Arbitrary Lagrangian-Eulerian Algorithm Research Articles

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.

Investigations on geopolymer-based seawater sea-sand high performance concrete slabs reinforced with basalt FRP bars under direct contact explosions

Adopting locally available raw materials like seawater and sea-sand in coastal areas and oceanic islands has facilitated meeting the demands of marine engineering. However, these raw materials contain corrosive elements that could threaten the steel reinforcement in concrete structures, thus non-corrosive fibre-reinforced polymer (FRP) bars are proposed. In the present study, the geopolymer-based seawater sea-sand high performance concrete (G-SHPC) slab reinforced with basalt FRP bars was designed to preliminarily evaluate its dynamic behaviour under contact explosions. Tests were conducted on three large-sized slabs with different TNT charge weights, including 0.8 kg, 1.6 kg and 2.2 kg. To complement the experimental investigation, a numerical simulation was then performed in ANSYS-DYNA. A Continuous Surface Cap (CSC) model was developed to accommodate the unique characteristics of G-SHPC. Two different blast modelling methods, including the Arbitrary Lagrangian-Eulerian (ALE) algorithm and a hybrid Finite-Element (FE) and Smooth Particle Hydrodynamics (SPH) algorithm, were examined to faithfully reproduce the contact explosion phenomena. The structural models considered the bond-slip behaviour, and three bond-slip models were compared. The numerical results obtained through the ALE algorithm and the beam-in-solid bond-slip model exhibited fair agreement with the test results, with a maximum error of less than 6.3%. A parametric study was further conducted to establish the damage identification diagram. Formulas based on empirical data were formulated to anticipate the damage degrees of G-SHPC slabs exposed to contact explosions.

Numerical analysis of interaction between flow characteristics and dynamic response of interlocked concrete block mattress during sinking process

Revetment can provide effective protection against wave overtopping and fluvial erosion along coastlines, estuaries, and rivers. The cost-effectiveness and rapid implementation make Interlocked Concrete Block Mattress (ICB mat) a viable alternative to unit armors. However, the intense hydrodynamic conditions may compromise the structural integrity of ICB mat during sinking construction, posing significant threats to both personnel and engineering safety. This study aimed to investigate the flow characteristics around the flexible mattress and its dynamic response. Recently, the fluid-structure interaction (FSI) method has been extended to multi-physics analysis in engineering applications due to its superior performance. A two-way coupling was employed to simulate the conceptualized cases of sinking process of ICB mat using the k-ω SST turbulence model, the Arbitrary Lagrangian-Eulerian algorithm, and the partitioned method in this study. The results indicated that the upstream surface velocity of the mattress increased exponentially with the growing water depth; meanwhile, the maximum velocity near the head beam was 23.8–31.2% larger than the average velocity. Additionally, the stress distribution on the mattress manifested transverse stripes influenced by the layout of interlocked blocks, with the highest stress primarily observed in the vicinity of the rotating plate and head beam. Furthermore, an estimation formula was proposed for the dynamic response of ICB mat considering the hydrodynamic conditions as well as structural properties. The current study can provide theoretical guidance for the structural design of ICB mat and engineering risk assessment during sinking construction.

Vulnerability analysis of HSR bridge under near-field blast based on response surface method

In this paper, the vulnerability analysis of a high-speed railway (HSR) bridge system attacked by the near-field blasts is conducted using the response surface method. An “explosive-air-ground” coupling analysis model is established by the ANSYS/LS-DYNA software. Through a comparison of the numerical simulated and the experimental results, the effectiveness of the Arbitrary Lagrangian Eulerian (ALE) algorithm and the accuracy of the analysis model are verified. Then, the dynamic responses of an HSR simply-supported bridge subjected to four types of car-bomb blasts are calculated. The damage levels of the bridge components are evaluated using the residual bearing capacities of the pier and beam, and the shear displacement of the bearings. By adopting the central composite design method, the response surface models for the evaluation indices of the bridge components are fitted. Furthermore, the failure probabilities of each component at various damage levels are calculated, and the vulnerability of the bridge system is analyzed based on the Boundary Estimation Method. The proposed method could predict the damage probability of the bridge system under various car-bomb blasts, and provide a reference for exploring a probability-based evaluation method for the post-blast safety of the HSR bridges.

