Technical Papers
May 17, 2018

Simulation of Impact Penetration and Perforation of Metal Targets Using the Smoothed Particle Galerkin Method

Publication: Journal of Engineering Mechanics
Volume 144, Issue 8

Abstract

This paper applies the smoothed particle Galerkin (SPG) method to the analysis of penetration and perforation of metal targets. The SPG weak form is integrated using the direct nodal integration (DNI) technique with a nonresidual penalty–type stabilization term derived from strain smoothing. An adaptive anisotropic Lagrangian kernel is used to model the large deformation in the penetration and perforation processes. To model material breakup and fragmentation while avoiding potential spurious self-healing of meshfree approximations used in the failure analysis, a strain-based bond failure mechanism is implemented and the sensitivity to the failure criterion is numerically investigated. Two experiments are analyzed using the SPG formulation. The numerical results are compared with the experimental data to evaluate the effectiveness of the present method. The convergence behavior of the SPG formulation is also studied.

Get full access to this article

View all available purchase options and get full access to this article.

Acknowledgments

The authors Dr. John O. Hallquist of Livermore Software Technology Corporation for his support of this research. The suggestions and comments provided by Dr. Len Schwer through private communications are also highly appreciated.

References

Asadi Kalameh, H., A. Karamali, C. Anitescu, and T. Rabczuk. 2012. “High velocity impact of metal sphere on thin metallic plate using smooth particle hydrodynamics.” Front. Struct. Civ. Eng. 6 (2): 101–110.
Belytschko, T., Y. Guo, W. K. Liu, and S. P. Xiao. 2000. “A unified stability analysis of meshless particle methods.” Int. J. Numer. Methods Eng. 48 (9): 1359–1400. https://doi.org/10.1002/1097-0207(20000730)48:9%3C1359::AID-NME829%3E3.0.CO;2-U.
Belytschko, T., and A. Lin. 1987. “A three-dimensional impact-penetration algorithm with erosion.” Int. J. Impact Eng. 5 (1–4): 111–127. https://doi.org/10.1016/0734-743X(87)90033-9.
Belytschko, T., Y. Y. Lu, and L. Gu. 1994. “Element-free Galerkin methods.” Int. J. Numer. Methods Eng. 37 (2): 229–256. https://doi.org/10.1002/nme.1620370205.
Ben-Dor, G., A. Dubinsky, and T. Elperin. 2005. “Ballistic impact: Recent advances in analytical modeling of plate penetration dynamics–A review.” Appl. Mech. Rev. 58 (6): 355–371. https://doi.org/10.1115/1.2048626.
Bishop, R. F., R. Hill, and N. F. Mott. 1945. “The theory of indentation and hardness tests.” Proc. Phys. Soc. 57 (3): 147–159. https://doi.org/10.1088/0959-5309/57/3/301.
Chandel, P. S., D. Sood, R. Kumar, P. Sharma, B. Sewak, V. Bhardwaj, M. Athwal, V. Mangla, I. Biswas, and M. Singh. 2012. “Hypervelocity impact of tungsten cubes on spaced armour.” J. Phys. Conf. Ser. 377 (Jul): 012048. https://doi.org/10.1088/1742-6596/377/1/012048.
Chen, J. S., M. Hillman, and M. Ruter. 2013. “An arbitrary order variationally consistent integration for Galerkin meshfree methods.” Int. J. Numer. Methods Eng. 95 (5): 387–418. https://doi.org/10.1002/nme.4512.
Chen, J. S., C. Pan, C. T. Wu, and W. K. Liu. 1996. “Reproducing kernel particle methods for large deformation analysis of non-linear structures.” Comput. Methods Appl. Mech. Eng. 139 (1–4): 195–227. https://doi.org/10.1016/S0045-7825(96)01083-3.
Chen, J. S., C. T. Wu, S. Yoon, and Y. You. 2001. “A stabilized conforming nodal integration for Galerkin meshfree methods.” Int. J. Numer. Methods Eng. 50 (2): 435–466. https://doi.org/10.1002/1097-0207(20010120)50:2%3C435::AID-NME32%3E3.0.CO;2-A.
