Multi-material Arbitrary Lagrangian Eulerian Research Articles

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.

A Numerical Sensitivity Analysis of Fluid-Structure Interaction Simulations on Slamming Loads and Responses

This paper presents a parametric study on the Multi Material Arbitrary Lagrangian–Eulerian (MMALE) method for hydroelastic analysis of a non-prismatic stiffened aluminium wedge. An explicit finite element formulation with a penalty-based coupling technique is employed to evaluate the impact-induced loads and responses during free-fall water entry. Based on the penalty factor, damping factor, and number of coupling points, a sensitivity analysis is carried out. It is shown that the penalty coupling method can generate high-frequency oscillations due to the nature of the phenomenon that may affect the predicted results of slamming loads. The computed results on the stiffened and unstiffened plates of the wedge are compared with published experimental data in terms of vertical acceleration, pressure distributions, and strain responses at different locations. A reasonable agreement can be found between the numerical results and the measured values. It is found that a combination of penalty and damping can improve the simulation results and reduce numerical instabilities in hydroelastic slamming simulations.

WITHDRAWN: Effect of geo-material on dynamic response of tunnel subjected to surface explosion

Prime materials involved in a problem such as underground structures are concrete, reinforcement steel and geo-material surrounding the tunnel. Among these three materials, concrete and steel are manufactured materials and their properties can be controlled up to a certain extent. However, geomaterial is a naturally occurring material whose constitutive properties vary from region to region making it highly unpredictable. Findings from one study cannot be applied to other geotechnical problems directly, especially, in the case of tunnels subjected to surface explosion. The blast wave generated has to travel through the geo-material before it interacts with the tunnel. As the shock wave propagates radially its characteristics are most likely to get altered by the geo-material. Limited study has been carried out considering this problem. In the present study, the effect of various types of geo-material on the blast response of tunnels subjected to surface explosion is investigated. Finite element analysis has been carried out using LS-DYNA® wherein the problem has been modelled using multi-material arbitrary Lagrangian Eulerian (MM-ALE) method. Materials with fluid behavior such as air, explosive and soil are modelled using ALE formulation. Other materials including tunnel lining, reinforcing steel and rock are modelled using Lagrangian formulation. Blast loading is simulated using Jones-Wilkins-Lee (JWL) equation of state. Geo-materials considered for the comparative study are sandy loam, sandstone, and granite. Vertical displacement measured at the crown of the tunnel is used to determine the response of tunnel. Sandy loam soil being a highly compressible soil, exhibits non-linear and fluid-like behavior under high strain loading such as explosion. Tunnel undergoes extreme deformation in the case of sandy loam soil as compared rock cases. Additionally, the effect of weathering of rock on the tunnel response is investigated in the case of sandstone and granite. It was observed that weathering rock led to more displacement of tunnel crown as compared to intact rock.

Experimental and Numerical Study on the Residual Axial Capacity of RC Bridge Piers after Contact Explosion

Bridge piers damaged by accidental or deliberate explosions lose a portion of their axial carrying capacity, which can induce partial and/or complete collapse of the entire bridge structure. With the aim of evaluating blast-damage and establishing blast-resistant design approaches for bridge piers, the dynamic behaviors and residual axial-load-bearing capacities (ALC) of RC piers subjected to contact explosions were studied experimentally and numerically. First, five circular cross-sectional 1/2-scale RC piers, with a height of 3 m and diameter of 450 mm, were fabricated. A field contact-explosion test on three pier specimens was conducted using TNT charge weights of 0.5, 1.0, and 2.0 kg. Then, these three postblast plus another two intact RC piers were transported to the laboratory to experimentally examine the axial bearing capacities using a hydraulic testing machine. The test data obtained included the incident overpressure–time histories and quantitative postblast damage profiles of the piers, and full curves for the axial force-displacement. Second, corresponding high-fidelity finite-element (FE) models of both the contact explosion and the succeeding axial compression tests were established. The refined numerical simulations were performed by adopting the fluid–structure interaction, multimaterial arbitrary–Lagrangian–Eulerian, and erosion algorithms implemented in the FE program LS-DYNA. The material model and the FE analysis approach were comprehensively verified by comparing the numerical simulated results with the test data. A series of numerical simulations were also conducted on seismically designed prototype bridge piers in order to examine the parametric influences on the damage mode and residual ALC, and the corresponding damage index of the piers. Finally, based on the parametric study, several blast-resistant design suggestions are proposed for prototype RC bridge piers against contact explosions.

