The Eulerian method in Abaqus
The Eulerian method is a numerical technique used to analyze fluid mechanics problems. In this approach, the fluid is treated as a fixed grid, where the nodes remain stationary while the fluid flows through them. This method is particularly useful when dealing with problems that involve large deformations or high strain rates, as it can simulate fluid dynamics without causing mesh distortion. Eulerian Abaqus modeling is fully discussed here.
In Abaqus, the Eulerian method can be used to analyze fluid-structure interactions, such as the fluid impact on structures or the behavior of fluids in containers. To use the Eulerian method in Abaqus, the desired geometry must first be meshed using Eulerian elements. The material behavior of the fluid is then defined using appropriate equations of state. Finally, the boundary conditions and loading are applied, and the system is solved using the appropriate numerical method, such as the finite element method.
The Eulerian method is important because it provides an efficient way to simulate complex fluid dynamics problems without causing mesh distortion or element distortion, which can lead to inaccurate results. Additionally, it can be used to analyze a wide range of fluid-structure interactions, including those involving high-velocity impacts or explosive phenomena. By accurately predicting the behavior of fluids, the Eulerian method can help improve the design and safety of structures that interact with fluids, such as pipelines, dams, and offshore platforms.
Workshop 1: Damage analysis of an underground box tunnel subjected to surface explosion
In recent times, the safety of tunnel structures has been significantly impacted by external terrorist activities due to the lack of adequate measures to detect such incidents in a timely manner and prevent them. To investigate the behavior of an underground box frame tunnel subjected to a surface explosion, a simulation was conducted using ABAQUS software. In this simulation, TNT waves were propagated through the air and soil using Explicit analysis, resulting in the creation of stress in the concrete tunnel.
Workshop 2: Damage mechanism and the response of reinforced concrete containment structure under internal explosion
It is imperative to construct and operate a reinforced concrete containment for nuclear power plants to safeguard both the population and environment against uncontrolled radioactive release during severe internal or external accidents like earthquakes, large fires, or jet aircraft impact, which may occur during the plant’s operational lifetime. Precisely determining the response of the reinforced concrete containment to blast loading parameters for a specific distance scale is essential. Most parameters for modeling the interactions of blast shock waves are available and have been extensively documented. This tutorial investigates the dynamic response and damage mechanism of the reinforced concrete containment under internal blast loading at varying distance scales. The extent of concrete cracking, the stress in steel bars and concrete after yielding, and deflections are presented as measures of the effects of an explosion inside the containment. This tutorial specifically examines a CEL explosion within the RC Concrete vessel, and the volume fraction method has been implemented to model the Eulerian explosion.
Workshop 3: Liquid storage tank dynamic analysis subjected to blast loading using coupled Euler–Lagrange method
The human civilization faces an increasing threat from terrorist attacks all around the world. Over the past 20 years, bomb explosions in crowded areas like business districts, underground railway stations, and busy roads have caused significant loss of life and property damage in various parts of the world. However, the blast response of many critical civil infrastructures still remains poorly understood due to the complex material behavior, loading, and nonlinearity involved. One such example of crucial civil infrastructure is liquid storage tanks, which are integral components of any society for storing water, milk, liquid petroleum, and chemicals in industries. A blast loading on these structures can lead to a crisis in water and milk supply, health hazards due to chemical spread, and fire hazards due to the spread of liquid fuel. Therefore, it is crucial to understand the dynamic behavior of liquid storage structures under blast loading through numerical simulations. This study presents 3D finite element simulations of a steel water storage tank for different tank aspect ratios using Abaqus software. The tutorial outlines the modeling procedure for a blast simulation over a water-filled tank, where the CONWEP procedure is implanted to model the blast effect. The water is modeled as an Eulerian part to visualize its sloshing during the explosion, and the tank is modeled using shell elements.
Workshop 4: Tunnel dynamic analysis subjected to internal blast loading using the CEL method
This tutorial uses the CEL method in Abaqus to explore the dynamic analysis of a soil tunnel subjected to internal blast loading. The concrete tunnel is modeled as a solid part, while the domain is represented by an Eulerian part. Additionally, the TNT and soil are modeled as solid parts, while the wire part represents the beam.
Underground tunnels, including roadways, railways, utility lines, and water pipelines, are essential components of civil infrastructure. However, in recent decades, the threat of explosion incidents caused by terrorist activities within these tunnels has increased, posing a significant risk to human safety. Internal explosions in tunnels can be particularly dangerous due to the multiple reflections of the shock wave on the tunnel walls, causing channeling of the shock wave. To protect tunnels from such incidents, it is necessary to design them to withstand blast loading, which requires a thorough understanding of their response to such loading, both experimentally and numerically. The current study focuses on advanced numerical analysis of tunnels subjected to blast loading, with the aim of improving their safety and resilience against potential terrorist threats.