Dikshit, S. N., and G. Sundararajan. 1992. “The penetration of thick steel plates by ogive shaped projectiles—Experiment and analysis.” Int. J. Impact Eng. 12 (3): 373–408. https://doi.org/10.1016/0734-743X(92)90134-F.
Engineering ToolBox. 2001. “Tools and basic information for design, engineering and construction of technical applications.” http://www.engineeringtoolbox.com.
Fahrenthold, E. P., and B. A. Horban. 2001. “An improved hybrid particle-element method for hypervelocity impact simulation.” Int. J. Impact Eng. 26 (1–10): 169–178. https://doi.org/10.1016/S0734-743X(01)00079-3.
Forrestal, M. J., and V. K. Luk. 1992. “Penetration into soil targets.” Int. J. Impact Eng. 12 (3): 427–444. https://doi.org/10.1016/0734-743X(92)90167-R.
Forrestal, M. J., D. Y. Tzou, E. Askari, and D. B. Longcope. 1995. “Penetration into ductile metal targets with rigid spherical-nose rods.” Int. J. Impact Eng. 16 (5–6): 699–710. https://doi.org/10.1016/0734-743X(95)00005-U.
Fountzoulas, C. G., G. A. Gazonas, and B. A. Cheeseman. 2007. “Computational modeling of tungsten carbide sphere impact and penetration into high-strength-low-alloy (HSLA)-100 steel targets.” J. Mech. Mater. Struct. 2 (10): 1965–1979. https://doi.org/10.2140/jomms.2007.2.1965.
Gingold, R. A., and J. J. Monaghan. 1977. “Smooth particle hydrodynamics: Theory and application to non-spherical stars.” Mon. Not. R. Astron. Soc. 181 (3): 375–389. https://doi.org/10.1093/mnras/181.3.375.
Golsdmith, W., and S. A. Finnegan. 1971. “Penetration and perforation processes in metal targets at and above ballistic velocities.” Int. J. Mech. Sci. 13 (10): 843–866. https://doi.org/10.1016/0020-7403(71)90111-1.
Goodier, J. N. 1964. On the mechanics of indentation and cratering in solid targets of strain-hardening metal by impact of hard and soft spheres. Menlo Park, CA: Stanford Research Institute.
Guan, P. C., J. S. Chen, Y. Wu, H. Teng, J. Gaidos, K. Hofstetter, and M. Alsaleh. 2009. “Semi-Lagrangian reproducing kernel formulation and application to modeling earth moving operations.” Mech. Mater. 41 (6): 670–683. https://doi.org/10.1016/j.mechmat.2009.01.030.
Hallquist, J. O. 2006. LS-DYNA keyword user’s manual. Livermore, CA: Livermore Software Technology.
Hohler, V., A. Stilp, and K. Weber. 1995. “Hypervelocity penetration of tungsten sinter-alloy rods into aluminum.” Int. J. Impact Eng. 17 (1–3): 409–418. https://doi.org/10.1016/0734-743X(95)99866-P.
Huang, P., X. Zhang, S. Ma, and X. Huang. 2011. “Contact algorithms for the material point method in impact and penetration simulation.” Int. J. Numer. Methods Eng. 85 (4): 498–517. https://doi.org/10.1002/nme.2981.
Ibne Islam, M. R., S. Chakraborty, A. Shaw, and S. Reid. 2017. “A computational model for failure of ductile material under impact.” Int. J. Impact Eng. 108 (Oct): 334–347. https://doi.org/10.1016/j.ijimpeng.2017.04.005.
Johnson, G. R., and W. H. Cook. 1983. “A constitutive model and data for metals subjected to large strains, high strain rates, and high temperatures.” In Proc., 7th Int. Symp. on Ballistics, 541–547. Hague, Netherlands.
Johnson, G. R., and R. A. Stryk. 1986. User instructions for the EPIC-2 code. Valparaiso, FL: Eglin Air Force Base.
Johnson, G. R., and R. A. Stryk. 1987. “Eroding interface and improved tetrahedral element algorithms for high-velocity impact computations in three dimensions.” Int. J. Impact Eng. 5 (1–4): 411–421. https://doi.org/10.1016/0734-743X(87)90057-1.
Lacerda, D., and J. L. Lacome. 2001. “Simulations of hypervelocity impacts with smoothed particle hydrodynamics.” In Proc., 3rd European LSYDNA Conf. Livermore, CA: LSTC.