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.

Compatible and energy conserving multi-material arbitrary Lagrangian Eulerian scheme for multi-group radiation hydrodynamics simulations

A compatible, bounds preserving and energy conserving multi-material arbitrary Lagrangian Eulerian (ALE) scheme suitable for an unstructured mesh is developed for multi-group radiation hydrodynamics (RHD) simulation of various high energy density physics (HEDP) phenomena involving large material deformations, such as intense thermal radiation or high-power laser driven systems. In order to study very short time scale HEDP phenomena, the electron and ion energy equations (with the effect of electron-ion energy relaxation) are solved separately with an assumption of single macroscopic fluid velocity for each species (two-temperature hydrodynamics model). The governing multi-material hydrodynamics equations are solved by using a higher-order cell-centered hydrodynamics (CCH) scheme. In multi-material flows, the remapping step introduces mixed computational cells in which multiple materials exist in a single cell. Therefore, material interfaces in mixed cells are required to be reconstructed and tracked. In our implementation, this is achieved by using moment-of-fluid (MOF) method. The information of these interfaces is further used to formulate an interface aware sub-scale dynamics (IASSD) scheme for multi-material closure in mixed computational cells. The IASSD scheme is generalized for the two-temperature hydrodynamics model in which separate equations are used to update the electron and ion energies. The multi-group radiation transport on an unstructured mesh is computed using a cell-centered, monotonic, nonlinear finite volume (NLFV) scheme. The flux-limited diffusion (FLD) approximation is used to recover the free-streaming limit of the radiation propagation in optically thin regions. In the ALE step, the electron, ion and radiation energies due to MG-RHD model are conservatively remapped using a center-of-mass (CM) reconstruction of the fields and a compatible and energy conserving remapping scheme. An exact integration based on the intersection between the new (rezoned) and old meshes is used in the remap step. Similar procedure is followed for the remap of cell mass and cell-centered momentum components. In this paper, the details of a compatible, bounds preserving and conservative ALE scheme developed for MG-RHD are described. The remapping of relevant physical quantities due to multi-physics models implemented in the code such as non-local electron energy transport are also discussed. Several validation test problems including laser driven shock propagation in multi-material geometries are provided to demonstrate the accuracy and performance of the ALE scheme implemented.

Effect of Horizontal Curve on the Response of Road Tunnels under Internal Explosion

Internal explosion in a tunnel is a complex loading phenomenon where the tunnel lining is subjected to not only direct impact of explosion but also loading due to multiple reflection of blast waves which could be of magnitude higher than that of incident blast wave. This kind of loading is complex in nature and difficult to predict using simple analysis tools. Further, it poses a serious threat to its structural integrity. Studies have been conducted in the past to understand the behaviour of tunnel under internal explosion. However, they have been focused on straight tunnels ignoring the convex and concave shapes introduced due to horizontal and vertical curves. Shape of the target surface has significant effect on the characteristics of blast wave. This study investigates the effect of horizontal curves on the damage behaviour of tunnel lining due to internal explosion. A series of numerical simulation are performed on box-shaped tunnel with varying curvature radius and the results are compared with that of straight tunnel adopting Multi-Material Arbitrary Lagrangian-Eulerian (MM-ALE) method using LS-DYNA®. Explosive and air are modeled using ALE formulation, whereas, tunnel and soil are modeled using Lagrangian formulation. Further, Jones-Wilkins-Lee equation of state is used to model the explosion. Damage to the tunnel lining is measured in terms of peak particle velocity (PPV) and von-Mises stress. It is observed that walls of curved tunnels undergo more PPV compared with straight tunnel wherein concave wall show the highest PPV. Propagation of blast wave along the tunnel length is significantly affected due to the introduction of curvature resulting in change in reflection patterns. This further leads to variation in stress contours on tunnel lining with higher concentration of stress in curved tunnels than in straight tunnel.