In this study, the materials used for the beams, soil, TNT, and concrete tunnel were selected based on their specific properties. The beams were made of steel with elastic-plastic behavior and a ductile damage criterion, while the soil was modeled with elastic and Mohr-Coulomb plasticity. The TNT was described using the JWL equation of state, and the concrete tunnel was modeled using the Johnson-Holmquist model due to the high pressure and potential for failure. A dynamic explicit procedure was considered appropriate for this type of analysis. General contact was used for all contacts in the domain, and an embedded region was used for the beams inside the concrete host. The volume fraction method was used to determine the location and amount of TNT in the Eulerian model. Proper boundary conditions were assigned to the Eulerian domain and concrete tunnel. The mesh size had a significant effect on the results, and a smaller mesh size was deemed necessary.
Once the simulation is complete, all results, including variables such as concrete damage, stress, damage to beams, and strain, can be obtained.
Workshop 5: Water column collapsing simulation using the Eulerian Abaqus simulation
In this workshop, a dynamic fluid flow event involving large deformation is modeled using the pure Eulerian analysis technique. The event involves the collapse of a water column under gravity load. To model the water and the domain, only one Eulerian part has been created. The dynamic explicit method is suitable for Eulerian analysis, and due to the height of the column, geostatic stress has been applied to it.
workshop 6: 3D orthogonal simulation using CEL method
Most of the current finite element models for cutting are limited to the 2D plane strain orthogonal cutting configuration. While this is useful for studying the fundamental aspects of the process, it does not fully represent practical cutting operations. On the other hand, 3D models typically involve a 2D tool path with a non-straight cutting edge, and the step just after 2D orthogonal cutting, which is the 3D orthogonal cutting, is rarely addressed. Due to its high complexity and involvement of various phenomena, the process is primarily studied in orthogonal cutting to reduce the geometrical difficulties and number of degrees of freedom of the models. However, the physical coupled phenomena, such as large strains, strain rates, high temperatures and temperature gradients, and friction, must still be considered and addressed. This has led to numerous publications. To address this issue, this video introduces a 3D finite element Coupled Eulerian-Lagrangian (CEL) model for the simulation of orthogonal cutting.
The Johnson-Cook constitutive model, which is well-known in metal cutting modeling, is used to describe the behavior of the Ti6Al4V titanium alloy workpiece material. The Johnson-Cook material model is suitable for analyzing high strains with rapid loading speeds. In this study, the Johnson-Cook equation with temperature is considered. Dynamic Temp Explicit is a suitable method for this type of analysis, and the Volume Fraction method is used to define the initial volume of the workpiece.
workshop 7: FSW of two pieces of copper
This file includes a CAE file and a video that provides a step-by-step explanation of the Friction Stir Welding process. The Eulerian element is used for two copper pieces, while the Lagrangian element is used for the tool. During the analysis, the temperature distribution in the two pieces can be observed.
Friction Stir Welding (FSW) is a joining process that involves the frictional heating and plastic deformation of two parts that are in contact with a non-consumable welding tool. Experiments for FSW can be time-consuming and expensive. To address these issues, numerical analysis has been increasingly used in recent years. Various simplified numerical models have been developed to better understand the complex thermo-mechanical phenomena associated with FSW.
workshop 8: Water jet spot welding simulation using the CEL method
Spot welding is a popular method for creating a quick and permanent joint between lightweight industrial metallic parts, particularly in the automotive industry. Electrical resistance welding is the most commonly used technique for spot welding, but it has some limitations, such as the inability to weld metals with far melting points and the risk of surface oxidation. To overcome these limitations, alternative methods such as explosive welding, laser spot welding, and impact spot welding have been introduced. Impact spot welding, in particular, offers a high-quality, steady, and reliable connection between parts by creating solid-phase bonding and interlock between surfaces. This involves a high-velocity projectile or slug of water impacting a predetermined point to create a permanent connection in the neighboring zone. Eulerian analysis is a suitable technique for problems involving extreme material deformations, especially in fluid flow modeling. In this technique, the nodes are fixed in space, allowing the material to undergo extreme deformations and strain rates while eliminating the possibility of element distortion. On the other hand, in Lagrangian analysis, the nodes are fixed within the material, and the material boundary coincides with element boundaries. Therefore, the elements deform as the material deforms. The Lagrangian technique is well-suited for problems involving solid materials. However, in situations where the strain rate in a solid medium is too high and the material behaves like a fluid medium, Eulerian analysis is more appropriate.