Li, Q. M., and X. W. Chen. 2003. “Dimensionless formulae for penetration depth of concrete target impacted by a non-deformable projectile.” Int. J. Impact Eng. 28 (1): 93–116. https://doi.org/10.1016/S0734-743X(02)00037-4.
Li, S., and W. K. Liu. 2004. Meshfree particle method. Berlin: Springer.
Liden, E., S. Mousavi, A. Helte, and B. Lundberg. 2012. “Deformation and fracture of a long-rod projectile induced by an oblique moving plate: Numerical simulations.” Int. J. Impact Eng. 40–41 (Feb–Mar): 35–45. https://doi.org/10.1016/j.ijimpeng.2011.09.003.
Liu, G. R., K. Y. Dai, and T. T. Nguyen. 2007. “A smoothed finite element method for mechanics problems.” Comput. Mech. 39 (6): 859–877. https://doi.org/10.1007/s00466-006-0075-4.
Liu, W. K., S. Jun, and Y. F. Zhang. 1995. “Reproducing kernel particle methods.” Int. J. Numer. Methods Fluids 20 (8–9): 1081–1106. https://doi.org/10.1002/fld.1650200824.
Lu, Z. C., and H. M. Wen. 2018. “On the penetration of high strength steel rods into semi-infinite aluminum alloy targets.” Int. J. Impact Eng. 111 (Jan): 1–10. https://doi.org/10.1016/j.ijimpeng.2017.08.006.
Lucy, L. B. 1977. “A numerical approach to the testing of the fission hypothesis.” Astron. J. 82 (12): 1013–1024. https://doi.org/10.1086/112164.
Mohotti, D., S. N. Raman, T. Ngo, and P. Mendis. 2015. “Use of coupled smooth-particle hydrodynamics/Lagrangian method in the simulation of deformable projectile penetration.” Int. J. Protective Struct. 6 (3): 419–437. https://doi.org/10.1260/2041-4196.6.3.419.
Nechitailo, N. 2015. “Hypervelocity penetration into soil.” Procedia Eng. 103 (May): 427–435. https://doi.org/10.1016/j.proeng.2015.04.042.
Nguyen-Xuan, H., T. Rabczuk, S. P. A. Bordas, and J. F. Debongnie. 2008. “A smoothed finite element method for plate analysis.” Comput. Methods Appl. Mech. Eng. 197 (13–16): 1184–1203. https://doi.org/10.1016/j.cma.2007.10.008.
Orphal, D. L., and R. R. Franzen. 1997. “Penetration of confined silicon carbide targets by tungsten long rods at impact velocities from 1.5 to 4.6  km/s.” Int. J. Impact Eng. 19 (1): 1–13. https://doi.org/10.1016/0734-743X(95)00064-H.
Orphal, D. L., R. R. Franzen, A. C. Charters, T. L. Menna, and A. J. Piekutowski. 1997. “Penetration of confined boron carbide targets by tungsten long rods at impact velocities from 1.5 to 5.0  km/s.” Int. J. Impact Eng. 19 (1): 15–29. https://doi.org/10.1016/S0734-743X(96)00004-8.
Park, C. K., C. T. Wu, and C. D. Kan. 2011. “On the analysis of dispersion property and stable time step in meshfree method using the generalized meshfree approximation.” Finite Elem. Anal. Des. 47 (7): 683–697. https://doi.org/10.1016/j.finel.2011.02.001.
Pedersen, B., and S. Bless. 2006. “Behind-armor debris from the impact of hypervelocity tungsten penetrators.” Int. J. Impact Eng. 33 (1–12): 605–614. https://doi.org/10.1016/j.ijimpeng.2006.09.007.
Plassard, F., J. Mespoulet, and P. Hereil. 2011. “Hypervelocity impact of aluminum sphere against aluminum plate: Experiment and LS-DYNA correlation.” In Proc., 8th European LS-DYNA Conf. Livermore, CA: LSTC.
Puso, M. A., J. S. Chen, E. Zywicz, and W. Elmer. 2008. “Meshfree and finite element nodal integration methods.” Int. J. Numer. Methods Eng. 74 (3): 416–446. https://doi.org/10.1002/nme.2181.
Rabczuk, T., T. Belytschko, and S. P. Xiao. 2004. “Stable particle methods based on Lagrangian kernels.” Comput. Methods Appl. Mech. Eng. 193 (12–14): 1035–1063. https://doi.org/10.1016/j.cma.2003.12.005.