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.

Dynamic behavior and retrofitting of RC frame building under vehicular bomb explosion

Although the terrorist explosion attacks on critical buildings caused by the Vehicle-Borne Improvised Explosive Device (VBIED) are low-probability events, the blast-induced progressive collapse of buildings generally lead to the catastrophic consequences of the events. Through the high-fidelity hybrid finite element (FE) model and numerical simulations, this work aims to get a deep insight into the progressive collapse behavior of high-rise reinforced concrete (RC) frame buildings under blast loadings induced by VBIED, as well as the feasibility of two blast-resistant external retrofitting measures, i.e., fiber reinforced polymer (FRP) and steel plate (SP). Firstly, the applicability of the hybrid FE modelling approach, element types and size, material models and parameters, as well as numerical algorithms, i.e., multi-material Arbitrary Lagrangian-Eulerian (MM-ALE) and Fluid-Structure Interaction (FSI), are fully validated by comparing with the explosion tests on 1/4-scale bare and prototype FRP/SP-retrofitted RC frame structures, respectively. Then, a twelve-story RC frame building is designed following the Chinese regulations, and the corresponding hybrid FE model is established. The failure modes and progressive collapse process of building under the explosions of cargo vans bomb (equivalent TNT of 1814 kg) specified by Federal Emergency Management Agency are numerically examined. Furthermore, the effectiveness of FRP/SP-retrofitted frame columns is assessed quantitatively. It derives that, the SP-retrofitted building is not collapsed for both the scaled distance of 1.0 and 0.55 m/kg1/3; by retrofitting FRP warps, the collapse of entire buildings can be prevented with the scaled distance of 1.0 m/kg1/3, while the progressive collapse of the retrofitted building occurs with a scaled distance of 0.55 m/kg1/3. The present work could provide helpful references for the blast-resistant evaluation, design and retrofitting of the as- and newly-built RC building structures.

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.

Effect of Geo-Material on Dynamic Response of Tunnel Subjected to Surface Explosion

Prime materials involved in a problem such as underground structures are concrete, reinforcement steel, and geo-material surrounding the tunnel. Among these three materials, concrete and steel are manufactured materials and their properties can be controlled up to a certain extent. However, geo-material is a naturally occurring material whose constitutive properties vary from region to region, making it highly unpredictable. Findings from one study cannot be applied to other geotechnical problems directly, especially in the case of tunnels subjected to surface explosions. The blast wave generated has to travel through the geo-material before it interacts with the tunnel. As the shock wave propagates radially, its characteristics are likely to be altered by the geo-material. Limited study has been carried out considering this problem. In the present study, the effect of various types of geo-material on the blast response of tunnels subjected to surface explosions is investigated. Finite element analysis has been carried out using LS-DYNA®, wherein the problem has been modeled using the multi-material arbitrary Lagrangian–Eulerian (MM-ALE) method. Materials with fluid behavior such as air, explosives, and soil are modeled using ALE formulation. Other materials including tunnel lining, reinforcement steel, and rock are modeled using Lagrangian formulation. Blast loading is simulated using the Jones–Wilkins–Lee (JWL) equation of state. Geo-materials considered for the comparative study are sandy loam, saturated clayey soil, sandstone, and granite. Vertical displacement measured at the crown of the tunnel is used to determine the response of the tunnel. Sandy loam soil, being a highly compressible soil, exhibits non-linear and fluid-like behavior under high-strain loading such as explosions. Tunnels undergo extreme deformation in the case of sandy loam soil and clayey soil compared to rock cases. Further, the effect of saturation in sandy loam on tunnel stability is studied. It is observed that with the increase in saturation of soil, more blast energy is transmitted to the structure, which results in higher deformation. Lastly, the effect of the weathering of rock on the tunnel’s response is investigated in the case of sandstone and granite. It was observed that weathering in rock led to more displacement of tunnel crown when compared to intact rock.

