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Correction and stabilization of smooth particle hydrodynamics methods with applications in metal forming simulations. (English) Zbl 0964.76071
Smooth particle hydrodynamics (SPH) is a robust and conceptually simple method which suffers from unsatisfactory performance due to lack of consistency. The kernel function can be corrected to enforce the consistency conditions and improve the accuracy. For simplicity, in this paper the SPH method with the corrected kernel is referred to as corrected smooth particle hydrodynamics. The numerical solutions can be further improved by introducing an integration correction which also enables the method to pass patch tests. It is also shown that the nodal integration of this corrected SPH method suffers from spurious singular modes. This spatial instability results from under integration of the weak form, and it is treated by a least-squares stabilization procedure. The effects of the stabilization and improvement in the accuracy are illustrated by simulation of metal forming problems.

76M28 Particle methods and lattice-gas methods
76T99 Multiphase and multicomponent flows
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[1] Lucy, The Astronomical Journal 82 pp 1013– (1977) · doi:10.1086/112164
[2] Gingold, Monthly Notices of the Royal Astronomical Society 181 pp 375– (1977) · Zbl 0421.76032 · doi:10.1093/mnras/181.3.375
[3] Smoothed particle hydrodynamics: a review. Harvard- Smithsonian. Center for Astrophysics, Preprint 2884, 1989.
[4] Monaghan, Annual Reviews of Astronomy and Astrophysics 30 pp 543– (1992) · doi:10.1146/annurev.aa.30.090192.002551
[5] Monaghan, Computer Physics Communication 48 pp 89– (1988) · Zbl 0673.76089 · doi:10.1016/0010-4655(88)90026-4
[6] Smooth particle hydrodynamics with strength of materials. In Advances in the Free Lagrange Method, Lecture Notes in Physics, vol. 395, 1990; 248-257.
[7] Libersky, Journal of Computational Physics 109 pp 67– (1993) · Zbl 0791.76065 · doi:10.1006/jcph.1993.1199
[8] Johnson, International Journal of Impact Engineering 14 pp 385– (1993) · doi:10.1016/0734-743X(93)90036-7
[9] Johnson, Nuclear Engineering Design 150 pp 265– (1994) · doi:10.1016/0029-5493(94)90143-0
[10] Liu, International Journal for Numerical Methods in Engineering 20 pp 1081– (1995) · Zbl 0881.76072 · doi:10.1002/fld.1650200824
[11] Corrected Smooth Particle Hydrodynamics?A reproducing kernel meshless method for computational mechanics. Computational Mechanics in UK?5th ACME Annual Conference, 1997.
[12] Corrected smooth particle hydrodynamics method for metal forming simulations. NUMIFORM ’98?The Sixth International Conference on Numerical Methods in Industrial Forming Processes, 1998.
[13] An analysis of smoothed particle hydrodynamics. Report No. SAND93-2513-UC-705, Sandia National Laboratory, Albuquerque, NM, 1994.
[14] Stabilizing SPH with conservative smoothing. Report No. SAND94-1932-UC-705, Sandia National Laboratory, Albuquerque, NM, 1994.
[15] Dyka, Internationl Jorunal for Numerical Methods in Engineering 40 pp 2325– (1997) · Zbl 0890.73077 · doi:10.1002/(SICI)1097-0207(19970715)40:13<2325::AID-NME161>3.0.CO;2-8
[16] Beissel, Computer Methods in Applied Mechanics and Engineering 139 pp 49– (1996) · Zbl 0918.73329 · doi:10.1016/S0045-7825(96)01079-1
[17] Belytschko, International Journal for Numerical Methods in Engineering 43 pp 785– (1998) · Zbl 0939.74076 · doi:10.1002/(SICI)1097-0207(19981115)43:5<785::AID-NME420>3.0.CO;2-9
[18] Liu, Computer Methods in Applied Mechanics and Engineering 139 pp 91– (1996) · Zbl 0896.76069 · doi:10.1016/S0045-7825(96)01081-X
[19] Liu, Computer Methods in Applied Mechanics and Engineering 143 pp 113– (1997) · Zbl 0883.65088 · doi:10.1016/S0045-7825(96)01132-2
[20] Liu, Archives of Computer Methods in Engineering: State of the Art Reviews 3 pp 3– (1996) · doi:10.1007/BF02736130
[21] Private communication, 4th World Congress of Computational Mechanics, Argentina, 1998.
[22] Belytschko, Computer Methods in Applied Mechanics and Engineering 146 pp 371– (1997) · Zbl 0894.73156 · doi:10.1016/S0045-7825(96)01234-0
[23] The viscoplastic approach for the finite element modelling of metal forming processes. In Numerical Modelling of Material Deformation Processes: Research, Development and Applications, et al. (eds). Springer: Berlin, 1992.
[24] Flow formulation for numerical solution of forming processes. In Numerical Analysis of Forming Processes, chapter 1, et al. (eds). Wiley: New York, 1984.
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