Multi-material Arbitrary Lagrangian Eulerian Method Research Articles

Computational assessment of leg response to extreme loadings using a detailed finite element model.

This study focuses on evaluating the response of the Total Human Model for Safety™ lower extremity finite element model under blast loading. Biofidelity of the lower extremity model was evaluated against experiments with impact loading equivalent to underbody blast. The model response was found to match well with the experimental data for the average impactor speeds of 7 and 9.3 m/s resulting in an overall correlation and analysis rating of 0.86 and 0.82, respectively. The model response was then used to investigate response for antipersonnel mine explosion where the numerical setup consists of a charge mass of 40 g trinitrotoluene placed at a depth of 50 mm below the heel. The explosion was modeled using Multi Material-Arbitrary Lagrangian Eulerian method. The model was subjected to the graded input in terms of variation in standoff distance and mass of explosive to investigate the sensitivity of the model. The model found sensitive to the threat definition and predicted an increase of 110% in peak fluid-structure interaction force with 20% reduction in its time to peak and 29% increase in peak calcaneus axial force with a reduction of 33% in its time to peak when explosive mass varied from 40 g to 100 g. The location of the explosive below the foot was discovered to have significant effect on the injury pattern in near-field explosion. A comparative study suggested that the model predicted similar response and damage pattern compared to experimental data.

A two‐dimensional multimaterial ALE method for compressible flows using coupled volume of fluid and level set interface reconstruction

AbstractIn this work, we present a two‐dimensional multimaterial arbitrary Lagrangian–Eulerian (ALE) method for simulating compressible flows in which a novel coupled volume of fluid and level set interface reconstruction (VOSET) method is developed for interface capturing. The VOSET method combines the merits of both the volume of fluid method and the level set method by using a geometrical iterative operation. Compared to the original VOSET method, the novel VOSET method proposed in this work further improves the accuracy and fidelity in interface reconstruction procedure, especially in under‐resolved regions. Several typical two‐dimensional numerical experiments are presented to investigate the effectiveness of the proposed VOSET method and its performance when coupling with the multimaterial ALE solver. Numerical results demonstrate its good capability in capturing material interfaces during the simulation of compressible two‐material flows.

Slamming loads and responses on a non-prismatic stiffened aluminium wedge: Part II. Numerical simulations

An experimental study was carried out to examine the impact-induced loads and structural responses of a three-dimensional non-prismatic aluminium wedge. The findings of the experimental study were presented in the first part of this publication, entitled “Slamming loads and responses on a non-prismatic stiffened aluminium wedge: Part I. Experimental study.” This paper describes the second part of the study, which deals with numerical simulations of slamming loads acting on the wedge and its dynamic responses. Two different two-way coupling methods are assessed and compared to simulate the water entry problem. Initially, an explicit nonlinear finite element method with a Multi-Material Arbitrary Lagrangian-Eulerian (MMALE) solver is employed to evaluate the elastic response of the structure following a free-fall water impact. Subsequently, the hydroelastic slamming problem is modelled using a two-way coupled technique with a k-ε turbulence model and implicit unsteady solver for both the fluid and structural domains (Star-CCM+/ABAQUS). The effect of viscosity on slamming loads and responses was examined, and numerical results are compared with experimental data. To investigate the effect of rigidity on structural response and bottom deflection, the wedge was designed with bottom plates of varying thickness. The computed results from the two numerical models and the experimental data are in good agreement. The study concluded that the bottom plates deformation affects hydrodynamic loads during slamming. It is also observed that impact-induced loads depend on the water impact velocity and the flexibility of the bottom plates. This suggests that the slamming pressure increases with an increase in impact velocity and decreases when the structures become more flexible. According to this study, both numerical models are suitable for accurate and efficient computations of hydroelastic slamming; however, the MMALE method results in larger numerical fluctuations.

