Arbitrary Lagrangian Eulerian Research Articles

On a nonlinear diffussive model for the evolution of cells within a moving domain

We investigate the dynamics of a nonlinear model describing the motion of cells under the effect of porous-medium diffusion and transport and in the presence of nutrient and drug application. The momentum equation for the evolution of the velocity field is governed by Darcy’s law, while the evolution of the chemical attractant (nutrient or drug) is governed by a diffusion equation. The system evolves within a moving domain in R 3 \mathbb {R}^3 accounting for the expansion or shrinkage of the tumor. The global existence of weak solutions is established with the aid of a regularized approximating scheme and an Arbitrary Lagrangian-Eulerian (ALE) mapping for the motion of the tumor. This work provides a variational framework suitable for both analysis and simulations.

Underwater implosion protection of a new concept composite structure for a deep-sea hollow ceramic sphere with CFRP shield

Carbon fiber–reinforced polymers (CFRP) and ceramics are lightweight, non-metallic materials with broad applications. However, their use in deep-sea engineering is limited owing to the potential risk of catastrophic implosions. This study introduces the concept of deep-sea ceramic-pressure-resistant hollow structures with CFRP shields for achieving a balance between safety and light weight. This research examines typical engineering cases, including the HROV Nereus and Titan accidents, and uses the Arbitrary Lagrangian–Eulerian method to investigate the fluid–structure interactions. First, the feasibility of the numerical method was verified, with the responses of the structure and flow field summarized. The advantages of ceramic hollow spheres with a CFRP shield were analyzed, leading to the development of a new implosion protection scheme with a composite structure. Furthermore, this study discusses the effects of the CFRP thickness, CFRP ratio, and trigger mode on implosion protection, with the results revealing that increasing the thickness and proportion of the CFRP shield considerably enhances the implosion suppression effect of the entire structure. These findings are valuable for designing pressure-resistant structures for practical engineering applications.

Lateral loading response of monopiles in sand considering installation effect

The effect of pile installation is a critical issue in the analysis and design of pile foundations but it is commonly ignored due to various numerical difficulties. In this paper, the installation process of an open-ended pipe pile into a sand deposit is simulated by using the zipper technique combined with the Arbitrary Lagrangian-Eulerian (ALE) method in the framework of three-dimensional (3D) finite element modeling. The subsequent lateral load response of the pile is also simulated and compared with that without consideration of the pile installation. The state dependent behavior of sand in associated with the pile installation and the subsequent lateral load is described using an advanced constitutive model. The study shows that for a relatively loose sand deposit, the sand surrounding the pile exhibits contraction and the disturbance zone takes the form of a trapezoid, whereas for a dense sand deposit, the sand near the pile will dilate and the disturbance zone takes the form of an inversed trapezoid. Furthermore, the deformation mode of the surrounding sand under the lateral load differs to some extent from that without consideration of the installation effect. Particularly, the location of the rotation point for the laterally loaded pile tends to move downwards when the pile installation process is considered.

Test and numerical analysis for water entry of elastic cabin from amphibious aircraft

Water-entry performance of amphibious aircraft is one of the main factors affecting the structural design. However, it is analyzed by rigid models in general, which is difficult to reflect the elastic characteristics of the structure. And it is difficult to obtain sufficient guidance for structural design from rigid-body analysis. In this study, water-entry model of an elastic cabin from amphibious aircraft was developed using the Arbitrary Lagrangian-Eulerian (ALE) method and validated by a designed 1:1 cabin water-entry test. Analysis under various conditions revealed the cabin's dynamic response in three steps: (1) the keel of the cabin section touches the water, (2) the bottom skin is wetted, and (3) the bottom skin is submerged. This study also compares the rigid-surface crashes and water-entry impacts of the cabin from the point of view of load and energy analysis. The results show that rigid-surface crash mainly affects bulkhead and keel, whereas water-entry energy is mainly absorbed by the skin, connectors, and stringers. Additionally, varying skin thicknesses showed a negative correlation with back surface deformation. The methodologies and conclusions presented in this study can offer valuable references for researchers in the field of water entry.

