Arbitrary Lagrangian Eulerian Code Research Articles

Laser-driven flyer plate impact: Computational studies guided by experiments

We present a computational approach using a multimaterial, arbitrary Lagrangian–Eulerian code termed ALE3D to model the nanosecond/micrometer dynamics of the launch of 0.5–4.5 km/s laser-driven metal flyer plates and the impact with stationary targets of Pyrex and fused silica glasses, and Lexan and Plexiglas polymers, producing pressures in the target in the range of 5–20 GPa. The simulations are compared to experimental results where the flyer velocity profile and the velocity profile imparted to the target material were measured with high-speed velocimetry. The experimental flyer launch by a high-intensity pulsed laser is modeled by depositing heat into a thin vaporizable layer under the flyer plate. This model produces a flyer plate that has not been exposed to the laser pulse, allowing us to compare the properties of the real flyer to a simulated ideal flyer. The simulations of target impact are generally in good agreement with the experiment except at the highest impact velocities where the shock release process in the experiment is slower than that in the simulation. The cause of this disagreement is attributed to an inadequate description of the shock viscosity during the nanosecond unloading process.

Investigation of material flow and thermomechanical behavior during friction stir welding of an AZ31B alloy for threaded and unthreaded pin geometries using computational solid mechanics simulation

In the friction stir welding process, the tool role in the material flow and its thermomechanical behavior is still not entirely understood. Several modeling approaches attempted to explain the material and tool relationship, but to this date, insufficient results were provided in this matter. Regarding this issue and the urgent need for trustful friction stir welding models, a computational solid mechanic's model capable of simulating material flow and defect formation is presented. This model uses an Arbitrary Lagrangian-Eulerian code comparing a threaded and unthread pin profile. The model was able to reproduce the tool's torque, temperatures, and material flow along the entire process, including the underreported downward flow effect promoted by threaded pin's. A point tracking analysis revealed that threads increase the material velocity and strain rate to almost 30% compared to unthreaded conditions, promoting a temperature increment during the process, which improved the material flow and avoided filling defects. The presented results showed the model's capability to reproduce the defects observed in real welded joints, material thermomechanical characteristics and high sensitivity to welding parameters and tool geometries. Nevertheless, the outcomes of this work contribute to essential guidelines for future friction stir welding modeling and development, tool design, and defect prediction.

Surface tension models for a multi-material ALE code with AMR

A number of surface tension models have been implemented in a 3D multi-physics multi-material code, ALE–AMR, which combines Arbitrary Lagrangian Eulerian (ALE) hydrodynamics with Adaptive Mesh Refinement (AMR). ALE–AMR is unique in its ability to model hot radiating plasmas, cold fragmenting solids, and most recently, the deformation of molten material. The surface tension models implemented include a diffuse interface approach with special numerical techniques to remove parasitic flow and a height function approach in conjunction with a volume-fraction interface reconstruction package. These surface tension models are benchmarked with a variety of test problems. Based on the results, the height function approach using volume fractions was chosen to simulate droplet dynamics associated with extreme ultraviolet (EUV) lithography.

Modes of propagation and deposition of granular flows onto an erodible substrate: experimental, analytical, and numerical study

An erodible substrate and a sharp slope break affect the dynamics and deposition of long runout landslides. We study the flow evolution of a granular mass (1.5–5.1 l of sand or gravel) released on a bilinear chute, i.e., an incline (between 35 and 66°) followed by a horizontal sector, either sand-free or covered (1–2-cm-thick sand layer). Monitoring the time evolution of the falling mass profiled at 120 Hz, the impact dynamics, erosion of the basal layer, and modes of deposition are studied. The frontal deposition is followed by a backward propagating shock wave at low slope angles (<45°), or by a forward prograding flow at greater angles. Experiments with colored sand layers show a complex sequence of dilation, folding and thrusting within both the collapsing sand flow and the substrate. Experimental results are compared with real rock avalanche data and nearly vertical collapses. The observed increase of the drop height divided by the runout (H/L or Heim’s ratio) with both chute slope angle and thickness of the erodible substrate is explained as an effect of vertical momentum loss at the slope break. Data suggest a complex evolution, different from that of a thin flow basal shear flow. To provide an approximate explanation of the dynamics, three analytical models are proposed. Erosion of a 1-cm-thick substrate is equivalent to 8–12 % increase of the apparent friction coefficient. We simulate the deposition and emplacement over an erodible layer with a FEM arbitrary Lagrangian Eulerian code, and find a remarkable similarity with the time evolution observed in the experiments. 2D models evidence the internal deformation with time; 3D models simulate deposition.

