflet prolapse conditions. Detailed geometry of the healthy human MV is derived from Computed Tomography imaging data. To provide prolapse condition, some chords attached to the posterior leaflet are removed from the healthy valve. Both normal and prolapsed valves are embedded separately in a straight tubular blood volume and simulated under physiological systolic pressure loads. The Arbitrary Lagrangian-Eulerian finite element method is used to accommodate the deforming intersection boundaries of the blood and MV. The stress values in the mitral components, and also flow patterns including the regurgitant flow rates are obtained and compared in both conditions through the simulation. These simulations have the potential to improve the treatment of patients with MVP, and also help surgeons to have more realistic insight into the dynamics of the MV in health and prolapse. In the prolapse model, computational results show incomplete leaflet coaptation, higher MR severity, and also a significant increment of posterior leaflet stress compared to the normal valve. Moreover, it is found more deviation of the regurgitant jet towards the left atrium wall due to the posterior leaflet prolapse.

Coupled Eulerian-Lagrangian Debris Flow Model with Flexible Barrier

Natural hazards such as large debris flow events can have catastrophic effects on the environment and critical infrastructure, posing a significant threat to human life. Debris flows often exhibit high velocity, high-pressure discharges due to their bulk volume, and the capacity to transport considerable volumes of large rocks, boulders, and woody debris. Although debris flow run-out simulations are commonly performed using hydraulic modelling software, these environments are seldom capable of assessing the interaction between the debris fluid, transported material, and protective structures. In this research, large deformation numerical models are calibrated using input parameters from hydraulic modelling software. Due to the computational cost of the large deformation models involving fluid-solid-structure simulation with flexible net barriers, an equivalent stiffness method is implemented to provide comparable performance through a membrane structure. The Coupled Eulerian-Lagrangian Finite Element method is used to model the impact forces of rocky boulders on the membrane, exhibiting damage characteristics consistent with flexible ring-net protective structures. The Coupled Eulerian-Lagrangian model results highlight the performance of the simplified membrane, as shown through a benchmark simulation of debris flow with boulders.

Coupled Eulerian-Lagrangian finite element analysis of penetration processes in silty clay for bucket foundation

ABSTRACT Bucket foundations, as an innovative type of offshore wind turbine foundation, have been widely adopted for their cost competitiveness and time effectiveness in construction and installation. For a successful installation, the penetration process prediction is crucial. This paper investigates the penetration process of both thin-walled and thick-walled bucket foundations in silty clay through small-scale experiments. Based on the experimental results, empirical formulas of penetration resistance are modified. Next, a Coupled Eulerian-Lagrangian (CEL) numerical method is validated and used to simulate the sinking process of engineering prototypes. The penetration resistance obtained by the calculated and numerical methods is in good agreement. Additionally, through the 3D CEL analysis, the disturbance of bulkheads and skirts on soil plugs is gained. The Eulerian volume fraction shows that the soil surface within the outer compartments is prone to rise to form a soil plug, which will bring out a sudden sharp increase in the penetration resistance due to the contact of lid and soil, and consequently affect the ultimate installation depth.