Comparative study on the forming characteristics and penetration effects of shaped charge jet in water and air

In order to analyze the influence of a water medium on the forming process and penetration performance of a shaped charge jet, a comparative study was carried out on an underwater shaped charge jet (USCJ) and a shaped charge jet (SCJ) in air. The virtual mass hypothesis is proposed to analyze the forming mechanism of USCJs. The arbitrary Lagrangian–Eulerian algorithm is adopted to carry out a series of simulation calculations considering the impact of standoff height and liner cone angle. The penetration test of the shaped charge jet in two media is carried out, and the experimental results verify the effectiveness of the theory and simulation. The differences of SCJ formation and penetration in air and water are analyzed. The results demonstrate that the USCJ exhibits a higher jet head velocity, higher cumulative kinetic energy, and a greater penetration ability than those of the jet in air. The depth of penetration (DOP) initially increases and subsequently decreases with an increase in the standoff height. The optimal standoff height of the USCJ is approximately 4–4.5 times greater than the charge diameter, whereas the SCJ in air is approximately 3.5–4 times greater than the charge diameter. Additionally, the DOP of the jet decreases at the optimal standoff height with an increase in the cone angle.

FE mesh density influence on blast loading analysis

To examine the influence of mesh density on the blast loads of anti-landmines (ALMs) and improvised explosive devices (IEDs) under an armored vehicle, models with different FE mesh densities were numerically analysed. The multi-material arbitrary Lagrangian-Eulerian (MM-ALE) algorithm was used to simulate under armored vehicle explosions. Explicit dynamic analysis was performed in LS-DYNA. Blast loading simulation was performed using the ConWep (conventional weapon) loading model, which is implemented in LS-DYNA. The material characteristics of high-strength steel were used to model the protective plates on the armored vehicle. Protective plates were modeled in a V-shape and as a deformable solid with the Johnson-Cook plasticity model. In this paper, the FE model with different mesh densities was numerically tested to analyse the influence of mesh density on the obtained results. For the purposes of the modeling, different types of finite elements were used for the FE models. The floor of the vehicle was modeled with 3D hexahedral eight-noded finite elements, and the protective plates were modeled with four-noded plate finite elements. The maximal value of plastic strain and the maximal value of the displacement of the central node on the protective plate was chosen as the parameters to compare the obtained results.

Reliability-based vulnerability analysis of bridge pier subjected to debris flow impact

In this paper, a finite element model of a highway bridge pier subjected to debris flow is established, which comprises a double-column pier, a gully channel, moving fluid and solid particles. By using the arbitrary Lagrangian-Eulerian (ALE) algorithm to calculate the fluid-solid coupling effect, the process of debris flow impacting on the pier is simulated. Based on the ‘two-phase flow’ theory, a simplified equation to calculate the impact force of debris flow containing both fluid and solid phases is proposed, and the variable parameters in the equation are determined through numerical simulation using the established FE model and the field-measured data. By comparing with the historical records of actual debris flows, the effectiveness of the numerical model and the proposed equation is verified. A reliability model of the pier subjected to debris flow is established, and the structural vulnerability is estimated by the MCS method. Using the site-observed data, the failure mode of a highway double-column pier subjected to impact of two-phase debris flow is studied. The critical velocities of debris flow causing the structure to have different modes of damage, and the critical impact height of debris flow on the pier suffering bending and shear failures are determined.