Rigorous benchmarking of an iterative IBM solver by comparison to body-fitted mesh results

This study addresses the validation challenges of Immersed Boundary Method (IBM) solvers by proposing a consistent benchmarking approach. A temporally second-order Arbitrary Lagrangian–Eulerian (ALE) solver implemented in OpenFOAM is verified against lid-driven cavity flow and flow past static and oscillating cylinders. It then serves as the underlying fluid flow solver for a fully implicit diffusive direct forcing IBM solver that achieves temporal second-order accuracy, verified by the static and oscillating cylinder cases. Leveraging the shared numerical framework, the IBM solver is rigorously validated against ALE using identical settings, parameters, and nearly identical grids across twenty test cases, including stationary cylinder flow (Re = 40, 100, 185), oscillating cylinder in quiescent flow (Re = 100, KC = 5), and transversely oscillating cylinders with varying amplitudes and frequencies (16 cases in total). The IBM solver demonstrates robustness (CFL up to 8) and accuracy over a wide Reynolds number range, with relative drag coefficient errors below 7% for all considered cases. Incorporating body force correction, which reduces slip errors at negligible added computational cost, drastically improves accuracy. Proper Rhie–Chow momentum interpolation, including body forces, is critical in the adopted collocated finite volume method. For unsteady problems, the computational cost is greatly reduced without compromising accuracy by using CFL≈1.5−2 with only two outer iterations. The proposed benchmarking framework can be easily used for validation of other IBM approaches and thus potentially help to advance the state of IBM.

Liquefaction-induced large deformation method with automatic time-step mapping and interfacial interpolation improvement: Case study of the San Fernando dam

This study constructed the u-p equation for saturated soil in the meshfree global weak form within the arbitrary Lagrangian-Eulerian (ALE) framework to solve the problem of liquefaction-induced large deformation induced by strong seismic loading. The interpolation improvement in the near-interface zone was achieved using domain truncation optimization and the local nodal refinement algorithm, and the relative error of the shape function was proposed as the judgment criterion for radial basis function (RBF) field variable mapping. Finally, a high precision meshfree liquefaction-induced large deformation method (MFLLDM) with automatic time step mapping and interfacial zone interpolation improvement was established. The MFLLDM achieved the efficient dynamic updating of soil stress state and pore pressure information in space during the deformation process and more accurately depicted the localized large shear deformation characteristics of the soil in the near-interface zone. The proposed method was integrated into a custom-built large-scale finite element method (FEM) computing system (GEODYNA), based on object-oriented and super element program design technology. This enabled the efficient coupled analysis of MFLLDM in the liquefied-induced large deformation zone and FEM in the small deformation zone. Numerical consolidation examples were used to validate the accuracy, convergence, and applicability of the soil elasto-plastic model for MFLLDM. The method was then used to simulate the liquefaction damage of the San Fernando dam, which reproduced the development process of large slip deformation and high-water pressure ratio for the upstream dam slope.

A first‐order hyperbolic arbitrary Lagrangian Eulerian conservation formulation for non‐linear solid dynamics

SummaryThe paper introduces a computational framework using a novel Arbitrary Lagrangian Eulerian (ALE) formalism in the form of a system of first‐order conservation laws. In addition to the usual material and spatial configurations, an additional referential (intrinsic) configuration is introduced in order to disassociate material particles from mesh positions. Using isothermal hyperelasticity as a starting point, mass, linear momentum and total energy conservation equations are written and solved with respect to the reference configuration. In addition, with the purpose of guaranteeing equal order of convergence of strains/stresses and velocities/displacements, the computation of the standard deformation gradient tensor (measured from material to spatial configuration) is obtained via its multiplicative decomposition into two auxiliary deformation gradient tensors, both computed via additional first‐order conservation laws. Crucially, the new ALE conservative formulation will be shown to degenerate elegantly into alternative mixed systems of conservation laws such as Total Lagrangian, Eulerian and Updated Reference Lagrangian. Hyperbolicity of the system of conservation laws will be shown and the accurate wave speed bounds will be presented, the latter critical to ensure stability of explicit time integrators. For spatial discretisation, a vertex‐based Finite Volume method is employed and suitably adapted. To guarantee stability from both the continuum and the semi‐discretisation standpoints, an appropriate numerical interface flux (by means of the Rankine–Hugoniot jump conditions) is carefully designed and presented. Stability is demonstrated via the use of the time variation of the Hamiltonian of the system, seeking to ensure the positive production of numerical entropy. A range of three dimensional benchmark problems will be presented in order to demonstrate the robustness and reliability of the framework. Examples will be restricted to the case of isothermal reversible elasticity to demonstrate the potential of the new formulation.

