Simulation of Energy Absorbing Materials
in Blast Loaded Structures
Michael J. Mullin,
Brendan J. O’Toole, bj@me.unlv.edu
Department of Mechanical Engineering
University Nevada Las Vegas
Abstract
Energy absorbing materials such as foam or honeycomb are of interest in blast protection becau of their ability to absorb energy through plastic deformation. After reaching their yield stress, the materials exhibit a region of constant stress for increasing strain until the material is completely compacted. The energy needed to crush the material is proportional to the area under the stress-strain curve. Becau foams and honeycombs have this “plateau” region, they absorb a considerable amount of energy relative to their low density. The materials are investigated to determine if their energy abs
orbing abilities can be ud to mitigate the load and shock transferred to a vehicle structure subject to blast loading.
Ballistic pendulum experiments show that energy absorbing materials increa the imparted impul from a blast. This behavior was contrary to expected results so computational models were created in LS-DYNA to understand the phenomenon that caus an increa in imparted impul. ConWep and Arbitrary-Lagrangian-Eulerian (ALE) techniques were ud in simulations to demonstrate their efficiency and accuracy. An additional ConWep aluminum foam model was created to directly compare simulations against ballistic pendulum experiments found in the literature.
1. Introduction
As the military industry moves forward into the 21st century, strong lightweight materials are changing their status from exotic to commonplace. Vehicles are being reevaluated to create a safer, more efficient, and more lethal vehicle with significant weight savings. Survivability from mine blast is of particular concern: as weight is reduced, the accelerations of the vehicle when subjected to mine blast aluminum increas. A sacrificial layer of material that can absorb some or all of the blast energy is one possibility for light vehicle survivability. Metal foams and honeycombs are materials that absorb a considerable amount of energy relative to their low density.
A simple device to measure impul imparted to a structure from a blast is a ballistic pendulum (Figure 1). With a charge detonated in front of the pendulum, the face is subjected to a pressure wave, which caus the pendulum to rotate a measurable amount. Knowing the rotation of the center of mass (cm in Figure 1) and the distance from the rotation center, the imparted impul from the blast can be calculated. Panels of various shapes and materials can be placed on the face of the pendulum to investigate their abilities to reduce the imparted impul. With the material absorbing some of the energy, the resulting rotation of the structure was expected to be reduced. Ballistic pendulum experiments show opposite results; energy absorbing materials placed on the front of the panel caud an increa in rotation [1][2].
Hansn et al. [1] performed ballistic pendulum tests on Al foam panels as early as 1998. Hannn showed an increa in imparted impul to Al foam panels subjected to clo range blast. This increa was attributed to collap of the foam under the blast (dishing), which allowed confinement of the blast. Hansn ud numerical models to show that although an
increa in impul was obrved, the transmitted force through the Al foam panels was decread.
Figure 1: Ballistic Pendulum and Reprentative Models Diagram.
This paper compares two loading methods available in LS-DYNA: one using a Lagrangian model and the ConWep air blast function and the other using Arbitrary Lagrangian-Eulerian (ALE) coupling i
ncluding the explosive material as part of the model. Although the models u the same standoff, equivalent charge mass and material properties, they are not reprentative of any physical experiment. A parate ConWep model is prented that compares ConWep’s capabilities against experimental values for simulating blast loading of Al foam panels.
2. Blast Loading Using LS-DYNA
Both ConWep and ALE techniques have been validated for simulating mine blast [3],[4],[5]. Randers-Pehrson [3] describes the ConWep air blast function and concluded the function as adequate for u in mine blast applications. Similarly, Wang [4] benchmarked material properties ud in ALE modeling of detonating landmines. Williams [5] compared ConWep to a commercially unavailable mine blast algorithm and concluded ConWep as apt if a scale factor is determined for the soils being ud. The ballistic pendulum, which is what the models prented here simulate, is more appropriately simulated with an air blast. The effect of soil is not an issue, so standard practice values [3],[4],[5],[6] are ud for the reprentative models.
In order to reduce the computational expen of modeling the maximum displacement of a pendulum (with a period of over 2.5 conds) with a time step appropriate for capturing ballistic phen
omena, simpler models were devid (Figure 1). The simpler models consist of a sled of known mass subjected to the same blast load the pendulum counterpart would be expod to. The sled has the same area expod to the blast as the pendulum bob as well as the same mass. When the sled is subjected to the impul of the blast, it will undergo acceleration until the sled reaches a maximum velocity (upon completion of the impul). The resulting kinetic energy, which is
calculated using the maximum velocity of the sled, is comparable to the potential energy calculated from the maximum height of the pendulum swing.
The following two subctions describe the models made to compare the different loading methods of ConWep and ALE. Both methods have a rigid body model and an Al foam model. For the foam models, the foam panel is attached to the front of a rigid body support using a contact card. The expod surface of the foam model has the same standoff as the expod surface of the rigid body model (Figure 1).
2.1 Lagrangian Models with ConWep Blast Function
LS-DYNA’s ConWep air blast function has inputs of TNT equivalent mass, type of blast (surface or air), location in space of detonation, and surface identification for which the pressure will be applied.