To accurately describe the behavior between two plates, a dynamic explicit step with surface-to-surface contact and frictional behavior is used. The uniform material assignment is applied to model water as an Eulerian part with an initial velocity. During the impact, the flyer plate moves through the base plate, resulting in significant stress between the two plates in the contact zone, which causes them to form a joint.
workshop 9: The effects of water mitigation on a blast wave simulation using the Eulerian method
The use of a water wall to surround an explosive has proven to be an effective way of reducing the impact of the shock wave and blast pressure resulting from an accidental explosion. When an explosion occurs, the high-pressure shock wave generated by detonation aerosolizes the water near the explosive, causing a phase change in the water and the redistribution of internal and kinetic energy among the detonation gases, blast waves, and barrier material. Due to its effectiveness in reducing the impact of explosions, the water mitigation concept is gaining attention in both defense and commercial applications for storing energetic materials. An explosion is a sudden release of energy that transforms the solid explosive into gaseous products at extremely high pressure, which can exceed one hundred thousand atmospheres. This pressure is converted into mechanical work by the transfer of momentum in the form of pressure waves that propagate into the surrounding medium. To model the pressure-volume-energy behavior of the detonation product gases of TNT, the standard Jones-Wilkins-Lee (JWL) equation of state is used, along with a detonation velocity of 6,930 m/s.
This simulation considers all parts as three-dimensional Eulerian parts. To model water, the EOS material model is used with the Us-Up equation, while the JWL material model is used for TNT. The dynamic explicit procedure is suitable for this type of analysis.
workshop 10: Water impact simulation on 3D body using CEL method
Ocean waves are a significant source of renewable and non-polluting energy, caused by wind blowing over the ocean’s surface. In areas where the wind is consistent and strong enough, it can provide continuous waves. Various technologies exist to harness wave energy, which differ in their orientation to the waves and the way they convert wave energy into usable electrical energy. Point absorbers are a type of wave energy converter that are small in size relative to the incident wave length and can capture wave energy from a larger wave front. The explicit finite element method with a CEL solver is used to investigate the hydrodynamic problem of water impact on three-dimensional buoys. The fluid is solved using an Eulerian formulation, while the structure is discretized using a Lagrangian approach. Different types of three-dimensional structures, including a hemisphere shape, are studied, and the Us-Up equations for water and ideal gas formulation for air are used to define material behavior. During the analysis, a projectile penetrates into the water, and the resulting water splash is observed.
workshop 11: Soil impact analysis using Eulerian method
The main objective of this study was to develop and implement an explicit nonlinear dynamic finite element methodology for investigating the crashworthiness of small, lightweight rigid bodies impacting soft soil. The dynamics of aircraft crashes are heavily influenced by the features of the impact terrain, as different terrains result in different structural responses. This paper focuses on the technique used to characterize and validate a numerical model for soft soil as an impact terrain. The technique primarily involves using a time-explicit Eulerian-based FE analysis code, which is demonstrated through the FEA of penetrometer drop tests into soft soil. The Eulerian-based FE approach is preferred over the more commonly used Lagrangian-based FE approach to reduce numerical instabilities that often occur with Lagrangian solvers in problems involving large deformations, which is typical in crash analyses. These numerical instabilities may prematurely terminate analyses and compromise results. Explicit FE codes have been widely used in nonlinear transient dynamic analyses. In this simulation, the projectile is modeled as a rigid body and the soil as an Eulerian part. During the analysis, the projectile penetrates the soil and creates a hole.
workshop 12: Ball impact simulation on the water
This workshop demonstrates the step-by-step simulation of a ball filled with air impacting water, using Abaqus. A hyperelastic material is used to model the ball’s shell element. The internal pressure, external pressure, and air specifications are modeled using the Fluid Cavity technique. For modeling water, an Eulerian element with the Us-Up equation is implemented. An explicit procedure is appropriate for this type of analysis. During the impact, the ball penetrates the water, and there is a sudden change in the pressure and volume of the fluid cavity.
workshop 13: Subsurface explosion simulation on buried steel pipelines using Eulerian-Lagrangian method
The significance of buried pipelines cannot be overstated, as they play a crucial role in distributing vital resources such as water, gas, oil, etc. However, underground gas pipelines that are pressurized are at risk of being damaged by accidental explosions in various industries and locations such as explosives factories, public works, quarries, open pit mines, and even intentional explosions near the pipeline. Unfortunately, there has been a rise in terrorist attacks and sabotage on oil and gas transmission pipelines in recent times, which has resulted in multiple explosions along their routes. In this tutorial, a coupled 3D finite element model using a combined Eulerian-Lagrangian approach has been developed to simulate CEL explosions. The simplified Johnson-Cook material model, JWL equation of state, and ideal gas equation of state were used to model the behavior of the pipe material, charge detonation, and air, respectively. Additionally, the behavior of the soil mass was modeled using Coulomb-Mohr plasticity.