A particle-level set-based sharp interface cartesian grid method for impact, penetration, and void collapse

Journal of Computational Physics

Volumn 193, Issue 2, 2004, Pages 469-510

  Tran, L B ^a   Udaykumar, H S ^a  

^a UNIVERSITY OF IOWA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

INTERFACES (MATERIALS); NUMERICAL METHODS; TURBULENT FLOW;

A-PARTICLES; CARTESIAN GRID METHODS; EULERIAN; IMMERSED BOUNDARY; MASS ENERGY; MASS EQUATION; MASS MOMENTUM; PARTICLE LEVEL SET; SHARP INTERFACE; VOID COLLAPSE;

EQUATIONS OF STATE;

EID: 0348222799     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcp.2003.07.023     Document Type: Article

References (56)

1. J.A. Zukas, T. Nicholas, H.F. Swift, L.B. Gresczuk, D.R. Curran, Impact Dynamics, Wiley, New York, 1982.
2. M.A. Meyers, Dynamic Behavior of Materials, John Wiley & Sons, New York, 1994.
3. C.E. Anderson Jr., S.R. Bodher, Ballistic impact: the status of analytical and numerical modeling, Int. J. Impact Eng. 7 (1988) 9-35.
4. D.J. Benson, Computational methods in Lagrangian and Eulerian hydrocodes, Comput. Methods Appl. Mech. Engrg. 99 (1992) 235-395.
5. W.-K. Liu, T. Belytschko, H. Chang, An arbitrary Lagrangian-Eulerian finite element method for path-dependent materials, Comput. Methods Appl. Mech. Engrg. 58 (1986) 227-245.
6. G.T. Camacho, M. Ortiz, Computational modeling of impact damage in brittle materials, Int. J. Solids Struct. 33 (1996) 2899-2938.
7. G.T. Camacho, M. Ortiz, Adaptive Lagrangian modeling of ballistic penetration of metallic targets, Comput. Methods Appl. Mech. Engrg. 142 (1997) 269-301.
8. A. Duarte, J.T. Oden, An h-p adaptive method using clouds, Comput. Methods Appl. Mech. Engrg. 139 (1996) 237-262.
9. G.R. Johnson, R.A. Stryk, S.R. Beissel, SPH for high velocity impact computations, Comput. Methods Appl. Mech. Engrg. 139 (1996) 347-373.
10. W.-K. Liu, S. Hao, T. Belytschko, S. Li, C.T. Chang, Multi-scale methods, Int. J. Numer. Methods Engrg. 47 (7) (2000).
11. T. Belytschko, Y. Guo, W.-K. Liu, S.P. Xiao, Unified stability analysis of meshless particle methods, Int. J. Numer. Methods Engrg. 48 (9) (2000).
12. J. Dolbow, John, N. Moes, T. Belytschko, Discontinuous enrichment in finite elements with a partition of unity method, Finite Elements Anal. Des. 36 (3) (2000).
13. N. Moes, J. Dolbow, T. Belytschko, Finite element method for crack growth without remeshing, Int. J. Numer. Methods Engrg. 46 (1) (1999) 131-150.
14. N. Sukumar, N. Moes, B. Moran, T. Belytschko, Extended finite element method for three-dimensional crack modelling, Int. J. Numer. Methods Engrg. 48 (2000) 1549-1570.
15. J.A. Trangenstein, A second-order algorithm for the dynamic response of soils, Impact Comput. Sci. Engrg. 2 (1990) 1-39.
16. J.A. Trangenstein, A second-order algorithm for two-dimensional solid mechanics, Comput. Mech. 13 (1994) 343-359.
17. J.A. Trangenstein, Adaptive mesh refinement for wave propagation in nonlinear solids, SIAM J. Sci. Comput. 16 (1995) 819-939.
18. J.A. Trangenstein, R.B. Pember, The Riemann problem for longitudinal motion in an elastic-plastic bar, SIAM J. Sci. Stat. Comput. 12 (1991) 180-207.
19. D.J. Benson, A multi-material Eulerian formulation for the efficient solution of impact and penetration problems, Comput. Mech. 15 (1995) 558-571.
20. S.R. Cooper, D.J. Benson, V.F. Nesterenko, A numerical exploration of the role of void geometry on void collapse and hot spot formation in ductile materials, Int. J. Plasticity 16 (2000) 525-540.
21. R. Menikoff, E. Kober, Compaction waves in granular HMX, Los Alamos National Lab Report, LA-13456-MS, 1999.
22. P. Glaister, An approximate Riemann solver for the Euler equations for real gases, J. Comput. Phys. 74 (1988) 382-408.
23. M. Arienti, E. Morano, J. Shepherd, Nonreactive Euler flows with Mie-Grüneisen equation of state for high explosives. Available from: http://www.caltech.edu/~eric/Papers/FM99-8.pdf, 1999.
24. J.K. Dukowicz, A general, non-iterative Riemann solver for Godunovs method, J. Comput. Phys. 61 (1985) 119-137.
25. G. Miller, E. Puckett, A high-order Godunov method for multiple condensed phases, J. Comput. Phys. 128 (1996) 134-164.
26. R.P. Fedkiw, T. Aslam, B. Merriman, S. Osher, A non-oscillatory Eulerian approach to interfaces in multimaterial flows (The Ghost Fluid Method), J. Comput. Phys. 152 (1999) 457-492.
27. H.S. Udaykumar, L. Tran, D.M. Belk, K.J. Vanden, An Eulerian method for computation of multimaterial impact with ENO-shock capturing and sharp interfaces, J. Comput. Phys. 186 (2003) 136-177.