Evaluation of collapse resistance of masonry-infilled RC frame building under blast loadings

As non-structural members, the masonry-infilled (MI) walls are always ignored in the numerical and experimental study on the blast and collapse resistance of RC frame buildings, while the contribution of MI walls on preventing the large-scale collapse has been observed according to the past explosion incidents. This paper aims to propose and verify a numerical simulation approach considering the blast- and collapse-resistant effects of MI walls, and further evaluate the collapse resistance of MI RC frame buildings under blast loadings. Firstly, based on our previously validated hybrid finite element (FE) modelling approach for RC frame structures and Multi-material Arbitrary Lagrangian-Eulerian method for applying blast loadings, the simplified micro-model and compressive strut model of the MI wall were adopted to characterize its blast and collapse resistance in the near- and far-regions of building, respectively. Secondly, the out-of-plane explosion test and in-plane quasi-static collapse test were numerically reproduced to verify the applicability of adopted FE modelling approaches for MI walls. Furthermore, by establishing the hybrid FE models of prototype bare and MI RC frame buildings, the propagation of blast waves, damage modes as well as dynamic responses of RC frame buildings under two design-based threat of explosion at corner and side columns were derived and examined. Finally, the applicability of the anti-collapse design method specified by U.S. Department of Defense, i.e., alternate path method (APM), for RC frame buildings under external explosions was examined. It derives that, (i) the presence of MI walls can efficiently block the blast waves into the building structures, and relieve the upward arch of slabs and damage degree of interior columns; (ii) compared with the bare RC frame buildings, the MI walls provide sufficient alternate load paths to enhance the structural robustness and restore the gravity stability of MI RC frame buildings after the explosions; (iii) the APM is only applicable to evaluate the collapse resistance of MI RC frames under the external explosion of cargo van bomb (1814 kg of equivalent TNT) or even less charge weight.

A multi-material ALE model for investigating impact dynamics of pile-soil systems

The dynamic pile-soil interaction is one of the most important and challenging problem in geomechanics, especially when geometrical, material-related, and dynamic contact-related nonlinearities exist. Geometrical nonlinearity is a fundamental obstacle to the popular Lagrangian finite element methods (FEM) that have been utilized in other areas of geomechanics research. This paper introduces a Multi-Material Arbitrary Lagrangian-Eulerian (MM-ALE) model for predicting the pile-soil interaction and forces during lateral dynamic impact events. The study used the MM-ALE method in conjunction with an elasto-viscoplastic soil material model that included strain softening and an elasto-plastic steel material model that incorporated strain rate effects to examine pile response during lateral vehicle impacts. The model was validated using large-scale, dynamic impact test data for piles embedded in soil, thus confirming its capability to simulate the complex dynamic impact pile-soil interaction. The effects of impact velocity, embedment depth, and soil strength on impact forces, energy dissipation, and impulse response of a pile-soil system were subsequently investigated. It was determined that average impact force, Favg, and impact velocity, are proportional to one another as Favg∝v2 regardless of pile embedment depth. This relationship provides evidence for the existence of inertial or hydrodynamic drag forces in the pile-soil system during lateral impacts similar to a solid object passing through a fluid.

A cell-centered discontinuous Galerkin multi-material arbitrary Lagrangian-Eulerian method in axisymmetric geometry

In this paper, a cell-centered discontinuous Galerkin (DG) multi-material arbitrary Lagrangian-Eulerian (MMALE) method is developed for compressible fluid dynamics in axisymmetric geometry. The MMALE method utilizes moment-of-fluid (MOF) interface reconstruction technology to simulate multi-materials of immiscible fluids. It is an explicit time-marching Lagrangian plus remapping type. In the Lagrangian stage, a volume-weighted scheme of updated cell-centered discontinuous Galerkin Lagrangian method is applied to discretize the hydrodynamic equations in pure cells, and Tipton's pressure relaxation closure model is used in mixed cells. A robust MOF interface reconstruction algorithm is used to provide the information on the material interfaces for remapping. In the rezoning stage, Knupp's algorithm is used for mesh smoothing. In the remapping stage, an efficient multi-material cell-intersection-based remapping method is proposed. It can be divided into four stages: polynomial reconstruction, polygon intersection, integration, and detection of problematic cells and limiting. Polygon intersection is based on the “clipping and projecting” algorithm, and detection of problematic cells depends on a troubled cell marker, and a posteriori multi-dimensional optimal order detection (MOOD) limiting strategy is used for limiting. Several numerical tests are given to demonstrate the robustness and accuracy of the method.

