Shock and Vibration

Volume 2015, Article ID 631493, 9 pages

http://dx.doi.org/10.1155/2015/631493

## Finite Element Simulation of Medium-Range Blast Loading Using LS-DYNA

^{1}Department of Civil Engineering, City University of New York, 160 Convent Avenue, New York, NY 10031, USA^{2}School of Civil Engineering and Mechanics, Huazhong University of Science and Technology, 1037 Luoyu Road, Wuhan, Hubei 430074, China

Received 22 January 2015; Revised 10 May 2015; Accepted 18 May 2015

Academic Editor: Gyuhae Park

Copyright © 2015 Yuzhen Han and Huabei Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This study investigated the Finite Element simulation of blast loading using LS-DYNA. The objective is to identify approaches to reduce the requirement of computation effort while maintaining reasonable accuracy, focusing on blast loading scheme, element size, and its relationship with scale of explosion. The study made use of the recently developed blast loading scheme in LS-DYNA, which removes the necessity to model the explosive in the numerical models but still maintains the advantages of nonlinear fluid-structure interaction. It was found that the blast loading technique could significantly reduce the computation effort. It was also found that the initial density of air in the numerical model could be purposely increased to partially compensate the error induced by the use of relatively large air elements. Using the numerical approach, free air blast above a scaled distance of 0.4 m/kg^{1/3} was properly simulated, and the fluid-structure interaction at the same location could be properly duplicated using proper Arbitrary Lagrangian Eulerian (ALE) coupling scheme. The study also showed that centrifuge technique, which has been successfully employed in model tests to investigate the blast effects, may be used when simulating the effect of medium- to large-scale explosion at small scaled distance.

#### 1. Introduction

The effect of blast loading has become a critical issue in the design, protection, and rehabilitation of engineering structures following the terrorist attacks on civil infrastructures in recent years. But analyzing the effects of blast loading on civil infrastructures is a difficult task, as it involves highly nonlinear fluid dynamics, structural dynamics, and fluid-structure interaction. At present, most blast resistant analyses make use of simplistic blast loading and structure models [1], but it is difficult to assume rational blast loading for a complicated structure that includes sophisticated surfaces and corners. Advanced numerical simulations thus become the economic and reliable approaches for this purpose. In this type of numerical simulations, generally all the critical components in the problem are properly modeled, including explosive, air, fluid-structure interaction, and structures. Many such numerical simulations can be found in the literature [2–9], and several computer codes have been designed to carry out such analyses [10, 11].

What remains a critical issue is the computation effort required to accomplish such an analysis. For example, simulating the effect of blast loading on a full-scale bridge could require more than 10 million Finite Elements. The bottleneck in this type of computer simulation mainly comes from the requirement of element size for the explosive and air domains. Some studies showed that, in order to capture the accurate release of blast energy from explosives, element size as small as 0.5–1.0 mm should be used [7, 12]. As for the blast wave propagation in the air domain, generally element size in the order of few mm was used to obtain reasonable results when the scaled distance is smaller than 1 m/kg^{1/3} [2, 13, 14].

This study investigated the Finite Element simulation of blast loading using LS-DYNA, focusing on the blast effect on a structure surface at a medium scaled distance ( m/kg^{1/3} to 1.0 m/kg^{1/3}). LS-DYNA has been commonly used to analyze the effects of blast loading on structures [5, 6, 8, 16], and this study hopes to shed some light on the application.

The presentations of this study are organized as follows: after the discussion of the theoretical background, the approaches for blast loading simulation in LS-DYNA are introduced. The findings from the simulation of free air blast are then presented, and they are employed to simulate the reflected blast pressure on a rigid surface. Finally, the findings from this study are validated against a model test.

#### 2. Theoretical Background

##### 2.1. Blast Wave Propagation in the Air

Blast wave propagation in the air is governed by three fundamental equations of fluid dynamics: mass conservation, momentum conservation, and energy conservation equations. These three equations can be combined to yield the Navier-Stokes equation that governs the blast wave propagation in the air [17]. In 1958, von Neumann [18] gave the solution of air blast from a point source explosion in an infinite three-dimensional space. He assumed that the air was ideal gas, the equation of state (EOS) of which was , and the total energy for the air was , with being the specific gas constant defined as and being the heat capacity ratio defined as . Here is the specific heat under constant pressure and is the one under constant volume. He showed that the free air blast pressure could be expressed asHere is the initial density of the air before blast, is time, and is a parameter representing the location of the point of interest in the free air domain. is a complicated function of , , and , the detail of which can be found in von Neumann [18]. This solution is valid for .

