Adaptive Lagrangian modelling of ballistic penetration of metallic targets. (English) Zbl 0892.73056

Summary: A Lagrangian finite element model of ductile penetration is developed. Adaptive meshing is accorded a key role in following the large deformations which develop during penetration. An explicit contact/friction algorithm is used to treat the multi-body dynamics. Rate-dependent plasticity, heat conduction and thermal coupling are also accounted for in the calculations. The properties and predictive ability of the model are exhibited in several applications: copper rod impact, perforation of aluminum plates by conical-nosed projectiles and penetration of high-strength steel targets by WHA long rods. The simulation show close agreement with experimental observations and numerical results.


74S05 Finite element methods applied to problems in solid mechanics
74M20 Impact in solid mechanics
80A20 Heat and mass transfer, heat flow (MSC2010)
Full Text: DOI


[1] Anderson, C.E.; Bodner, S.R., Ballistic impact: the status of analytical and numerical modelling, Int. J. impact engrg., 16, 9-35, (1988)
[2] Zukas, J., Survey of computer codes for impact simulation, (), 593-714
[3] Kimsey, K.; Randers-Pehrson, G., Terminal effects codes, ()
[4] Anderson, C.E., An overview of the theory of hydrocodes, Int. J. impact engrg., 5, 33-59, (1987)
[5] Johnson, G.R.; Stryk, R.A., User instruction for the 1990 version of the combined (1D,2D,3D) EPIC code, ()
[6] Whirley, R.G.; Hallquist, J.O., ()
[7] McGlaun, J.M., ()
[8] Matuska, D.A.; Osborn, J.J., ()
[9] Hughes, T.J.R., The finite element method, (1987), Prentice Hall Englewood Cliffs, NJ
[10] Hughes, T.J.R.; Belytschko, T., A précis of developments in computational methods for transient analysis, J. appl. mech., 50, 1033-1041, (1983) · Zbl 0533.73002
[11] Belytschko, T., An overview of semidiscretization and time integration procedures, (), 1-65
[12] Hughes, T.J.R., Analysis of transient algorithms with particular reference to stability behavior, (), 67-155
[13] Mathur, K.K.; Needleman, A.; Tvergaard, V., Dynamic 3D analysis of the charpy V-notch test, Model. simul. mater. sci. engrg., 1, 467-484, (1993)
[14] Nagtegaal, J.C.; Parks, D.M.; Rice, J.R., On numerically accurate finite element solutions in the fully plastic range, Comput. methods appl. mech. engrg., 4, 469-484, (1974) · Zbl 0284.73048
[15] Camacho, G.T., Computational modelling of impact damage and penetration of brittle and ductile solids, () · Zbl 0929.74101
[16] Taylor, L.; Flanagan, D., PRONTO 2D: A two-dimensional transient solid dynamics program, (1987), Sandia National Laboratories, SAND86-0594
[17] Camacho, G.T.; Ortiz, M., Computational modelling of impact damage in brittle materials(1996), Int. J. solids structures, 33, 2899-2938, (1996) · Zbl 0929.74101
[18] Taylor, G.I.; Quinney, H., The plastic distortion of metals, Philos. trans. roy. soc. London, A230, 323-362, (1931) · Zbl 0003.08003
[19] Kobayashi, S.; Oh, S.-I.; Altan, T., Metal forming and the finite element method, (1989), Oxford University Press
[20] Marusich, T.D.; Ortiz, M., Modelling and simulation of high-speed machining, Int. J. numer. methods engrg., 38, 3675-3694, (1995) · Zbl 0835.73077
[21] Park, K.C.; Felippa, C.A., Partitioned analysis of coupled systems, (), 157-219 · Zbl 0546.73063
[22] Lemonds, J.; Needleman, A., Finite element analysis of shear localization in rate and temperature dependent solids, Mech. mater., 5, 339-361, (1986)
[23] Sekhon, G.S.; Chenot, J.L., Numerical simulation of continuous chip formation during non-steady orthogonal cutting, Engrg. comput., 10, 31-48, (1993)
[24] Cuitiño, A.M.; Ortiz, M., A material-independent method for extending stress update algorithms from small-strain plasticity to finite plasticity with multiplicative kinematics, Engrg. comput., 9, 437-451, (1992)
[25] Klopp, R.W.; Clifton, R.J.; Shawki, T.G., Pressure shear impact and the dynamic viscoplastic response of metals, Mech. mater., 4, 375-385, (1985)
[26] Clifton, R.J.; Klopp, R.W., Pressure shear plate impact testing, (), 230-239
[27] Zhou, M.; Clifton, R.J.; Needleman, A., Shear band formation in a W-ni-fe alloy under plate impact,, ()
[28] ()
[29] Mackerle, J., Error analysis, adaptive techniques and finite and boundary elements—A bibliography (1992-1993), Finite elem. anal. des., 17, 231-246, (1994) · Zbl 0815.73001
[30] Oden, J.T., Research directions in computational mechanics, (1991), National Academy Press Washington, D.C
[31] Zienkiewics, O.C.; Huang, G.C.; Liu, Y.C., Adaptive FEM computation of forming processes—application to porous and non-porous materials, Int. J. numer. methods engrg., 30, 1527-1533, (1990) · Zbl 0716.73084
[32] Chenot, J.-L., Finite element modelling of metal forming: recent achievements and future challenges, (), 1019-1036
[33] Camacho, G.T.; Marusich, T.D.; Ortiz, M., Adaptive meshing methods for the analysis of unconstrained plastic flow, ()