28. D. Enright, R. Fedkiw, J. Ferziger, I. Mitchell, A hybrid particle level set method for improved interface capturing, J. Comput. Phys. 176 (2002) 205-227.
29. G.I. Taylor, H. Quinney, The latent energy remaining in a metal after cold working, Proc. R. Soc., Ser. A 143 (1934) 307-326.
30. G.R. Johnson, W.H. Cook, Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures, Eng. Fract. Mech. 21 (1) (1985) 31-48.
31. K.J. Vanden, Characteristic analysis of the uniaxial stress and strain governing equations with thermal-elastic and Mie-Gruneison equation of state, Technical Memorandum, AFRL, Eglin AFB, Eglin, FL, 1998.
32. C.-W. Shu, S. Osher, Efficient implementation of essentially non-oscillatory shock-capturing schemes, J. Comput. Phys. 77 (1988) 439-471.
33. C.-W. Shu, S. Osher, Efficient implementation of essentially non-oscillatory shock-capturing schemes II, J. Comput. Phys. 83 (1989) 32-78.
34. B. Olinger, P.M. Halleck, H.H. Cady, The isothermal linear volume compression of PETN to 10 GPa and the calculated shock compression, J. Chem. Phys. 62 (1975) 4480-4483.
35. 2 -bounding surface plasticity using Prager's translation rule, Int. J. Numer. Methods Engrg. 55 (2002) 1129-1166.
36. A. Bilotta, Integration of constitutive equations for 2D elasto-plastic bodies, Manuscript available from: http://www.labmec.unical.it/libreria/download/report_23.pdf, 2001.
37. A. van Le, G. de Saxcé, Exact expression for the plastic corrections and the consistent tangent modulus in rate-independent elastoplasticity, in: European Congress on Computational Methods in Applied Sciences and Engineering, ECCCOMAS, Barcelona, September 11-14, 2000.
38. J.-P. Ponthot, An extension of the radial return algorithm to account for rate-dependent effects in frictional contact and viscoplasticity, J. Mater. Process. Technol. 80-81 (1998) 628-634.
39. X.-D. Liu, S. Osher, Convex ENO high order schemes without field-by-field decomposition or staggered grids, J. Comput. Phys. 142 (1998) 304-330.
40. L. Tran, R. Vilsmeier, D. Haenel, A local level set method for the treatment of discontinuities on unstructured grids, in: Finite Volumes for Complex Application II, Hermes Science Publications, Paris, 1999, pp. 849-856.
41. R. Menikoff, Errors when shock waves interact due to numerical shock width, SIAM J. Sci. Stat. Comput. 15 (5) (1994) 1227-1242.
42. R. Donat, A. Marquina, Capturing shock reflections: an improved flux formula, J. Comput. Phys. 125 (1996) 42-58.
43. R.P. Fedkiw, A. Marquina, B. Merriman, An isobaric fix for the overheating problem in multimaterial compressible flows, J. Comput. Phys. 148 (1999) 545-578.
44. D.J. Benson, A mixture theory for contact in multi-material Eulerian formulations, Comput. Methods Appl. Mech. Engrg. 140 (1997) 59-86.
45. C.S. Peskin, Numerical analysis of blood flow in the heart, J. Comput. Phys. 25 (1977) 220-252.
46. M. Sussman, P. Smereka, S. Osher, A level set approach for computing solutions to incompressible two-phase flow, J. Comput. Phys. 114 (1994) 146-159.
47. R.J. Leveque, Z. Li, The immersed interface method for elliptic equations with discontinuous coefficients and singular sources, SIAM J. Numer. Anal. 31 (4) (1994) 1019-1044.
48. D. Adalsteinson, J. Sethian, A fast level set method for propagating interfaces, J. Comput. Phys. 118 (1995) 269-277.
49. D. Peng, B. Merriman, S. Osher, H.-K. Zhao, M. Kang, A PDE-based fast local level set method, J. Comput. Phys. 155 (1999) 410-438.
50. Y.Y. Zhu, S. Cescotto, Unified and mixed formulation of the 4-node quadrilateral elements by assumed strain method: application to thermomechanical problems, Int. J. Numer. Methods Engrg. 38 (1995) 685-716.
51. J.O. Hallquist, DYNA3D User's Manual, University of California, Lawrence Livermore Laboratory, Livermore, 1987.
52. C.E. Anderson Jr., V. Hohler, J.D. Walker, A.J. Stilp, Time-resolved penetration of long rods into steel targets, Int. J. Impact Engrg. 16 (1) (1995) 1-18.
53. F.P. Bowden, A.D. Yoffe, Initiation and Growth of Explosions in Liquids and Solids, Cambridge University Press, Cambridge, 1952.
54. M.M. Carroll, A.C. Holt, Static and dynamic pore-collapse relations for ductile porous materials, J. Appl. Phys. 43 (4) (1972).
55. J. Kang, P.B. Butler, M.R. Baer, A thermomechanical analysis of hot spot formation in condensed-phase, energetic materials, Combust. Flame 89 (1992) 117-139.
56. B.A. Khasainov, A.A. Borisov, B.S. Ermolaev, A.I. Korotkov, Two phase visco-plastic model of shock initiation of detonation in high density pressed explosives, in: Seventh Symposium (International) on Detonation, Naval Surface Weapons Center, NSWC MP 82-334, 1981.