Local damage of precast concrete columns with grout sleeve connections under contact detonation

Over the past several decades, the global terrorism is looming large and public buildings have become targets of terrorist bomb attacks. To obtain the blast performance of precast concrete (PC) columns with grout sleeve connections at the background of terrorist attacks, the contact detonation is concerned in this paper. An experimental program with six PC columns and one reinforced concrete column against contact detonation was conducted in a blast testing vessel, in which the effects of charge weight and location as well as connection type of columns on blast damage were studied. Then the finite-element-based (FE) numerical models were built up with LS-DYNA and validated with comparison of experimental results. In the FE model, blast load is simulated using multi-material Arbitrary-Lagrangian-Eulerian (MM-ALE) algorithm. After careful validation, the numerical models are extended to conduct parametric studies, including the effects of longitudinal and transverse reinforcement ratio, column section depth (or aspect ratio), charge weight and location, axial compression ratio on the blast damage of PC columns. Finally, curve-fitting-based models are derived to build up relationships between local damage sizes and the studied parameters, and then verified with part of numerical results. The results show that contact detonation destroyed all the concrete cover at the front face supporting the charge, and resulted in severe spall damage along the four corners and side faces, in which the corner connecting the side and rear face suffered larger damage than that connecting the side and front face. Moreover, the grout sleeves are able to mitigate the damage if the detonation is at the splicing segments. Increasing reinforcement ratio, section depth and axial compression ratio are able to reduce damage sizes, but the beneficial effect differs for the local damage at the column corners and front face.

NUMERICAL PREDICTION OF SLAMMING LOADS DURING WATER ENTRY OF BOW-FLARED SECTIONS

The two-dimensional water entry of bow-flared sections is studied by using a Multi-Material Arbitrary Lagrangian- Eulerian (MMALE) formulation and a penalty-coupling algorithm. A convergence study is carried out, considering the effects of mesh size, the dimension of fluids domain, and fluid leakage phenomenon through the structure. The predicted results on the wetted surface of a bow-flared section are compared with published experimental values in terms of vertical slamming force, pressure distributions at different time instances and the pressure histories at different points. Comparisons between the numerical results and measured values show satisfactory correlation. An approximation method is adopted to estimate the sectional slamming force showing good consistency for the peak forces.

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%.

Response of R.C. plates under blast loading using FEM-SPH coupled method

Response of reinforced concrete (R.C.) plates subjected to blast loading is numerically investigated through a hybrid discretization combining FEM and smoothed particle hydrodynamics (SPH). Initially, the structure is discretized via Lagrangian finite elements. If any element undergoes large deformation, it is replaced by particles. Interaction between FEM and SPH is established through a transition layer. Three different idealizations of the actual blast event involving multiphase continuum (explosive, air and structure) is considered, viz. Load Blast Enhanced (LBE) where only the structure is modeled and empirically calculated blast pressure is applied to the structure; Multi-Material Arbitrary Lagrangian Eulerian (MM_ALE) where the explosive, air and structure all are explicitly modeled; and coupled LBE & MM_ALE where the structure is encapsulated in a receptor and blast pressure is applied on the receptor. Simulations are performed to investigate the effects of various parameters such as standoff distance, boundary conditions etc., on the overall response of the structure.

Computational modeling and dynamic response of highway bridge columns subjected to combined vehicle collision and air blast

Vehicle impacts into supporting bridge columns can cause significant damage and, when combined with an air blast, could result in, at best, an unsafe situation for the bridge or, at worst, complete collapse. Limited studies have been conducted that investigate the response of bridge substructure units subjected to a combined collision and blast loading. This paper summarized results from a numerical study examining the response of highway bridge columns subjected to a combined vehicle collision and air blast using LS-DYNA, the computational tool used for this research. Numerical models consisting of a circular reinforced concrete (RC) bridge column, its pile cap and pile foundation system, and a surrounding soil volume were developed and validated. Validated models were then subjected to simulated impacts from a Ford F800 Single-Unit Truck (SUT) and air blasts represented using a Multi-Material Arbitrary Lagrangian-Eulerian (MM-ALE) formulation with applied blast loads being taken from the fluid-structure interaction (FSI) algorithm in LS-DYNA. The validated computational modeling technique presented in this study provides a vital source for producing information in the combined collision and blast design field and determining the combined impact-blast behavior of bridge columns. A detailed investigation was performed to determine a critical impact and blast sequence for this research study. Furthermore, numerical simulations of SUT collision with RC column coupled with air blast were conducted considering variations of vehicle velocity, blast scaled distance, and column diameter. The demand and performance of RC bridge columns were examined with representative damage categories identified in this study to provide insights on column design to withstand the collision and blast combination.