Study on explosion resistance process simulation and blast fracture failure of Ti[sbnd]6Al[sbnd]4V titanium alloy sheet

The application of high-strength and high-toughness titanium alloy in armour protection is increasing with its excellent properties. However, there is little research on titanium alloy in explosion protection, especially the dynamic response process under localised explosion load and finite element simulation of the explosion resistance process of titanium alloy sheet. In this paper, the deformation and fracture failure features of the 1.6 mm thick Ti6Al4V titanium alloy sheet during the blast loading process were studied by combining LS-DYNA finite element simulation and air explosion experiments. The error of the overpressure peak value of explosion shock wave between the value obtained by improved theoretical empirical formula calculation of cylindrical charge and the value obtained by numerical simulation is only 0.2%. By studying the influence of explosive shape and air domain mesh size on the overpressure value in the process of detonation wave propagation, the Structured Arbitrary Lagrangian-Eulerian (S-ALE) algorithm was selected for finite element simulation. When the air domain mesh size is 1 mm, the tensile failure criterion was introduced into the finite element simulation process. The results show that the numerical simulation results of the full-scale model and the test results were consistent. The destruction morphology of the target showed severe asymmetry. Under 50 g TNT blast load, the 1.6 mm thick Ti6Al4V titanium alloy target was damaged seriously, and the central area of the target was completely torn. The failure features were mainly petal-shaped warping tearing cracks and localised plastic deformation. The tensile stress is the main stress mode of the target failure. Therefore, dynamic tensile strength should be used as one of the selection criteria for explosion-resistant titanium alloy sheets. The target failure mode is dominated by adiabatic shear fracture.

G-UHPC slabs strengthened with high toughness and lightweight energy absorption materials under contact explosions

This study investigates the dynamic characteristics of geopolymer-based ultra-high performance concrete (G-UHPC) slabs strengthened with high toughness and lightweight energy absorption materials under the 1 kg TNT contact explosions. A total of four slabs were tested, including plain G-UHPC slab (G-UHPC-P), 20-layer basalt textile reinforced G-UHPC slab (G-UHPC-BFM), 20-layer steel wire mesh reinforced G-UHPC slab (G-UHPC-SWM) and 1.5 vol-% steel fibre reinforced G-UHPC slab with polyurethane coating (G-UHPC–SF–PU). The test results revealed that the steel wire mesh reinforcement was more effective in resisting contact explosions than the basalt textile reinforcement for G-UHPC. The polyurethane coating on the rear face of the slab exhibited its high tensile strength and deformability to absorb the blast-induced energy so as to enhance the anti-explosion performance of the slab, and additionally prevented the splash of slab fragments upon contact explosions to minimise secondary hazards. Based on the multi-material arbitrary Lagrangian-Eulerian (ALE) algorithm, local damage of G-UHPC-SWM and G-UHPC–SF–PU induced by contact explosions was reproduced using the explicit finite element software LS-DYNA. Fair agreement between the numerical and test results demonstrated that the numerical model could simulate the response of G-UHPC-SWM and G-UHPC–SF–PU with reasonable accuracy. Extensive numerical studies by varying polyurethane strain rate, coating thickness and the bonding between the polyurethane coating and the slab were further performed to analyse their effect on the maximum bulge depth of the polyurethane coating subjected to contact explosions.

Numerical study on load-shedding performance of a high-speed water-entry vehicle based on an ALE method

Aiming at the problem of load shedding in high-speed water entry of a vehicle, a composite structural buffer has been designed. Meanwhile, an accurate numerical model with the fluid-solid coupling is established to analyze the crushing process based on the arbitrary Lagrangian-Eulerian (ALE) algorithm and evaluate the effects of different schemes. The results show that the designed buffer can absorb the impact energy, leading to the damage and separation from the vehicle properly. The layered design of cushion foam changes the damage mode of the nose cap and causes it to be failure in advance. When the buffer is in contact with water, stress concentration occurs at the top of nose cap and preset groove. The groove effectively guides the destruction mode of the cap, such that the layered foam will not be too easy to be completely destroyed and the phenomenon of secondary cushion can occur. The velocity curve of the vehicle with the buffer changes more smoothly, the displacement is greater in the same time, and the load reduction rate of the layered foam scheme can reach 73.2% which is better than the single-layer foam scheme.

