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Finite Element Simulation for Blast Response of Structures
I. Introduction
The assessment of blast loading and damage to structures and equipment is very important in a wide range of military applications ranging from the design of military vehicles and structures to protect against improvised explosive devices (IED's) and other blast threats to the design of buildings and other civil infrastructure to protect against a terrorist blast threat, such as a truck bomb attack.
During development of military equipment, prototypes are typically built and used for destructive field testing in order to determine the level of blast protection. This testing is both time consuming and costly and does not ensure an optimized design. In addition, a variety of field conditions and other related factors tend to make each blast test unique to some degree and comparison of candidate blast protection designs can be difficult. Similarly, destructive testing on buildings and other civil structures is not practical.
Simulation capabilities to accurately predict both the blast loading and subsequent structural response are important for generating improvements in blast protection. Recent advances in commercially available finite element codes have introduced numerical methodologies suitable for simulation of coupled blast-structural response. The nonlinear finite element code LS-DYNA™[1] has Arbitrary Lagrangian-Eulerian (ALE) or Smooth Particle Hydrodynamics (SPH) methods, coupled with classical Lagrangian structural analysis methods. which allow a fully coupled approach to solving blast-structure interactions.
II. Blast Loading from Shallow Buried Explosives
One blast application of importance is the loading from mines and shallow buried explosives. The damage to a structure from a buried mine is a result of load delivered from the combination of an airblast and soil impact. For typical mine charge sizes and depths of burial (5 to 10 cm), the loading is frequently dominated by soil loading. The following simulations were performed using SPH and ALE and compare the deformation of an aluminum plate with an experiment performed by Defense R&D Canada (DRDC) [2]. In the experiment, a 6.0 kg bare explosive charge was buried in 5 cm of sand. A 3.175 cm thick aluminum (Al 5083) plate was placed on a support stand 40.64 cm from the top of the soil. A steel support and 10 metric tons of mass were placed on top of the aluminum plate to simulate proper vehicle weight. The LS-DYNA SPH model of this test configuration is shown in Figure 1.
The computed plate deformation from the SPH simulation is shown in Figure 4, and matches well with the published experimental results. The experiment showed a 30 cm displacement at the center of the plate compared with 35 cm for the calculation. Both the experiment and the calculation showed a 5 cm edge displacement.
The computed plate deformation from the ALE simulation is shown in Figure 5. Overall, the computed shape of the plate matches experimental observations. The agreement between the experiment and the calculation demonstrates the utility of the SPH and ALE methods for mine blast loading simulations.
lII. Airblast Load on a Structure
Blast Methodology Simulation
The modeling of airblast threats has been an issue of recent concern in military and security protection communities. The following example shows the suitability of ALE modeling techniques in LS-DYNA for accurately modeling airblast fluid-structure interaction with a reacting structure. That is, a structure with a structural response time on the same order as the airblast event. A controlled experiment by Lindberg and Florence [3] on the dynamic pulse buckling of a thin aluminum shell was selected. In the airblast loading experiments analyzed in this study, thin shells were subject to asymmetric loading applied perpendicular to the shell axis. The experimental configuration was to suspend cylinders in free air at various standoff distances from a suspended spherical explosive charge. For the problem selected, the measured pressure time history could be approximated as a step rise and exponential decay with a peak pressure of 6.9 by 107 dyne/cm2 (1000 psi) and impulse applied to the cylinder of 4.8 ktaps (1 tap = 1 dyne-s/cm2).
A model of the aluminum shell, end caps, and surrounding air was developed, as shown in Figure 6. The shell was represented with Lagrangian shell elements of 6061-T6 aluminum. It had a 6 inch outside diameter, a 9 inch length, and a 0.125 inch wall thickness. Steel plugs matching the inside diameter of the shell and 1.5 inches long were fixed in each end of the shell for support. The cylinder was placed inside the air mesh and a pressure-time history applied on one face of the air boundary. The airblast wave was then propagated through the ALE mesh and allowed to interact with the aluminum structure.
The cylinder buckling response was calculated and compared to the measured buckling response, as shown in Figure 7. Although small details of the buckled shape differ, the overall amount of radial deformation and dent shape in the simulation compare well with the experiment. Note that in each case the deformation is asymmetric. The dynamic buckling of shells is affected by initial imperfections in the shell geometry and non-uniformity in the explosively-delivered impulsive load, leading to asymmetry in the buckled shape.
Blast Methodology Vehicle Blast Simulation
To further demonstrate the utility of this modeling methodology, a second calculation was performed with a much more complex geometry. The objective of this second calculation was to apply the ALE airblast modeling techniques developed in the first example to a complex vehicle structure representative of an improvised explosive device threat. For this idealized case, the vehicle modeled in the simulation was a 1989 Chevrolet C2500 pickup truck. The pickup model was previously developed under FHWA sponsorship for highway crash worthiness studies. Figure 8 shows the simulation setup, with the Lagrangian truck placed inside an ALE mesh of air. The air model was the same as that used in the shell-buckling simulations. A pressure-time load was applied as a planar wave on the mesh boundary, creating a wave to impinge on the vehicle model.
The interaction of the pressure wave with the vehicle, at various times, is shown in Figure 9. As the wave sweeps through the domain and over the truck, its peak pressure drops considerably. By 4.4 ms, the pressure wave has passed completely over the vehicle. During the interaction with the pressure wave, local deformation of the truck fenders and hood begins.
The local damage to the vehicle at 13.0 ms is shown in Figure 10. Additional simulations of controlled airblast experiments on light ground vehicles need to be conducted to fully verify the approach.
lV. Conclusion
Within the last decade there have been significant advances in commercially available dynamic structural analysis codes. One of these advances is the inclusion of new solution methodologies that are applicable for blast simulations. Examples are the ALE and SPH methodologies that allow Eularian or meshless solution strategies to interact with traditional Lagrangian structural solutions. These capabilities have enabled coupled blast response simulations to be performed with a commercially available finite element code and are leading to improvements in blast protection.
Acknowledgements
Support for this research by the Army RDECOM under the direction of Richard C. Goetz is gratefully acknowledged.
References
[1] LS-DYNA, Livermore Software Technology Corporation, Ver. 970, Livermore, CA, April 2003.
[2] Williams, Kevi "Validation of a Loading Model for Simulating Blast Mine Effects on Armored Vehicles", Ӡ7th International LS-DYNA Users Conference, Penetration/Explosive Section 6, Livermore Software Technology Corporation, May 2002, pp. 35-44.
[3] Lindberg, H.E., Florence, A.L., Dynamic Pulse Buckling, Martinus Nijhoff Publishers, Boston, MA, 1987.
For inquiries or comments, please contact:
Dr. Steven Kirkpatrick
Principal Engineer
e-mail: skirkpatrick@ara.com
Dr. Robert T. Bocchieri
Principal Engineer
e-mail: rbocchieri@ara.com
Brian Peterson
Principal Engineer
e-mail: bpeterson@ara.com
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