Equation (1) showed that, by increasing the initial air density , the blast pressure in the air due to explosion would increase. This theoretical fact can be employed to increase the blast pressure in numerical simulation and to partially compensate the loss of energy, or numerical damping, due to large element size.

##### 2.2. Blast Wave Propagation and Finite Element Size

Extensive experiences of numerical simulations have shown that large element size may lead to smaller free air blast pressure than the theoretical and experimental values. Apparently, in blast simulation, significant “numerical damping” exists due to relatively large element size. There exist a few studies investigating the required element size in the simulations of blast waves and their effects on structures. Chapman et al. [2] found that a grid size of less than 3 mm was necessary to simulate the blast pressure and specific impulse at a scaled distance of 0.95 m/kg^{1/3}. The amount of explosive simulated was 0.075 kg TNT. Luccioni et al. [19] compared their simulated peak pressures with those presented by Kinney and Graham [20] and concluded that a grid size of 100 mm was adequate to simulate the peak pressure due to the explosion of 100 kg TNT at a scaled distance of larger than 1.2 m/kg^{1/3}. The parametric study by Shi et al. [13] showed that a grid size of 100 mm was able to capture the peak pressure and specific impulse at a scaled distance of 2.0 m/kg^{1/3} due to an explosion of 1000 kg TNT. Recently, Wu et al. [12] used an element size of 10 mm to model the air blast effect at a scaled distance of 2 m/kg^{1/3} from an explosion of 0.2 kg TNT. These analyses were all carried out using the Finite Element code AUTODYN. It can be seen that large air element size may be employed if the targeted structure is at large scaled distance.

The relationship between element size and amount of explosive is related to the blast wavelength , which is defined as the length of positive pulse in the air due to an explosion according to UFC 3-340-02 [1]. There exists a unique relationship between scaled wavelength (unit: ) and scaled distance of incident blast due to a free air explosion [1]. This means that, for the same targeted scaled distance, larger amount of explosive resulted in larger wavelength, which may in turn relax the requirement on element size [21]. This can also be seen from the results of available studies [2, 13, 19]. However, it is not known whether the same scale ratio can be used to determine the element size for large-scale explosion simulation based on that of a small-scale explosion simulation. For example, if a grid size of 3 mm is adequate to simulate the blast effect on a structure due to 0.1 kg TNT, it is not known whether, for the same targeted scaled distance, a grid size of 30 mm is enough for an explosion of 100 kg TNT.

#### 3. Simulation of Blast Loading in LS-DYNA

Conventionally, blast loading may be simulated by employing the Multimaterial Arbitrary Lagrangian Eulerian (MM_ALE) solver in LS-DYNA. In this approach, Lagrangian formulation is used to model solid continua and structures, and Eulerian formulation is used for large distortions of fluids, gases, and explosives. The two domains are coupled through appropriate schemes. The explosive must be properly modeled using very small Finite Element size [7] and a large number of fluid elements must be simulated between the explosive and structures to transfer the blast wave. It is therefore extremely demanding to complete a full-scale simulation involving large structures.

There also exists a simplified approach, which imposes pressure time-history on structure surfaces based on the CONWEP reflected pressure on a rigid surface [1]. A disadvantage of this approach is that wave reflection and superposition cannot be accounted for as would occur at the corners of a structure. The reflected pressure time-history on a deformable surface is also not the same as that on a rigid surface. Børvik et al. [22] demonstrated that this approach resulted in large errors in the simulation of a simple container structure subjected to external blast loading.

The combination of the CONWEP incident pressure and the MM-ALE solver can be used to obtain acceptable results with less computational efforts [14]. This coupling method is explained in Figure 1. Only the air immediately surrounding the target structure is modeled with an ALE domain. Incident blast pressure time-history based on CONWEP is applied to a layer of ALE elements (the ambient layer shown in Figure 1), which faces the explosive charge and acts as a source for the adjoining air elements. The blast wave then propagates through the air domain and eventually interacts with the structure. The loading on the structure due to wave reflection and superposition can then be captured by the ALE domain. This capacity can be realized in LS-DYNA by employing the key word LOAD_BLAST_ENHANCED (LBE) and defining a layer of special elements (the ambient layer). Figure 2 compares the blast pressure inside the ambient layer with that of CONWEP in a blast simulation [14]. The sizes of the air elements and the ambient layer elements were all 3 mm. Almost identical results were obtained. Different thicknesses of the ambient layer were also tested, which resulted in identical air pressure in the layer.