Uncertainty due to discretization on the ALE algorithm for predicting water slamming loads

Numerical uncertainty due to discretization on the Arbitrary Lagrangian-Eulerian (ALE) Finite Element method is investigated in the study. The paper quantifies uncertainty using two ITTC recommended methods, and also applies a constant Courant-Friedrichs-Lewy (CFL) number based discretization approach, instead of performing the independent grid and time-based discretization recommended by ITTC. As a case study, water entry of a flat bottom rigid and flexible plate is simulated considering various entry velocities. The total slamming loads and structural responses on both the rigid and elastic bottom plates are predicted and validated against available experimental data. Results indicate that numerical errors due to discretization differ in the various parameters and from case to case. They do affect the analysis of slamming loads and associated structural responses, and the hydroelasticity analysis as well. The hydroelasticity effects on the slamming force generally increase as the entry velocity increases, however, the quantitative results differ much for models with different grids. For example, when the hydroelasticity effect is estimated using the finer model, the deviation of the total slamming force on the elastic plate relative to the one on the rigid body are 56%, 57%, and 63% respectively for the three constant entry velocities, whereas the estimations are −27%, −4% and 3% with the coarser model. The study concludes that the uncertainty due to discretization in ALE is not just case-specific, but also parameter specific. The uncertainty quantification procedures with a constant CFL number based refinement are recommended to investigate the uncertainty comparing to the individual grid and time step study, in particular for the ALE solution where the time step is adjusted automatically as the grid changes. Thus, consideration should be given to updating the ITTC guidelines to incorporate the constant CFL based discretization approach.

Design and optimization of multi-V hulls of light armoured vehicles under blast loads

To mitigate the blast loads of mines and improvised explosive devices (IEDs) under a vehicle and reduce the injury of occupants, three hull shapes have been designed according to the bottom structure of a light armoured vehicle: double-V hull (DVH), triple-V hull (TVH), and trapezoidal hull (TH). The multimaterial arbitrary Lagrangian-Eulerian (MM-ALE) algorithm was used to simulate vehicle bottom explosions. The simulation results show that DVH has the best load transfer path, rendering smaller occupant damage parameters with DVH installation and indicating that the best protection performance premised on meeting light weight requirements can be provided by DVH. Furthermore, multiobjective optimization of DVH has been carried out so that the protection performance can be further improved only by changing its dimension parameters. Compared with the performance of the original bottom structure of the vehicle, the optimized design of DVH could reduce the left and right lower tibia forces by 33.3% and 41.75%, respectively, and the mass decreased by 43.05%.

Dynamic simulation of sugarcane milling process based on Arbitrary Lagrangian–Eulerian algorithm

Understanding the process of the sugarcane milling is important for improving sugar extraction. The Arbitrary Lagrangian–Eulerian algorithm within LS-DYNA was successfully used for the first time to simulate the dynamic process of milling. The predictions of the numerical model were validated using experimental crushing data from a previous study and dynamic process of milling was examined in detail. The draining performance during milling needs to be carefully considered. It was found that the deformation of the sugarcane in the XY cross-section under loads consisted of two main phases; compression and expansion with reabsorption mostly occurring during the expansion phase. The feeding side of the nip is the main area for the draining of juice. A sensitivity analysis of parameters influencing load and pressure was conducted. This research method could be applicable to similar engineering problems where there is contact, collision, extrusion, large displacement, and large deformation.

