Velocity and Shape of Explosive Computation using Multi-Material and ALE Formulations

J Puryear, M Souli, B Harrison

Abstract


In this paper, a mathematical and numerical description of the bulk viscosity for an equation of state that is linear in density is presented. The bulk viscosity is used in many academic and industrial dynamic codes, and there is no description concerning the smearing of the shock for engineers and researchers in the manuals or in published papers.  To clearly show the usefulness of the bulk viscosity, a simple one dimensional problem is used, where a shock is developed through a pressure wave travelling inside a compressible fluid. By adding a viscous pressure to equilibrium equations, high oscillations in the front shock have been considerably attenuated, by thickening the shock over few element mesh sizes.

The method is developed mathematically for one dimensional hydrodynamic problem, but has been used successfully for more complex applications including high-impact problems, explosive detonation in air and underwater explosions. Application of the method to a complex problem is illustrated in calculation of the peak velocity and shape of an explosively-formed projectile (EFP).The symmetry common to most EFPs permits their characterization using 2D axisymmetric analysis. Formation of an EFP entails volumetric expansion of the explosive and extensive plastic flow of the metal plate, both of which can be calculated using an Arbitrary Lagrangian Eulerian (ALE) method. Accordingly, a 2D axisymmetric ALE was used to calculate the velocity and shape of an EFP. The methodology was validated against EFP velocity and shape measurements published in SAND-92-1879 [Hertel 1992].

The Jones-Wilkins-Lee (JWL) equation of state (EOS) were used for the LX-14 high explosive backing the copper plate. The explosive burn was initiated using a high explosive material which converts the explosive charge into a gas at high pressure and temperature. The copper plate and steel casing were included using the constitutive model developed by Johnson and Cook. An equation of state developed by Grüneisen for high-pressure simulation was used for the metals. The calculated peak velocity of the EFP was in excellent agreement with the peak velocity published by Hertel. However, the calculated shape did not agree with the experimental shadowgraph of the plate. Specifically, the calculated shape was elongated compared to the measurement and continued to elongate as long as the calculation was continued. In other words, the shape of the copper plate did not reach a dynamic equilibrium.

The methodology for calculating the EFP peak velocity and shape is described. The calculated results are compared to measurements from Hertel. Finally, possible sources for the inaccuracy of the calculated shape are investigated. These include the element size and formulation, initial geometry of EFP, explosive equation of state and the constitutive model for the copper plate.     


Full Text:

PDF

References


Souli M, Paul Du Bois, Al-Bahkali E, (2018): Numerical Shock Viscosity for Impact Analysis Using ALE Formulation. CMES-Computer Modeling in Engineering and Sciences Vol 117. pp 91-107 · Oct 2018 Crossref

Al-Bahkali, E.; Elkanani H.; Souli M. (2015): Experimental and numerical investigation for membrane deployment using SPH and ALE formulations. CMES-Computer Modeling in Engineering and Sciences Journal, vol. 104, no. 5, pp. 405-424.

Al-Bahkali, E.; Souli, M.; Al-Bahkali T. (2015): SPH and FEM Investigation of Hydrodynamic Impact Problems, CMC-Journal of Computers, Materials, and Continua, vol.46, no.1, pp. 57-78.

Aquelet, N.; Souli, M.; Olovson, L. (2005): Euler Lagrange coupling with damping effects: Application to slamming problems, Computer Methods in Applied Mechanics and Engineering, vol. 195, pp. 110-132. Crossref

Aquelet, N.; Souli, M.; Gabrys, J.; Olovson L. (2003): A new ALE formulation for sloshing analysis, International Journal of Structural Engineering and Mechanics, vol. 16, pp. 423-440. Atlas of Stress-Strain Curves (2002): ASM International, Materials Park, OH. Crossref

Barras, G.; Souli, M.; Aquelet, N.; Couty, N. (2012): Numerical simulation of underwater explosions using an ALE method, The pulsating bubble phenomena, Ocean Engineering, vol. 41, pp. 53-66.