Numerical evaluation of hypothetical core disruptive accident in full-scale model of sodium-cooled fast reactor

A hypothetical core destructive accident (HCDA) has received widespread attention as one of the most serious accidents in sodium-cooled fast reactors. This study combined recent advantages in numerical methods to realize realistic modeling of the complex fluid–structure interactions during HCDAs in a full-scale sodium-cooled fast reactor. The multi-material arbitrary Lagrangian–Eulerian method is used to describe the fluid–structure interactions inside the container. Both the structural deformations and plug rises occurring during HCDAs are evaluated. Two levels of expansion energy are considered with two different reactor models. The simulation results show that the container remains intact during an accident with small deformations. The plug on the top of the container rises to an acceptable level after the sealing between the it and its support is destroyed. The methodology established in this study provides a reliable approach for evaluating the safety feature of a container design.

A High-Order Cell-Centered Discontinuous Galerkin Multi-Material Arbitrary Lagrangian-Eulerian Method

A High-Order Cell-Centered Discontinuous Galerkin Multi-Material Arbitrary Lagrangian-Eulerian Method

A hybrid subcell-remapping algorithm for staggered multi-material arbitrary Lagrangian-Eulerian methods

A new flux-based hybrid subcell-remapping algorithm for staggered multimaterial arbitrary Lagrangian-Eulerian (MMALE) methods is presented. This new method is an effective generalization of the original subcell-remapping method to the multi-material regime (LOUBERE, R. and SHASHKOV, M. A subcell remapping method on staggered polygonal grids for arbitrary-Lagrangian-Eulerian methods. Journal of Computational Physics, 209, 105–138 (2005)). A complete remapping procedure of all fluid quantities is described detailedly in this paper. In the pure material regions, remapping of mass and internal energy is performed by using the original subcell-remapping method. In the regions near the material interfaces, remapping of mass and internal energy is performed with the intersection-based fluxes where intersections are performed between the swept regions and pure material polygons in the Lagrangian mesh, and an approximate approach is then introduced for constructing the subcell mass fluxes. In remapping of the subcell momentum, the mass fluxes are used to construct the momentum fluxes by multiplying a reconstructed velocity in the swept region. The nodal velocity is then conservatively recovered. Some numerical examples simulated in the full MMALE regime and several purely cyclic remapping examples are presented to prove the properties of the remapping method.

A robust and efficient polyhedron subdivision and intersection algorithm for three-dimensional MMALE remapping

The Multi-Material Arbitrary Lagrangian Eulerian (MMALE) method is an effective way to simulate the multi-material flow with severe surface deformation. Comparing with the traditional Arbitrary Lagrangian Eulerian (ALE) method, the MMALE method allows for multiple materials in a single cell which overcomes the difficulties in grid refinement process. In recent decades, many researches have been conducted for the Lagrangian, rezoning and surface reconstruction phases, but less attention has been paid to the multi-material remapping phase especially for the three-dimensional problems due to two complex geometric problems: the polyhedron subdivision and the polyhedron intersection. In this paper, we propose a “Clipping and Projecting” algorithm for polyhedron intersection whose basic idea comes from the commonly used method by Grandy (1999) [29] and Jia et al. (2013) [34]. Our new algorithm solves the geometric problem by an incremental modification of the topology based on segment–plane intersections. A comparison with Jia et al. (2013) [34] shows our new method improves the efficiency by 55% to 65% when calculating polyhedron intersections. Moreover, the instability caused by the geometric degeneracy can be thoroughly avoided because the geometry integrity is preserved in the new algorithm. We also focus on the polyhedron subdivision process and describe an algorithm which could automatically and precisely tackle the various situations including convex, non-convex and multiple subdivisions. Numerical studies indicate that by using our polyhedron subdivision and intersection algorithm, the volume conversation of the remapping phase can be exactly preserved in the MMALE simulation.