Rajendran, A. M. 1998. “Penetration of tungsten alloy rods into shallow—Cavity steel targets.” Int. J. Impact Eng. 21 (6): 451–460. https://doi.org/10.1016/S0734-743X(98)00005-0.
Randles, P. W., T. C. Carney, L. D. Libersky, J. D. Renick, and A. G. Petschek. 1995. “Calculation of oblique impact and fracture of tungsten cubes using smoothed particle hydrodynamics.” Int. J. Impact Eng. 17 (4–6): 661–672. https://doi.org/10.1016/0734-743X(95)99889-Y.
Roy, S. K., et al. 2016. “Study of hypervelocity projectile impact on thick metal plates.” Shock Vibr. 2016: 1–11.https://doi.org/10.1155/2016/4313480.
Sataphathy, S. 2001. “Dynamic spherical cavity expansion in brittle ceramics.” Int. J. Solids Struct. 38 (32–33): 5833–5845. https://doi.org/10.1016/S0020-7683(00)00388-7.
Schwer, L. E. 2009. “Aluminum plate perforation: A comparative case study using Lagrange with erosion, multi-material ALE, and smooth particle hydrodynamics.” In Proc., 7th European LS-DYNA Conf. Livermore, CA: LSTC.
Sherburn, J. A., M. J. Roth, J. S. Chen, and M. Hillman. 2015. “Meshfree modeling of concrete slab perforation using a reproducing kernel particle impact and penetration formulation.” Int. J. Impact Eng. 86 (Dec): 96–110. https://doi.org/10.1016/j.ijimpeng.2015.07.009.
Silling, S. A., and E. Askari. 2005. “A meshfree method based on the peridynamic model of solid mechanics.” Comput. Struct. 83 (17–18): 1526–1535. https://doi.org/10.1016/j.compstruc.2004.11.026.
Simkins, D. C., and S. Li. 2006. “Meshfree simulation of thermo-mechanical ductile fracture.” Comput. Mech. 38 (3): 235–249. https://doi.org/10.1007/s00466-005-0744-8.
Simo, J. C., and T. J. R. Hughes. 1986. “On the variational foundations of assumed strain methods.” J. Appl. Mech. 53 (1): 51–54. https://doi.org/10.1115/1.3171737.
Sorensen, B. R., K. D. Kimsey, G. F. Silsby, D. R. Scheffler, T. M. Sherrick, and W. S. Rosset. 1991. “High velocity penetration of steel targets.” Int. J. Impact Eng. 11 (1): 107–119. https://doi.org/10.1016/0734-743X(91)90034-D.
Violeau, D. 2012. Fluid mechanics and the SPH method: Theory and applications. Oxford, UK: Oxford University Press.
Wang, D., and J. S. Chen. 2004. “Locking-free stabilized conforming nodal integration for meshfree Mindlin–Reissner plate formulation.” Comput. Methods Appl. Mech. Eng. 193 (12–14): 1065–1083. https://doi.org/10.1016/j.cma.2003.12.006.
Wang, D., and J. S. Chen. 2006. “A locking-free meshfree curved beam formulation with the stabilized conforming nodal integration.” Comput. Mech. 39 (1): 83–90. https://doi.org/10.1007/s00466-005-0010-0.
Wang, D., and Z. Li. 2013. “A two-level strain smoothing regularized meshfree approach with stabilized conforming nodal integration for elastic damage analysis.” Int. J. Damage Mech. 22 (3): 440–459. https://doi.org/10.1177/1056789512455938.
Wang, D., and H. Peng. 2013. “A Hermite reproducing kernel Galerkin meshfree for buckling analysis of thin plates.” Comput. Mech. 51 (6): 1013–1029. https://doi.org/10.1007/s00466-012-0784-9.
Watson, E., and M. O. Steinhauser. 2017. “Discrete particle method for simulating hypervelocity impact phenomena.” Materials 10 (12): 379. https://doi.org/10.3390/ma10040379.
Wu, C. T., T. Q. Bui, Y. Wu, T. L. Luo, M. Wang, C. C. Liao, P. Y. Chen, and Y. S. Lai. 2017a. “Numerical and experimental validation of a particle Galerkin method for metal grinding simulation.” Comput. Mech. https://doi.org/10.1007/s00466-017-1456-6, 365–383.
Wu, C. T., S. W. Chi, M. Koishi, and Y. Wu. 2016a. “Strain gradient stabilization with dual stress points for the meshfree nodal integration method in inelastic analysis.” Int. J. Numer. Methods Eng. 107 (1): 3–30. https://doi.org/10.1002/nme.5147.