Finite volume arbitrary Lagrangian-Eulerian schemes using dual meshes for ocean wave applications

For reasons of efficiency and accuracy, water wave propagation is often simulated with potential or inviscid models rather than Navier-Stokes solvers, but for wave-induced flows, such as wave-structure interaction, viscous effects are important under certain conditions. Alternatively, general purpose Navier-Stokes (CFD) models can have limitations when applied to such free-surface problems when dealing with large amplitude waves, run-up, or propagation over long distances. Here we present an Arbitrary Lagrangian-Eulerian (ALE) algorithm with special care to the time-stepping and boundary conditions used for the free-surfaces, integrated into Code_Saturne, and we test its capabilities for modeling a variety of water wave generation and propagation benchmarks, and finally consider interaction with a vertical cylinder. Two variants of the mesh displacement computation are proposed and tested against the discrete Geometric Conservation Law (GCL). The more robust variant, for highly curved or sawtoothed free-surfaces, uses a Compatible Discrete Operator scheme on the dual mesh for solving the mesh displacement, which makes the algorithm valid for any polyhedral mesh. Results for standard wave propagation benchmarks for both variants show that, when care is taken to avoid grids with excessive numerical dissipation, this approach is effective at reproducing wave profiles as well as forces on bodies.

Traffic Capacity Assessment of the Urban Elevated Bridge after Near-Field Explosion Based on the Response Surface Method

The traffic capacity of the urban elevated bridge is assessed after it is attacked by a near-field explosion, using the residual bearing capacity of the damaged pier as the assessment index. First, the finite element model of a reinforced concrete slab under near-field explosion is established by ANSYS/LS-DYNA software and compared with the experimental results, which verifies the effectiveness of the ALE (arbitrary Lagrangian–Eulerian) algorithm and the accuracy of the mesh size and material properties. Then, an “explosive-air-pier” coupling analysis model is constructed using the finite element method, and the damage of the reinforced concrete pier under three types of car bombs is evaluated. Furthermore, a response surface model for the residual bearing capacity of the pier is utilized to calculate the failure probabilities of various damage levels of the pier under the three types of car bombs and to assess the traffic capacity of the bridge after near-field explosion. The established assessment method can be used to predict the probability of bridge structural damage at various levels under different types of car bombs and to provide a reference for exploring a probability-based safety assessment method of post-explosion bridges.

Experimental and Numerical Study of the Hydroelastic Response of a River-Sea-Going Container Ship

The hydroelastic behaviour of a river-sea-going ship hull is analysed experimentally and numerically. A segmented ship model connected by a steel backbone is tested in regular waves, and its high-frequency vibrations such as springing and whipping responses are identified. The hydroelastic response of the ship is numerically calculated using a hydroelastic time domain method based on strip theory, which is extended to include an improved model of the slamming load. The slamming forces in the bow section are determined using the Modified Longvinovich Model (MLM) instead of the Von Karman model. The vertical motions and wave-induced loads are calculated and compared with the experimental results. The response amplitude operators of the vertical loads and the high-order harmonics are analysed under different speeds, showing good agreement with the experiments. The slamming loads on the bow section of a river-to-sea ship are predicted utilizing the MLM model and compared with the Arbitrary Lagrangian Eulerian algorithm by LS-DYNA and with the measured results.

Replacing Detonation by Compressed Balloon Approaches in Finite Element Models

The evaluation of blast effects from malicious or accidental detonation of an explosive device is really challenging especially on large buildings. Indeed, the time and space scales of the explosion together with the chemical reactions and fluid mechanics make the numerical model really difficult to achieve acceptable structural design. Nevertheless, finite element methods and especially Arbitrary Lagrangian Eulerian (ALE) have been extensively used in the past few decades with some simplifications. Among them, the replacement of the explosive event by a compressed balloon of detonation products has been proven useful in numerous different situations. Unfortunately, the ALE algorithm does not achieve a proper energy balance through the numerical integration of the discrete scheme; this important drawback is not compensated by the use of the classical compressed balloon approach. The paper focuses on increasing the radius of the equivalent ideal gas balloon in order to achieve better energy balance and thus better results at later stages of the blast wave propagation.