Virtual tryout and optimization of the extrusion die for an aluminum profile with complex cross-sections

In this paper, the “trial-and-repair” process of the extrusion die is transferred from the workshop to the computer for a complex hollow aluminum profile used in high-speed trains. Firstly, a finite element (FE) model of the extrusion process is established with the arbitrary Lagrangian–Eulerian code HyperXtrude. To balance the material flow velocity in the die cavity, more than ten baffle plates are used and distributed in the welding chamber. Then, taking the exit velocity uniformity as the evaluating criterion, the initial extrusion die is modified by adjusting the shapes, the layout, and the heights of the baffle plates. Through a series of modifications, the velocity difference in the cross-section of the extrudate decreases significantly from 102.3 mm/s with the initial die to 26.6 mm/s with the final one. The local twisted or bent deformation of the extrudate is well controlled with the optimal die. Finally, a real extrusion die is manufactured and a practical profile is extruded. The difference in the rib thickness of the profile between the experimental measurements and desired dimensions is 0.12 mm, which satisfies the practical requirements. Moreover, the microstructures in the profile and its ribs are examined, and no heat defects are observed in the profile. Therefore, the virtual tryout of the extrusion die in this work are well verified, and the design rules of extrusion dies could provide theoretical guidance for practical repairs of complex extrusion dies in workshop.

Prediction of charge welds in hollow profiles extrusion by FEM simulations and experimental validation

In direct extrusion of aluminum alloys, billets are discretely loaded into the press and joined by the high hydrostatic pressure field. The contamination of the billet-to-billet interface by oxides, dust, or lubricant produces a welded zone (charge weld) with reduced mechanical properties that requires profile discharge. For an efficient material scrapping, both the position of the transition zone and its extent in the profile must be accurately identified. In industrial practice, in relation to a lack of experimental and numerical studies on this specific matter, the determination of the zone to be discarded is still performed mainly by experience or labor-intensive analyses. The aim of the present study is to bridge this gap by investigating the evolution of the charge welds inside an industrial multi-profiles and determining their exact position and extension by experimental microstructural analyses coupled with comprehensive 3D FE simulations performed with the Arbitrary Lagrangian–Eulerian code HyperXtrude®. Skin and rest defects are also experimentally investigated and a numerical sensitivity study on the influence of the friction model selection is performed. Comparison between numerical and experimental results shows a good agreement both in terms of general trend and exhausting points of the charge welds. The results prove that the FE code is a reliable tool in assisting and driving the die and process design stages, not only for process optimization as reported in literature but also for the scrap length determination. Finally, a process efficiency index is defined and, for the specific case study, it is found to be increased from 82.6 %, as resulting from the actual industrial practice, to a 88.3 % as optimized by the performed coupled experimental and numerical activities.

Extrudate swell of linear and branched polyethylenes: ALE simulations and comparison with experiments