Evaluation of Appropriate Material Models in LS-DYNA for MM-ALE Finite Element Simulations of Small-Scale Explosive Airblast Tests on Clay Soils

This study conducted finite element simulations of a small scale, explosive airblast on clay soil in LS-DYNA using multi-material arbitrary Lagrangian–Eulerian methods. An explosive mass of 100.9 g with a 7.6 cm blast height was simulated in this study under two-dimensional conditions. The study compared four different material models to evaluate their ability to simulate explosively-induced airblast loads on cohesive soils. Material models included the Soil and Foam pressure dependent strength model, the Pseudo Tensor pressure dependent strength model, the FHWA Drucker–Prager model and the Two-Invariant Geologic Cap model. Crater dimensions were measured from the simulations and compared to the results of airblast experiments performed in another study. Three material models ran to completion with the exception of the Geologic Cap model, which terminated early in the calculation due to plasticity algorithm errors caused by the large strain increments. While the remaining three models somewhat over-predicted crater depth, the diameter dimensions and crater volumes from the Soil and Foam and particularly the Pseudo Tensor model compared very well to the experimental data. The crater shape from the FHWA model did not match particularly well with experimental results and was larger than the experimental crater. A simplified, pressure dependent strength model such as Soil and Foam model or the Pseudo Tensor model is therefore recommended for modeling small-scale airblast events on cohesive soils. The Pseudo Tensor model compared particularly well to experimental results and predicted crater dimensions very well. Additional studies with the Geologic Cap model implementing smoothed particle hydrodynamics are recommended which may resolve the errors associated with large strain increments.

Modeling and Evaluation of Loads in Vehicles Subjected to Mine Blast

In the paper, the numerical and experimental approach to the blast load evaluation was presented. The evaluation process is done in two steps. In the first, the full scale blast test is carried out with a simply mock-up resembling geometry of the bottom part of a vehicle. The pressure impulse is measured indirectly using a high speed camera and the motion analysis software. In the second step, a numerical simulation with the use of Multi Material Arbitrary Lagrangian-Eulerian method is utilized to assess the influence of the fluid-structure interaction and the real vehicle mass on the value of the applied pressure impulse. In the paper, the application of method was presented and the results were discussed.

Constrained optimization framework for interface-aware sub-scale dynamics closure model for multimaterial cells in Lagrangian and arbitrary Lagrangian–Eulerian hydrodynamics

A systematic description of the new interface-aware sub-scale-dynamics (IA-SSD) closure model for the Lagrangian stage of multimaterial arbitrary Lagrangian–Eulerian methods is presented. The IA-SSD closure model consists of two stages. During the first, bulk, stage, the well known equal compressibility model is used. During the second stage, sub-scale interactions of the materials inside the multimaterial cell are taken into account. At this stage, information about the topology of the materials inside the multimaterial cell is utilized, allowing the orientations of internal interfaces to be included in the model. Each material interacts in a pair-wise fashion with the materials with which it has a common boundary. The interactions are based on the solution of the acoustic Riemann problem between each pair of materials and is limited using physically justified constraints: positivity of volume, positivity of internal energy and controlled rate of pressure relaxation. To determine the values of the limiter coefficients, a constrained-optimization framework is employed using a quadratic objective function with linear constraints. The algorithm guarantees the positivity of the material volume and internal energy as well as the smooth relaxation of the pressure – this allows a significant increase in the robustness of the overall algorithm.The results of comprehensive testing of the new model have been presented for one- and two-dimensional multimaterial Lagrangian hydrodynamics along with representative results for 2D multimaterial arbitrary Lagrangian–Eulerian (ALE) calculations. The numerical tests have shown that in most cases the new IA-SSD closure model produces better results compared to the well known Tipton's closure model.

MMALE numerical simulation for multi-material large deformation fluid flows

Multi-material arbitrary Lagrangian Eulerian (MMALE) method, coupled with moment of fluid (MOF) interface reconstruction, was studied and applied to multi-material large deformation flow problems. In MMALE method, the mesh lines are allowed to cross the material interfaces and mixed cells are introduced. In mixed cells, the MOF method is used to reconstruct the interfaces. The numerical examples show the high accuracy and resolution of MOF-MMALE, it is validated that MOF-MMALE method is an effective way to simulate flow problems of multi-material large deformation.

Numerical modeling of large deformations in soil structure interaction problems using FE, EFG, SPH, and MM-ALE formulations

Present design practice for soil structure interaction (SSI) problems most frequently assumes linear elastic properties of the soil and disregards geometrical nonlinearities, treating the displacements as small. However, there are numerous problems that require a more advanced approach. This paper presents an application of such numerical approaches to modeling SSI problems in the presence of large soil deformations. Simulations using Lagrangian finite element, element-free Galerkin, smoothed particle hydrodynamics (SPH), and multi-material arbitrary Lagrangian Eulerian (MM-ALE) approaches were performed for two previously conducted experimental tests: (1) large-scale steel pad penetration into silty clay with sand and (2) standard cone penetration test performed on poorly graded sand. In this paper, the usefulness and the efficiency of the methods was assessed in terms of modeling robustness and computational cost. Results show that to some extent each of the utilized methods is able to capture large deformations. However, the most robust turned out to be SPH and MM-ALE methods as the only two that were successful in simulating both experiments.