Wu, C. T., and M. Koishi. 2012. “Three-dimensional meshfree-enriched finite element formulation for micromechanical hyperelastic modeling of particulate rubber composites.” Int. J. Numer. Methods Eng. 91 (11): 1137–1157. https://doi.org/10.1002/nme.4306.
Wu, C. T., M. Koishi, and W. Hu. 2015a. “A displacement smoothing induced strain gradient stabilization for the meshfree Galerkin nodal integration method.” Comput. Mech. 56 (1): 19–37. https://doi.org/10.1007/s00466-015-1153-2.
Wu, C. T., N. Ma, K. Takada, and H. Okada. 2016b. “A meshfree continuous-discontinuous approach for the ductile fracture modeling in explicit dynamics analysis.” Comput. Mech. 58 (3): 391–409. https://doi.org/10.1007/s00466-016-1299-6.
Wu, C. T., C. K. Park, and J. S. Chen. 2011. “A generalized approximation for the meshfree analysis of solids.” Int. J. Numer. Methods Eng. 85 (6): 693–722. https://doi.org/10.1002/nme.2991.
Wu, C. T., and B. Ren. 2015. “A stabilized non-ordinary state-based peridynamics for the nonlocal ductile material failure analysis in metal machining process.” Comput. Methods Appl. Mech. Eng. 291 (Jul): 197–215. https://doi.org/10.1016/j.cma.2015.03.003.
Wu, C. T., Y. Wu, J. E. Crawford, and J. M. Magallanes. 2017b. “Three-dimensional concrete impact and penetration simulations using the smoothed particle Galerkin method.” Int. J. Impact Eng. 106 (Aug): 1–17. https://doi.org/10.1016/j.ijimpeng.2017.03.005.
Wu, C. T., Y. Wu, and M. Koishi. 2015b. “A strain-morphed nonlocal meshfree method for the regularized particle simulation of elastic-damage induced strain localization problems.” Comput. Mech. 56 (6): 1039–1054. https://doi.org/10.1007/s00466-015-1217-3.
Wu, Y., J. M. Magallanes, and J. E. Crawford. 2014a. “Fragmentation and debris evolution modeled by a point-wise coupled reproducing kernel-finite element formulation.” Int. J. Damage Mech. 23 (7): 1005–1034. https://doi.org/10.1177/1056789514520797.
Wu, Y., D. Wang, and C. T. Wu. 2014b. “Three dimensional fragment simulation of concrete structures with a nodally regularized meshfree method.” Theor. Appl. Fract. Mech. 72 (Aug): 89–99. https://doi.org/10.1016/j.tafmec.2014.04.006.
Wu, Y., D. Wang, C. T. Wu, and H. Zhang. 2016c. “A direct displacement smoothing meshfree particle formulation for impact failure modeling.” Int. J. Impact Eng. 87 (Jan): 169–185. https://doi.org/10.1016/j.ijimpeng.2015.03.013.
Xiao, Y. K., H. Wu, Q. Fang, W. Zhang, and X. Z. Kong. 2017. “Hemisphere nosed steel projectile high-speed penetration into aluminum target.” Mater. Des. 133 (Aug): 237–254. https://doi.org/10.1016/j.matdes.2017.08.002.
Zhang, X., K. Y. Sze, and S. Ma. 2006. “An explicit material point finite element method for hypervelocity impact.” Int. J. Numer. Methods Eng. 66 (4): 689–706. https://doi.org/10.1002/nme.1579.

Information & Authors

Information

Published In

Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 144Issue 8August 2018

History

Received: Sep 15, 2017
Accepted: Dec 28, 2017
Published online: May 17, 2018
Published in print: Aug 1, 2018
Discussion open until: Oct 17, 2018

Permissions

Request permissions for this article.

Authors

Affiliations

Youcai Wu, Ph.D. [email protected]
Senior Scientist, Livermore Software Technology Corporation, 7374 Las Positas Rd., Livermore, CA 94551 (corresponding author). Email: [email protected]
C. T. Wu, Ph.D. [email protected]
Senior Scientist, Livermore Software Technology Corporation, 7374 Las Positas Rd., Livermore, CA 94551. Email: [email protected]

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share