Extrudate swell is a common phenomenon observed in the polymer extrusion industry. Accurate prediction of the dimensions of an extrudate is important for appropriate design of dies for profile extrusion applications. Prediction of extrudate swell has been challenging due to (i) difficulties associated with accurate representation of the constitutive behavior of polymer melts, and (ii) difficulties associated with the simulation of free surfaces, which requires special techniques in the traditionally used Eulerian framework. In a previous work we had argued that an Arbitrary Lagrangian Eulerian (ALE) based finite element formulation may have advantages in simulating free surface deformations such as in extrudate swell. In the present work we reinforce this argument by comparing our ALE simulations with experimental data on the extrudate swell of commercial grades of linear polyethylene (LLDPE) and branched polyethylene (LDPE). Rheological behavior of the polymers was characterized in shear and uniaxial extensional deformations, and the data was modeled using either the Phan–Thien Tanner (PTT) model or the eXtended Pom–Pom (XPP) model. Additionally, flow birefringence and pressure drop measurements were done using a 10:1 contraction–expansion (CE) slit geometry in a MultiPass Rheometer. Simulated pressure drop and contours of the principal stress difference were compared with experimental data and were found to match well. This provided an independent test for the accuracy of the ALE code and the constitutive equations for simulating a processing-like flow. The polymers were extruded from long ( L/ D = 30) and short ( L/ D = 10) capillaries dies at 190 °C. ALE simulations were performed for the same extrusion conditions and the simulated extrudate swell showed good agreement with the experimental data.

Multiple levels of cell by cell Adaptive Mesh Refinement in the Lagrangian step of the ALE code CORVUS

A multi-level cell by cell Adaptive Mesh Refinement (AMR) hydrodynamics capability has been developed for the Lagrangian step of the 2D Arbitrary Lagrangian Eulerian (ALE) code CORVUS. Connectivity arrays are used rather than a hierarchical data structure. We solve only on the dynamic unstructured mesh rather than on every level of a refinement hierarchy. The strength, artificial viscosity, slide and programmed burn methods have been generalised to work with AMR. Results are presented for a range of Lagrangian test problems.

Arbitrary Lagrangian–Eulerian 3D ideal MHD algorithms

AbstractWe discuss algorithmic approaches and verification results associated with the Lagrangian–Eulerian algorithms for ideal magnetohydrodynamics as implemented in the ALEGRA arbitrary Lagrangian–Eulerian code. We discuss the form of the Lagrangian step discretization including the forces and the time step control. We also discuss our constrained transport approach for remap of the magnetic flux density and a deBar‐type approach for total energy conservation which permits the capturing of shocks. We demonstrate the benefit of a predictor–corrector methodology for time discretization. Directions for further research are indicated. Copyright © 2010 John Wiley &amp; Sons, Ltd.

Rate-dependent dynamic ALE analysis of finite deformation of elasto-viscoplastic solids

In this paper, formulation and implementation of finite element analysis within an Arbitrary Lagrangian Eulerian (ALE) description is presented for large deformation analysis of elasto-viscoplastic materials. The rate effects are included using a consistent procedure. An implicit algorithm with backward Euler integration scheme is used to integrate the elasto-viscoplastic constitutive equations. Also, the closed form of the consistent tangent operator is derived using the momentum balance equation to reduce the computation time. A fully coupled ALE procedure is used which includes dynamic effects. The proposed algorithm is implemented in an ALE code and its effectiveness and efficiency is verified through several numerical simulation problems and comparison with available experimental results.

Modeling of multi-interface, diverging, hydrodynamic experiments for the National Ignition Facility

The National Ignition Facility (NIF) will soon provide experiments with far more than ten times the energy than has been previously available on laser facilities. In the context of supernova-relevant hydrodynamics, this will enable experiments in which hydrodynamic instabilities develop from multiple, coupled interfaces in a diverging explosion. This paper discusses the design of such blast-wave-driven explosions in which the relative masses of the layers are scaled to those within the star. It reports scaling simulations with CALE to model the global dynamics of such an experiment. CALE is a hybrid, Arbitrary Lagrangian-Eulerian code. The simulations probed the instability growth and multi-interface interactions in mass-scaled systems using different materials. The simulations assist in the target design process and in developing an experiment that can be diagnosed.