Baker, E.; Cornell, R.; Stiel, L.: "Understanding Experimental and Computation Gurney Energies," in U.S. Army ARDEC, Picatinny, NJ. Crossref

Benson, D. J. (1992): Computational Methods in Lagrangian and Eulerian Hydrocodes, Computer Methods in Applied Mechanics and Engineering, vol. 99, pp. 235-394. Crossref

Elkanani, H.; Al-Bahkali, E.; Souli, M. (2017): Numerical Investigation of Pulse Wave Propagation in Arteries Using Fluid Structure Interaction Capabilities, Computational and Mathematical Methods in Medicine, vol. 2017, pp. 1-12. Crossref

Erchiqui, F.; Souli, M.; Ben Yedder, R. (2007): Nonisothermal finite-element analysis of thermoforming of polyethylene terephthalate sheet: Incomplete effect of the forming stage , Polymer Engineering and Science, vol. 47, no.12, pp. 2129-2144. Crossref

Fan, L.; , Yao, j.; Yang, C.; Xu, D.; Tang, D. (2018): Patient-Specific Echo-Based Fluid-Structure Interaction Modeling Study of Blood Flow in the Left Ventricle with Infarction and Hypertension, CMES-Computer Modeling in Engineering & Sciences, vol. 114, no. 2, pp.221-237.

Fuller, B.; Rigby, S.; Tyas, A.; Clarke, S.; Warren, J.; Reay, J.; Gant, M.; Elgy, I. (2016) "Experimentation and Modeling of Near Field Explosions," in Military Aspects of Blast and Shock, Halifax, NS, Canada.

Hallquist, J. (2013): LSDYNA Theory Manual, Livermore Software Technology Corp.

Hertel, E. (1992): SAND-92-1879 A Comparison of the CTH Hydrodynamics Code with Experimental Data, Sandia National Laboratories, Albuquerque, NM.

Khan, M.U.; Moatamedi, M.; Souli, M. (2008): Multiphysics out of position airbag simulation, International Journal of Crashworthiness, vol. 13, no. 2, pp. 159-166. Crossref

Johnson, G.; Cook, W. A Constitutive Model and Data for Metals Subjected to Large Strains, High Strain Rates and High Temperatures Contract F08635-81-C-0179 U.S. Air Force and Honeywell Independent Development Program.

Johnson, G.; Cook, W. (1985) Fracture Characteristics of Three Metals Subjected to Various Strains, Strain Rates, Temperatures and Pressures, Engineering Fracture Mechanics, vol. 21, no. 1, pp. 31-48. Crossref

Lindholm, U.; Bessey, R. (1969) AFML-TR-69-119 A Survey of Rate Dependent Strength Properties of Metals, Air Force Material Laboratory, Wright-Patterson Air Force Base, OH.

Longatte, E.; Verreman, V.; Souli, M. (2009): Time marching for simulation of Fluid-Structure Interaction Problems, Journal of Fluids and Structures, vol. 25, no.1, pp. 95-111. Crossref

Moatamedi, M.; Souli M.; Al-Bahkali E. (2014): Fluid Structure Modelling of Blood Flow in Vessels, MCB-Molecular & Cellular Biomechanics, vol. 11, no. 4, pp. 221-234. Otsuka.

M.; Matsui, Y.; Murata, K.; Kato, Y.; Itoh, S. (2004), "A Study on Shock Wave Propagation Process in the Smooth Blasting Technique," Livermore Software Technology Corporation, Livermore, CA.

Ozdemir, Z.; Souli, M.; Fahjan, Y.M. (2010): Application of nonlinear fluid–structure interaction methods to seismic analysis of anchored and unanchored tanks, Engineering Structures, vol. 32, no. 2, pp. 409-423. Crossref




DOI: http://dx.doi.org/10.21152/1750-9548.13.1.31

Copyright (c) 2019 M Souli, J Puryear, B Harrison

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.