[34] Simo, J.C.; Oliver, J.; Armero, F., An analysis of strong discontinuities induced by strain-softening in rate-independent inelastic solids, Comput. mech., 12, 277-296, (1993) · Zbl 0783.73024
[35] Cuitiño, A.M.; Ortiz, M., Computational modelling of single crystals, Model. simul. mater. sci. engrg., 1, 225-263, (1992)
[36] Devloo, P.; Oden, J.T.; Strouboulis, R., Implementation of an adaptive refinement technique for the SUPG algorithm, Comput. methods appl. mech. engrg., 61, 339, (1987) · Zbl 0596.73066
[37] Oden, J.T.; Demkowicz, L.; Strouboulis, T.; Devloo, P., Adaptive methods for problems in solid and fluid mechanics, () · Zbl 0593.76080
[38] Baehmann, P.L.; Wittchen, S.L.; Shephard, M.S.; Grice, K.R.; Yerry, M.A., Robust, geometrically based, automatic two-dimensional mesh generation, Int. J. numer. methods engrg., 24, 1043-1078, (1987) · Zbl 0618.65116
[39] Jin, H.; Wiberg, N.E., Two dimensional mesh generation, adaptive remeshing and refinement, Int. J. numer. methods engrg., 29, 1501-1526, (1990)
[40] Peraire, J.; Vahdati, M.; Morgan, K.; Zienkiewicz, O.C., Adaptive remeshing for compressible flow computations, J. comput. phys., 72, 449-466, (1987) · Zbl 0631.76085
[41] Sloan, S.W., A fast algorithm for constructing Delaunay triangulations in the plane, Adv. engrg. software, 9, 34-55, (1987) · Zbl 0628.68044
[42] Shephard, M.; Georges, M.K., Automatic three dimensional mesh generation by the finite octree technique, Int. J. numer. methods engrg., 32, 709-749, (1991) · Zbl 0755.65116
[43] Blacker, T.D.; Stephenson, M.B., Paving: A new approach to automated quadrilateral mesh generation, Int. J. numer. methods engrg., 32, 811-847, (1991) · Zbl 0755.65111
[44] Lohner, R., Some useful data structures for the generation of unstructured grids, Comm. appl. numer. methods, 4, 123-135, (1988) · Zbl 0643.65075
[45] Diaz, A.R.; Kikuchi, N.; Taylor, J.E., A method of grid optimization for finite element methods, Comput. methods appl. mech. engrg., 41, 29-45, (1983) · Zbl 0509.73071
[46] Zienkiewicz, O.C.; Zhu, J.C., A simple error estimator and adaptive procedure for practical engineering analysis, Int. J. numer. methods engrg., 24, 337-357, (1987) · Zbl 0602.73063
[47] Belytschko, T.; Tabbara, M., H-adaptive finite element methods for dynamic problems, with emphasis on localization, Int. J. numer. methods engrg., 36, 4245-4265, (1993) · Zbl 0794.73071
[48] Babuska, I., The p- and hp versions of the finite element method: the state of the art, (), 199-239
[49] Batra, R.C.; Ko, K.-I., An adaptive mesh refinement technique for the analysis of shear bands in plane strain compression of a thermoviscoplastic solid, Comput. mech., 10, 369-379, (1992) · Zbl 0775.73237
[50] Chen, X.; Batra, R.C., Axisymmetric penetration of thick thermoviscoplastic targets, () · Zbl 0848.73017
[51] Ortiz, M.; Quigley, J.J., Adaptive mesh refinement in strain localization problems, Comput. methods appl. mech. engrg., 90, 781-804, (1991)
[52] Peiro, J.; Peraire, J.; Morgan, K., The generation of triangular meshes on surfaces, () · Zbl 0771.76042
[53] Baehmann, P.L.; Shephard, M.S.; Ashley, R.A.; Jay, A., Automated metal-forming modeling utilizing adaptive remeshing and evolving geometry, Comput. struct., 30, 319-325, (1988) · Zbl 0668.73039
[54] Mohan, R.; Ortiz, M.; Shih, C.F., An analysis of cracks in ductile single crystals 0—I. anti-plane shear, J. mech. phys. solids, 40, 291-313, (1992)
[55] Zhu, Y.Y.; Cescotto, S., Unified and mixed formulation of the 4-node quadrilateral elements by assumed strain method: application to thermomechanical problems, Int. J. numer. methods engrg., 38, 685-716, (1995) · Zbl 0823.73074
[56] Hallquist, J.O., ()
[57] Kamoulakos, A., A simple benchmark for impact, bench mark, (), 31-35
[58] Belytschko, T.; Yen, H.-J.; Mullen, R., Mixed methods for time integration, Comput. methods appl. mech. engrg., 17/18, 259-275, (1989) · Zbl 0403.73002
[59] Forrestal, M.J.; Luk, V.K.; Brar, N.S., Perforation of aluminum armor plates with conical nosed projectiles, Mech. mater., 10, 97-105, (1990)
[60] Chen, E.P., Finite element simulation of perforation and penetration of aluminum targets by conical shaped steel rods, Mech. mater., 10, 107-115, (1990)
[61] Wulf, G.L., The high strain rate compression of 7039 aluminum, Int. J. mech., 20, 609-615, (1978)
[62] A. Rosakis and G. Ravichandran (1995) Private communication.
[63] Anderson, C.E.; Hohler, V.; Walker, J.D.; Stilp, A.J., Time resolved penetration of long rods into steel targets, Int. J. impact engrg., 16, 1-18, (1994)
[64] Johnson, G.R.; Cook, W.H., Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures, Engrg. fract. mech., 21, 31-48, (1985)
[65] Mescall, J., Material issues in computer simulations of penetration mechanics, (), 47-62
[66] Camacho, G.T.; Ortiz, M., Computational modelling of fragmentation and penetration of ceramic plates, () · Zbl 0892.73056
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