Numerical study on the damage of liquid-filled containers subjected to shaped charge jet impact

In the studies of the vulnerability of armored vehicles, the impact of high-velocity penetrators on liquid-filled container components is one of the critical concerns. The purpose of this study is to investigate the structural damage of the liquid-filled container subjected to shaped charge jet impact utilizing the Structural Arbitrary Lagrangian–Eulerian method in ANSYS/LS-DYNA. The numerical model is validated against available experimental data. The validation effort of the numerical model showed very good agreements with experiments in terms of radial shock wave and radial crater formation as a function of time. Using the validated model, the liquid pressure, the energy transfer as well as the influence of overmatch on the impact process were analyzed. The results indicate that the structural damage modes of containers under shaped charge jet impact include perforation and wall deformation. Perforation results from the penetration of the jet tip and tail, while wall deformation is caused by the high-velocity impact of the flowing liquid. In cases where the overmatch (OM) is equal to 1, the contribution of the tip to front and back wall perforation increment primarily depends on the impact velocity. In cases with OM less than 1, the “filtering effect” of the Rolled Homogeneous Armor (RHA) armor plate leads to the loss of the tail's contribution to front wall perforation.

Numerical modelling of electromechanical coupling behaviors in HTS coil with implementation of H formulation in FE software

(Re)Ba2Cu3O7-x (REBCO) coated conductors (CCs) have attracted considerable concern because of their outstanding current carrying capacity in magnetic fields of high strengths. A huge electromagnetic force is generated in the superconducting coil when conducting large currents in strong magnetic field. Thus, management of stress and strain has become a key technical challenge for the stability and safety of superconducting coil during operation. To accurately predict the electro-magnetic and mechanical characteristics of superconducting coil in strong magnetic field, an electromechanical model on the basis of the H-formulation and arbitrary Lagrangian-Eulerian (ALE) method is proposed here with FE software. To verify the proposed model, the simulation outcomes of the coil during magnetization are compared with the experimental outcomes. The coupling effect of magnet at high field strengths is dependent on the position of the coil. To reduce the screening current effect, the overshoot method with plateau is found superior to the traditional overshoot method, and an increase in the stabilization time can decrease the maximum value of stress. Finally, the electromechanical behaviors of single winding coil and two-tapes co-winding coil are compared.

Continuously bounds-preserving discontinuous Galerkin methods for hyperbolic conservation laws

For finite element approximations of transport phenomena, it is often necessary to apply a form of limiting to ensure that the discrete solution remains well-behaved and satisfies physical constraints. However, these limiting procedures are typically performed at discrete nodal locations, which is not sufficient to ensure the robustness of the scheme when the solution must be evaluated at arbitrary locations (e.g., for adaptive mesh refinement, remapping in arbitrary Lagrangian–Eulerian solvers, overset meshes, etc.). In this work, a novel limiting approach for discontinuous Galerkin methods is presented which ensures that the solution is continuously bounds-preserving (i.e., across the entire solution polynomial) for any arbitrary choice of basis, approximation order, and mesh element type. Through a modified formulation for the constraint functionals, the proposed approach requires only the solution of a single spatial scalar minimization problem per element for which a highly efficient numerical optimization procedure is presented. The efficacy of this approach is shown in numerical experiments by enforcing continuous constraints in high-order unstructured discontinuous Galerkin discretizations of hyperbolic conservation laws, ranging from scalar transport with maximum principle preserving constraints to compressible gas dynamics with positivity-preserving constraints.