Conservative multi-material remap for staggered multi-material Arbitrary Lagrangian-Eulerian methods

Remapping is one of the essential parts of most multi-material Arbitrary Lagrangian-Eulerian (ALE) methods. In this paper, we present a new remapping approach in the framework of 2D staggered multi...

Conservative multi-material remap for staggered multi-material Arbitrary Lagrangian–Eulerian methods

Remapping is one of the essential parts of most multi-material Arbitrary Lagrangian–Eulerian (ALE) methods. In this paper, we present a new remapping approach in the framework of 2D staggered multi-material ALE on logically rectangular meshes. It is based on the computation of the second-order material mass fluxes (using intersections/overlays) to all neighboring cells, including the corner neighbors. Fluid mass is then remapped in a flux form as well as all other fluid quantities (internal energy, pressure). We pay a special attention to the remap of nodal quantities, performed also in a flux form. An optimization-based approach is used for the construction of the nodal mass fluxes. The flux-corrected remap (FCR) approach for flux limiting is employed for the nodal velocity remap, which enforces bound preservation of the remapped constructed velocity field. Several examples of numerical calculations are presented, which demonstrate properties of our remapping method in the context of a full ALE algorithm.

An effective integration of methods for second-order three-dimensional multi-material ALE method on unstructured hexahedral meshes using MOF interface reconstruction

This paper presents an effective second-order three-dimensional unstructured multi-material arbitrary Lagrangian–Eulerian (MMALE) method for compressible fluid dynamics. This is an integration work. The MMALE method utilizes Moment of Fluid (MOF) capability with interface reconstruction for multi-material modeling of immiscible fluids. It is of the explicit time-marching Lagrange plus remap type. In the Lagrangian phase, the staggered compatible discretization for Lagrangian gas dynamics is used also with Tipton’s pressure relaxation model for the closure of mixed cells. For the remapping phase, an improved second-order cell-intersection-based method for three-dimensional unstructured mesh is presented. It is conservative for remapping cell-centered variables such as density and internal energy. It is suitable for remapping between two meshes with different topology. By using this remapping method, the new material centroid position in the rezoned cells can be geometrically computed. This enables it to be combined with the MOF algorithm for constructing a second-order MMALE method. The MMALE method can be implemented on three-dimensional unstructured hexahedral meshes. Numerical results have proved the accuracy and robustness of the MMALE method.

One-step hybrid remapping algorithm for multi-material arbitrary Lagrangian–Eulerian methods

In this paper, a new flux-based one-step hybrid remapping method for multi-material arbitrary Lagrangian–Eulerian (ALE) approach is introduced. In the vicinity of material interfaces, the swept region is intersected with pure material polygons in the Lagrangian mesh to construct the material fluxes. Far from interfaces, the fluxes are constructed in a standard swept-region manner without intersections. This method is conservative, second-order accurate and linearity-preserving (in case of straight material interfaces), and faster than method based on intersections, as shown on selected numerical examples.

자유낙하식 구명정의 가속도 응답 추정을 위한 LS-DYNA 에서의 다중물질 ALE 와 단일물질 ALE의 비교

An interest in Arbitrary Lagrangian Eulerian (ALE) finite element methods has been increased due to more accurate responses in Fluid-Structure Interaction(FSI) problems. The multi-material ALE approach was applied to the prediction of the acceleration response of free-fall lifeboat, and its responses were compared to those of the single-material ALE one. It could be found that even though there was no big difference in the simulation responses of two methods, the single-material and multi-material ALE ones, the latter multi-material ALE method showed a little bit more close response to those of experimental results compared to the former single-material ALE one, especially in the x- and z-direction acceleration responses. Through this study, it could be found that several parameters in the ALE algorithms have to be examined more carefully for a good structural safety assessment of FSI problems.