Numerical Simulation of Blast Loaded CFRP Retrofitted Steel Plates

This paper reports on the results of a numerical study to simulate the response of carbon fibre reinforced polymer (CFRP) retrofitted steel plates to applied blast loads using finite element software, LS-DYNA. The results of the simulation were validated against plate response and magnitude of deformation obtained from previous experiments. The uniform blast load was generated in the experiment by detonating a cylindrical charge down the end of a square tube. The finite element code LS-DYNA was used to simulate the structural response of the respective blast structures. For the numerical model, the blast load was simulated using the mapping feature available in LS-DYNA for the multi-material arbitrary Lagrangian-Eulerian (MM-ALE) elements which significantly reduced the size of the air domain in the model. The simulations showed a satisfactory correlation with the experiments for the blast results and post-failure deformations that occurred in CFRP retrofitted steel plates.

Prediction of slamming pressure considering fluid-structure interaction. Part I: numerical simulations

ABSTRACT Marine structures are subjected to slamming loads characterised by high hydrodynamic pressure within short time durations. Such loads can cause local and global damages to structures. This paper, which is Part I in a series, reports a numerical investigation of slamming loads acting on flat stiffened plates and their dynamic response. The nonlinear explicit finite element code LS-Dyna with the Multi-Material Arbitrary Lagrangian-Eulerian (MMALE) solver was adopted to simulate the slamming impact on marine structures. The numerical method was validated by the relevant experimental data from the open literature in a comparison of slamming pressure and deflection data, as well as existing formulations. The Eulerian formulation was applied to describe the fluid flow, and a Lagrange formulation was employed to model flat stiffened plates. A penalty coupling algorithm was utilised to realise the fluid-structure interaction (FSI) between the plate and the fluid. Bilinear strain hardening with no strain-rate hardening and effect of the heat-affected zone (HAZ) were considered for the numerical simulation of the aluminum model, while nonlinear strain hardening and strain-rate hardening were adopted to verify the steel models. Effects of key influenced parameters such as water impact velocity, material behaviour, and air cushion on the slamming response were addressed accordingly. Additionally, a simulation of water hitting structure was proposed to investigate the slamming load characteristics acting on the bottom decks of offshore structures. As the next paper in this continuing series, Part II will present empirically derived formulations for prediction of slamming loads based on extensive parametric studies of actual scantlings of offshore structures, using the simulation methodology of water hitting proposed herein in Part I.

Numerical Analysis of Shock Initiation on Highly Energetic Material LX-04

The paper presents investigation of shock initiation effects on highly energetic material LX-04, an HMX based one, by a blunt brass projectile using numerical modelling methods implemented in LS-Dyna software. Multi – Material Arbitrary Lagrangian Eulerian (MM-ALE) formulation has been used to provide the possibility of fulfilment of the elements with multiple materials accordingly to multiple phases of the composition detonated. The work is focused on LS-Dyna’s equation of the state keyword *EOS_IGNITON_AND_GROWTH_IN_HE. Proper comparison with experimental data is presented. The introduction into the subject of highly nonlinear transient dynamic finite element analysis, possibilities, and superiority of this kind of modelling are being discussed. Reasons of sustaining the need of data by numerical solutions rather than experimental handling in military applications are given. Some of typical technical issues, occurring during such a fast-performing phenomenon, and the need of experimental validation of the models are typed together with detonation-state determination’s observation capabilities.