Identification of the Constitutive and Friction Models Parameters via a Multi-Objective Surrogate-Assisted Algorithm for the Modeling of Machining—Application to Arbitrary Lagrangian Eulerian Orthogonal Cutting of Ti6Al4V

Abstract The evolution of high-performance computing facilitates the simulation of manufacturing processes. The prediction accuracy of a numerical model of the cutting process is closely associated with the selection of constitutive and friction models. The reliability and the accuracy of these models highly depend on the value of the parameters involved in the definition of the cutting process. Direct of inverse methods are used to determine these model parameters. However, these identification procedures often neglect the link between the parameters of the material and the friction models. This article introduces a novel approach to inversely identify the best parameters value for both models at the same time and by taking into account multiple cutting conditions in the optimization routine. An artificial intelligence (AI) framework that combines the finite element modeling with an adaptive Bayesian multi-objective evolutionary algorithm (AB-MOEA) is developed, where the objective is to minimize the deviation between the experimental and the numerical results. The arbitrary Lagrangian–Eulerian (ALE) formulation and the Ti6Al4V alloy are selected to demonstrate its applicability. The investigation shows that the developed AI platform can identify the best parameters values with low computational time and resources. The identified parameters values predicted the cutting and feed forces within a deviation of less than 4% from the experiments for all the cutting conditions considered in this work.

The destructive form and response analysis of buried concrete pipes under the action of internal explosion loads

This research analyzes the damage mechanism of subterranean concrete pipelines subjected to internal explosive loads using a mix of field blasting tests and numerical simulations. The field tests reveal that, under the effect of internal explosion loads, axial and circumferential cracks occur in the concrete pipelines, with the crown, invert, and springline being damaged firstly, leading to penetrating cracks. In addition, an arbitrary Lagrangian Euler (ALE) method is used to establish a coupled model of underground concrete pipeline under the condition of internal explosion. The influence of the explosion mass on the destructive effects and dynamic characteristics of the pipeline is investigated, and the internal wall strain at the explosion center and in the central part of the pipeline is analyzed. Furthermore, the propagation and attenuation laws of shock waves in pipelines are investigated, and an attenuation law formula of shock waves inside the pipeline with two ends open is provided, which will be useful for future research.

Experimental and Simulation Investigation on Fatigue Performance of H13 Steel Tools in Friction Stir Welding of Aluminum Alloys.

As the central component in friction stir welding, the design and manufacture of welding tools for aluminum alloys have garnered substantial attention. However, the understanding of tool reliability during the welding process, especially in terms of fatigue performance, remains unclear. This paper focuses on the welding of AA2219-T4 as a case study to elucidate the predominant failure mode of the tool during the friction stir welding (FSW) of aluminum alloys. Experimental methods, including FSW welding and fracture morphology analysis of the failed tool, coupled with numerical simulation, confirm that high-cycle mechanical fatigue fracture is the primary mode of the tool failure. Failures predominantly occur at the tool pin's root and the shoulder end face with scroll concave grooves. The experimental and simulation results exhibit a noteworthy agreement, validating the reliability of the simulation model. The FSW Arbitrary Lagrangian-Eulerian (ALE) model developed in this study analyzes stress distribution and variation under the thermo-mechanical coupling effect of the tool. It reveals that stress concentration resulting from structural changes in the tool is the primary driver of fatigue crack initiation. This is attributed to exposure to alternating cyclic stresses such as bending, tension, and torsion at the tool pin's root, manifesting as multiaxial composite mechanical fatigue. Among these stresses, bending alternating cyclic stress exerts the most significant influence. The paper employs the Tool Life module in DEFORM software to predict the fatigue life of the tool. Results indicate that reducing welding speed or increasing rotation speed can enhance the tool's fatigue life to some extent. The methodology proposed in this paper serves as a valuable reference for optimizing FSW structures or processes to enhance the fatigue performance of welding tools.