From this information, ConWep calculates the appropriate pressure to be applied to the designated surface. This method is computationally less expensive than the ALE method at the cost of accuracy: ConWep is unable to account for confinement (focusing of the blast due to geometry) or shadowing (when an object is blocking a surface from direct loading)[3].
Figure 2: Discretization of Lagrangian panels. Foam elements (numbering 86,400) are shown in yellow, rigid body elements (numbering 10,800) are displayed in green.
The rigid body model has dimensions (in x, y, z) of (50cm, 5cm, 25cm), consists of 10,800 elements, and is positioned 26.14 cm away from the source of the blast. The foam model (Figure 2) adds a panel of foam elements of the same dimensions as the rigid body and splitting each solid element into 8 equally sized smaller elements. All the Lagrangian elements u a single integration point element formulation and have a 1:1:1 aspect ratio. Quarter symmetry was ud to reduce the number of elements in the model; all nodes on the planes of symmetry were constrained to stay on the planes of symmetry. *Contact_tied_surface_to_surface_offt was ud to tie the rigid body to the foam plate. The “offt” option is necessary when tying a deformable part to a rigid body. The rigid body was chon as the master and the foam as the slave for the contact algorithm.
One pound of C-4 was chon for the blast load simulations to be similar to ballistic pendulum experiments performed by Skaggs [2]. The ConWep air blast function requires an input for equivalent mass of TNT. C-4 explosives relea more energy per pound than TNT by a
factor of 1.14 [5], [6]. Using that factor and converting from lb to gm, the equivalent mass of the TNT ud in the studies is 517.1gm.
2.1.1 Material Properties
Material properties for the ConWep and ALE models are listed in Table 1. Some of the material properties required in the material cards are not easily described, so the values are displayed according to what is required for the LS-DYNA material cards. Wang [4] ud a similar table structure and it is felt that this format displays the data in a format most uful to the end ur.
Table 1: Material Properties Ud For ConWep And ALE Models.
*MAT_RIGID (material 20) was ud for the rigid body model. Material properties for steel were ud with the exception of density. For all models, the overall mass of the sled was 4 kg; with a volume of 25000cm3 the density of the rigid body in the rigid body model was t to 0.16 gm/cc. The foam model has a rigid body support panel and a foam panel each with a volume of 25000 cm3. With the Al foam density at 0.15gm/cc, the rigid body’s density was t at 0.01gm/cc to keep the overall mass of the sled the same.
*MAT_HONEYCOMB (material 26) was chon for the Al foam material model. Material 26 offers uncoupled orthotropic behavior as en in foams. Nonlinear elastoplastic material behavior can be defined parately (for each direction) for all normal and shear stress. The curves can be ud to define elastic-perfectly-plastic-rigid material behavior as en in the majority of papers modeling foams subjected to high strain rates [1], [7],[8]. The values ud for the foam material model were gathered from a couple of sources [1],[8].
2.2 ALE Models
Using ALE in LS-DYNA involves modeling the charge and surrounding fluid with an Eulerian mesh, which is then coupled with a Lagrangian mesh (ud for the foam and rigid body
panel). Equations of State (EOS) are ud for the High Explosives (HE) and air. The ALE method models the explosion and calculates the pressure profile throughout the Eulerian mesh. ALE is computationally more expensive than ConWep, and is only appropriate for small standoff distances: with the small Eulerian mesh needed to appropriately capture the pressure wave front, large amounts of elements are needed.
Figure 3: Discretization of the ALE Eulerian mesh. There are 88,200 air elements and 304 HE elements in the original mesh; 128,284 and 4,000 elements in the refined mesh respectively.
Several ALE models were constructed to improve the accuracy and efficiency of the models. The list includes an eighth symmetry rigid body model, a fourth symmetry rigid body model, a rigid body model with a refined Eulerian mesh, a rigid body model with an incread number of quadrature points, a foam model, and a foam model with a refined Eulerian mesh. The same amounts of Lagrangian elements (10,800 rigid and 86,400 foam) were ud in the ALE models as were the ConWep models. In the eighth symmetry rigid body model (Figure 3), the number of Eulerian elements ud to model the HE and air were 304 and 88,200 respectively. The mesh en in (Figure 3) labeled “Original” was created by Powers [9] in a previous ALE parametric study. In the figure the red mesh shows the discretization of the air Eulerian elements, the blue mesh shows the High Explosive (HE) discretization. The darker area (highlighted) shows the Lagrangian part overlapping the Eulerian mesh, which explains why the mesh looks different in that region. The overall dimensions ud in the x, y, and z directions are 55 cm, 40 cm, and 30 cm respectively. A 1:1:1 ratio was not achievable with the Eulerian mesh becau of the spherical nature of the charge, but all elements are hexahedral. Boundary conditions disallowing motion normal to the planes were placed on the XY, XZ, and YZ planes (the three planes interct at the center of the spherical explosive).
A quarter symmetry model was constructed to address a boundary condition concern inherent with the eighth symmetry model: the constraints on the XZ plane of the eighth symmetry (Figure 3) model simulate another plate mirrored across the XZ plane. It was necessary to model quarter symmetry conditions to e if the affect, if any, the reflected blast wave from the mirrored plate had on the solution. A total of 18,598 (304 HE, 18,294 air) elements were mirrored about the XZ