Semi-Infinite Target Penetration by Ogive-Nose Penetrators: ALEGRA/SHISM Code Predictions for Ideal and Nonideal Impacts

The physics of ballistic penetration mechanics is of great interest in penetrator and countermeasure design. The phenomenology associated with these events can be quite complex, and a significant number of studies have been conducted ranging from purely experimental to “engineering” models based on empirical and/or analytical descriptions to fully coupled penetrator/target, thermomechanical numerical simulations. Until recently, however, there appears to be a paucity of numerical studies considering “nonideal” impacts (Goldsmith, 1999, “Non-Ideal Projectile Impact on Targets,” Int. J. Impact Eng., 22, pp. 95–395). The goal of this work is to demonstrate the SHISM algorithm implemented in the ALEGRA multimaterial arbitrary Lagrangian Eulerian code (Boucheron, et al., 2002, ALEGRA: User Input and Physics Descriptions, Version 4.2, SAND2002-2775, Sandia National Laboratories, Albuquerque, NM). The SHISM algorithm models the three-dimensional continuum solid mechanics response of the target and penetrator in a fully coupled manner. This capability allows for the study of nonideal impacts (e.g., pitch, yaw, and/or obliquity of the target/penetrator pair). In this work predictions using the SHISM algorithm are compared with previously published experimental results for selected ideal and nonideal impacts of metal penetrator-target pairs. These results show good agreement between predicted and measured maximum depths-of-penetration (DOPs), for ogive-nose penetrators with striking velocities in the 0.5–1.5 km/s range. Ideal impact simulations demonstrate convergence in predicted DOP for the velocity range considered. A theory is advanced to explain disagreement between predicted and measured DOPs at higher striking velocities. This theory postulates uncertainties in angle-of-attack for the observed discrepancies. It is noted that material models and associated parameters used here were unmodified from those in literature. Hence, no tuning of models was performed to match experimental data.

A compatible finite element multi‐material ALE hydrodynamics algorithm

AbstractThe main ideas of compatible Lagrangian hydrodynamics were originally developed in the form of a finite volume scheme by Caramana et al. at LANL. A new compatible finite element Lagrangian hydrodynamics method has been developed and implemented in a 2D arbitrary Lagrangian Eulerian (ALE) code CORVUS. The new finite element method was developed in preference to the published finite volume schemes in order to see if the fundamental principles of compatible hydro could be translated across to other numerical methods in use in hydrocodes and to facilitate a more direct comparison of the performance of the compatible hydro scheme with the existing finite element scheme in CORVUS. The new finite element scheme provides total energy conservation to round off for the Lagrangian step. The edge artificial viscosities and sub‐zonal pressures that have been introduced through the framework of the compatible hydro scheme provide further improvements in terms of accuracy and robustness for Lagrangian calculations. The details of the compatible finite element Lagrangian scheme and the extensions required to the scheme to allow it to be applied as the Lagrangian step of a multi‐material ALE code are discussed. Test problems will be presented to demonstrate some of the benefits and the performance of the new method for hydrocode applications. © British Crown Copyright 2007/MOD. Reproduced with permission. Published by John Wiley &amp; Sons, Ltd.

KIVA-4: An unstructured ALE code for compressible gas flow with sprays

The KIVA family of codes was developed to simulate the thermal and fluid processes taking place inside an internal combustion engine. In this latest version of this open source code, KIVA-4, the numerics have been generalized to unstructrured meshes. This change required modifications to the Lagrangian phase of the computations, the pressure solution and fundamental changes in the fluxing schemes of the rezoning phase. This newest version of the code inherits all the droplet phase capabilities and physical sub-models of previous versions. The integration of the gas phase equations with moving solid boundaries continues to employ the successful arbitrary Lagrangian–Eulerian (ALE) methodology. Its new unstructured capability facilitates grid construction in complicated geometries and affords a higher degree of flexibility. The numerics of the code, emphasizing the new additions, are described. Various computational examples are performed demonstrating the new capabilities of the code.

ALE simulations of high-velocity impact problem

We describe here our newly developed ALE code on 2D quadrilaterals. The code is employed here in the numerical simulations of the erater formation during impact of small accelerated object on bulk target. The simulation of the high-velocity impact problem by the Lagrangian hydrodynamical codes leads in later stages to severe distortion of the Lagrangian grid which prevents continuation of computation. Such situations can however be treated by the Arbitrary Lagrangian Eulerian (ALE) method. In order to maintain the grid quality, the ALE method applies grid smoothing regularly after several time steps of Lagrangian computation. After changing the grid, the conservative quantities have to be conservatively remapped from the old grid to the new, better one. After remapping, Lagrangian computation can continue.