Analysis of finite creep strains in aluminum plates at static and cyclic loading

The formulation of the problem and the basis of the method for solving two-dimensional creep problems for the case of finite strains are presented. The method is based on the Arbitrary Lagrange-Euler (ALE) approach in numerical modeling using FEM. The method is implemented in the form of additional units to the creep calculation software. The plane stress state is considered. The results of an experimental study of the creep of AlMg6 alloy specimens under static and cyclic loading are described. The obtained creep curves were used to verify the calculation method. It is shown that for a material with viscous creep properties, calculations using finite strains quite satisfactorily describe the tertiary, accelerated section of the creep curve. The creep of square plates in tension by static and cyclically varying traction was considered, data on their shape change and stress redistribution were obtained. A significant intensification of creep due to the addition of a cyclic component to the static loading was established.

Study on load characteristics and structural impact response propagation law of cabin internal explosion

Aiming at the problem that the distribution of explosion load in the cabin and the propagation law of structural impact response was unclear, this paper established the numerical calculation model of explosion in a closed cabin by ALE (Arbitrary Lagrangian Eulerian) method. There was an apparent convergence of shock waves at the cabin's corners, and the pressure relief hole's area and its position significantly affected the peak of quasi-static pressure. The peak acceleration of the deck structure decreased exponentially as the distance from the location of charge increased. Peak acceleration decreased by approximately 50% for each bulkhead crossing. There was a “paper window effect” during the cabin interior explosion on the whole ship. It meant there was a limit to the value for the energy generated by the explosion to be transmitted along the frame structure. When the charge was 150 kg, it reached the limit of the energy transferred by the structure in this paper. The response of the distant structure did not change significantly with the increase in the charge quality. The research revealed the impact response propagation mechanism in the structure and provided a reference for designing protective structures.

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.

Dynamic response and performance assessment of subsea sandwich pipelines with different interlayer subjected to underwater explosion

The sandwich pipelines have been developed and applied in subsea due to their better resistance than single-layer pipelines. Explosive shock loads can cause fatal damage to subsea pipelines, thus the objective of this paper is to systematically evaluate the safety of subsea sandwich pipelines under explosion loading. The uniqueness of this study is to analyze the dynamic response of sandwich pipeline filled with different interlayer materials subjected to underwater explosion, especially considering the fluid-solid interaction (FSI) effect. Based on the Arbitrary Lagrangian-Eulerian (ALE) algorithm, the propagation of the blast shock wave in sea water and the FSI effect with the pipeline were investigated by using LS-DYNA code. The accuracy of the numerical method was verified, and then the evolution of the explosive pressure in sandwich pipes with different interlayer material was simulated. The energy absorbing capacity of each layer was analyzed. The structural dynamic response and deformation of the subsea sandwich pipelines was investigated by considering the influencing factors including the diameter-to-thickness ratio (λ) of the inner pipe and outer pipe, the interlayer material, and the explosive charge (Me). The results show that with the increase of λ and Me, the ovality of the pipe increase correspondingly. Moreover, the results demonstrate that with different material as the interlayer, each layer of the sandwich pipe shows different ability to absorb the internal energy caused by explosive shock wave, thus the deformation of the pipe differs significantly. This study can provide a reference for the optimized design of subsea sandwich pipelines to support the operational safety of deep-sea pipeline systems.