Numerical simulation of the pressing of polycrystalline diamond compact cutter into the rock based on arbitrary Lagrangian-Eulerian algorithm

For the polycrystalline diamond compact (PDC) bit, the first step of rock breaking is to press the bit into the rock. However, it is very difficult to theorize the pressing process, due to the complex structure of cutting tooth, the large deformation of the rock, and the nonlinearity of the cutter-rock contact. To solve the problem, this paper takes the parabolic Mohr strength criterion as the judging condition of rock failure, and establishes a numerical simulation program for the pressing process based on the arbitrary Lagrange-Eulerian (ALE) method and the general contact algorithm. The proposed program can adjust the mesh of the rock automatically, preventing the grid distortion caused by rock deformation and contact nonlinearity. The finite-element model created by the ALE method was analyzed by explicit dynamic algorithm, and the stress and strain fields of the PDC cutter were obtained by solving the model. In addition, the author analyzed how the weight on the bit (WOB) is affected by the diameter and back rake angle of the PDC cutter, as well as the friction coefficient between cutter and rock. The results show that the WOB increases with the increase of PDC cutter diameter, the WOB increases with the increase of dip angle in the range of 0–30°, and the WOB increases with the increase of friction coefficient. The established program fully reveals the interaction between PDC cutter and rock in the pressing process, facilitating further analysis on the rock-break mechanism of the PDC bit.

Adaptive mesh refinement immersed boundary method for simulations of laminar flows past a moving thin elastic structure

One of the critical issues in numerical simulation of fluid-structure interaction problems is inaccuracy of the solutions, especially for flows past a stationary thin elastic structure where large deformations occur. High resolution is required to capture the flow characteristics near the fluid-structure interface to enhance accuracy of the solutions within proximity of the thin deformable body. Hence, in this work, an algorithm is developed to simulate fluid-structure interactions of moving deformable structures with very thin thicknesses. In this algorithm, adaptive mesh refinement (AMR) is integrated with immersed boundary finite element method (IBFEM) with two-stage pressure-velocity corrections. Despite successive interpolation of the flow field by IBM, the governing equations were solved using a fixed structured mesh, which significantly reduces the computational time associated with mesh reconstruction. The cut-cell IBM is used to predict the body forces while FEM is used to predict deformation of the thin elastic structure in order to integrate the motions of the fluid and solid at the interface. AMR is used to discretize the governing equations and obtain solutions that efficiently capture the thin boundary layer at the fluid-solid interface. The AMR-IBFEM algorithm is first verified by comparing the drag coefficient, lift coefficient, and Strouhal number for a benchmark case (laminar flow past a circular cylinder at Re = 100) and the results showed good agreement with those of other researchers. The algorithm is then used to simulate 2-D laminar flows past stationary and moving thin structures positioned perpendicular to the freestream direction. The results also showed good agreement with those obtained from the arbitrary Lagrangian-Eulerian (ALE) algorithm for elastic thin boundaries. It is concluded that the AMR-IBFEM algorithm is capable of predicting the characteristics of laminar flow past an elastic structure with acceptable accuracy (error of ∼0.02%) with only ∼1% of the computational time for simulations with full mesh refinement.

Simulation of Wire Bonding Process Using Explicit Fem with Ale Remeshing Technology

ABSTRACTThermosonic wire bonding is a common fabrication process for connecting devices in electronic packaging. However, when the free air ball (FAB) is compressed onto the I/O pad of the chip during bonding procedure, chip cracking may occur if the contact pressure is too large. This study proposes an effective simulation technique that can predict the wire ball geometry after bonding in an accurate range. The contact force obtained in the simulation can be used for possible die cracking behavior evaluation. The simulation in this study used the explicit time integration scheme to deal with the time marching problem, and the second-order precision arbitrary Lagrangian-Eulerian (ALE) algorithm was used to deal with the large deformation of the wire ball during the bonding process. In addition, the equilibrium smoothing algorithm in LS-DYNA can make the contact behavior and geometry of the bonding wire almost the same as the experiment, which can also significantly reduce the distortion of the mesh geometry after remeshing.