Adjacency-based, non-intrusive model reduction for vortex-induced vibrations

Vortex-induced Vibrations (VIV) pose computationally expensive problems of high practical interest to several engineering fields. In this work we develop a non-intrusive, reduced-order modeling methodology, applied to two-dimensional (2D), VIV cases subject to a laminar, incompressible flow. Performing a physics-informed approximation of the Arbitrary Lagrangian–Eulerian (ALE) incompressible Navier–Stokes (NS), we derive a discrete-time, quadratic-bilinear model structure for the velocity flowfield on a reference domain. This structure, along with a predefined sparsity pattern motivated by the adjacency-based sparsity of the discretized NS-ALE operators, leads to the formulation of a sparse, full-order model (sFOM) inference problem. Thus, the data-driven inference task requires solving many “local” least squares (LS) problems, isolating the contribution of geometrically “nearest neighbours” for each degree of freedom. Numerical aspects of inference such as data centering and regularization, as well as the direct enforcement of boundary conditions under the sFOM formulation are extensively discussed. The inferred, sFOM operators are then projected to a non-intrusive reduced-order model (ROM) for the velocity flowfield via the Proper Orthogonal Decomposition (POD). The resulting non-intrusive ROM (sFOM-POD) is coupled with the first-principle, 2D solid oscillation equations, resulting to a hybrid physics-informed/first-principle VIV dynamics model, simulated using an implicit time integration scheme. The mapping of the coupled solution from the ALE reference domain to the current configuration is also presented. This methodology is applied to two testcases of an elliptical, non-deformable solid mounted on springs, subject to Re=90,180 flows. Numerical results indicate a successful coupling between the data-driven flowfield and solid dynamics, with prediction errors of less than 3% for both the flowfield and the solid oscillation. A comparative study with respect to the sFOM-POD dimension indicates the robustness and potential of the approach.

Comparative study of WCSPH, EISPH and explicit incompressible-compressible SPH (EICSPH) for multi-phase flow with high density difference

This study presents three Smoothed Particle Hydrodynamics (SPH) methods capable of handling high-density differences in violent incompressible multiphase flows. The conventional Weakly Compressible SPH (WCSPH) is reformulated into a quasi-Lagrangian framework based on Arbitrary Lagrangian–Eulerian (ALE) context. The Explicit Incompressible SPH (EISPH) method is extended to handle multiphase flows and reformulated in the ALE framework. The Explicit Incompressible-Compressible SPH (EICSPH) method, which can handle both compressible and incompressible phases, is developed by combining these two approaches in a fully explicit algorithm. The proposed methods are validated and compared through four benchmark problems including Rayleigh-Taylor instability, hydrostatic, liquid sloshing and dam break problems. Firstly, the stability and accuracy of interface modeling of the three methods were verified through Rayleigh-Taylor instability with small density differences. In the hydrostatic problem with a large density difference, the results from all three methods exhibit good agreement in the pressure distribution. Particularly, EICSPH demonstrates the faster convergence when compared to WCSPH, with EISPH showing fastest convergence overall. In the transient sloshing problem, all three methods quantitatively converged to the experimental results and exhibited good agreement, although slight pressure noise was observed in WCSPH initially. Finally, in the dam break problem, all three methods successfully simulated sharp interfaces without non-physical voids. The temporal variations of pressure and height were well predicted by all three methods, with EISPH showing better conformity to the water-air interface morphology obtained from other incompressible numerical methods compared to WCSPH and EICSPH. Additionally, the impact of air speed of sound was examined in EICSPH, where while the difference in pressure variation at the probe was minimal, differences were observed in energy dissipation and the progression of the free surface due to the air cushion effect.

A combined ALE-cohesive fracture approach for the arbitrary crack growth analysis

This work introduces an advanced numerical model, based on a cohesive zone approach and the moving mesh technique, for simulating fracture propagation in quasi-brittle materials. The proposed procedure involves two stages: first, a mesh boundary representing the crack is selected and aligned with the crack growth direction by using the Arbitrary Lagrangian-Eulerian (ALE) methodology; next, a zero-thickness interface cohesive element, equipped with a traction-separation law, is adaptively inserted along the previously selected mesh boundary, in order to describe the nonlinear fracture process. The proposed model allows for multiple crack onset and propagation without requiring mesh-updated procedures and sensibly reduces the well-known mesh dependency issues of the standard discrete fracture approaches. Numerical analyses of mixed-mode fracture in concrete specimens are performed and suitable comparisons with experiments show the effectiveness and reliability of the proposed model in predicting arbitrary crack growth.