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**A density-adaptive SPH method with kernel gradient correction for modeling explosive welding.**
*(English)*
Zbl 1386.74107

Summary: Explosive welding involves processes like the detonation of explosive, impact of metal structures and strong fluid-structure interaction, while the whole process of explosive welding has not been well modeled before. In this paper, a novel smoothed particle hydrodynamics (SPH) model is developed to simulate explosive welding. In the SPH model, a kernel gradient correction algorithm is used to achieve better computational accuracy. A density adapting technique which can effectively treat large density ratio is also proposed. The developed SPH model is firstly validated by simulating a benchmark problem of one-dimensional TNT detonation and an impact welding problem. The SPH model is then successfully applied to simulate the whole process of explosive welding. It is demonstrated that the presented SPH method can capture typical physics in explosive welding including explosion wave, welding surface morphology, jet flow and acceleration of the flyer plate. The welding angle obtained from the SPH
simulation agrees well with that from a kinematic analysis.

### MSC:

74M20 | Impact in solid mechanics |

74F05 | Thermal effects in solid mechanics |

74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |

76M28 | Particle methods and lattice-gas methods |

74S30 | Other numerical methods in solid mechanics (MSC2010) |

### Keywords:

smoothed particle hydrodynamics; explosive welding; impact welding; kernel gradient correction; density adaption; wavy interface
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\textit{M. B. Liu} et al., Comput. Mech. 60, No. 3, 513--529 (2017; Zbl 1386.74107)

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### References:

[1] | Cutler, D, What you can do with explosion welding, Weld J, 5, 177-199, (2006) |

[2] | Grignon, F; Benson, D; Vecchio, KS; Meyers, MA, Explosive welding of aluminum to aluminum: analysis, computations and experiments, Int J Impact Eng, 30, 1333-1351, (2004) |

[3] | Kacar, R; Acarer, M, An investigation on the explosive cladding of 316L stainless steel-din-P355GH steel, J Mater Process Technol, 152, 91-96, (2004) |

[4] | Kahraman, N; Gülenç, B; Findik, F, Joining of titanium/stainless steel by explosive welding and effect on interface, J Mater Process Technol, 169, 127-133, (2005) |

[5] | Bahrani, AS; Crossland, B, The mechanics of wave formation in explosive welding, Proc R Soc Lond A, 296, 123-136, (1967) |

[6] | Stanyukovich K (2002) Explosion physics, 3rd edn. Nauka, Moscow |

[7] | Salem, SAL; Lazari, LG; Al-Hassani, STS, Explosive welding of flat plates in free flight, Int J Impact Eng, 2, 85-101, (1984) |

[8] | Birnbaum NK, Cowler MS, Itoh M, Katayama M, Obata H (1987) AUTODYN—an interactive non-linear dynamic analysis program for microcomputers through supercomputers. In: Ninth international conference on structural mechanics in reactor technology, Lausanne, Switzerland · Zbl 1257.74117 |

[9] | Hageman LJ, Walsh JM, Hageman LJ, Walsh JM (1971) HELP, a multi-material Eulerian program for compressible fluid and elastic-plastic flows in two space dimensions and time, vol 1. System, Science and Software Inc, La Jolla |

[10] | Hallquist JO (1986) DYNA3D user’s manual (nonlinear dynamic analysis of structures in three dimensions). Lawrence Livermore National Laboratory, Livermore |

[11] | Mousavi, AAA; Burley, SJ; Al-Hassani, STS, Simulation of explosive welding using the williamsburg equation of state to model low detonation velocity explosives, Int J Impact Eng, 31, 719-734, (2004) |

[12] | Mousavi, AAA; Al-Hassani, STS, Finite element simulation of explosively-driven plate impact with application to explosive welding, Mater Des, 29, 1-19, (2008) |

[13] | Sui, GF; Li, JS; Sun, F; Ma, B; Li, HW, 3D finite element simulation of explosive welding of three-layer plates, Sci China Phys Mech Astron, 54, 890-896, (2011) |

[14] | Zhang X, Chen Z, Liu Y (2016) The material point method—a continuum-based particle method for extreme loading cases. Elsevier, Amsterdam |

[15] | Koshizuka, S; Oka, Y, Moving-particle semi-implicit method for fragmentation of incompressible fluid, Nuclear Sci Eng, 123, 421-434, (1996) |

[16] | Li, SF; Liu, WK, Meshfree and particle methods and their applications, Appl Mech Rev, 55, 1-34, (2002) |

[17] | Liu GR (2003) Mesh free methods moving beyond finite element method. Crc Press, Boca Raton · Zbl 1031.74001 |

[18] | Liu, WK; Chen, Y; Jun, S; Chen, JS; Belytschko, T; Pan, C; Uras, RA; Chang, CT, Overview and applications of the reproducing kernel particle methods, Arch Comput Methods Eng, 3, 3-80, (1996) |

[19] | Lian, YP; Zhang, X; Zhou, X; Ma, S; Zhao, YL, Numerical simulation of explosively driven metal by material point method, Int J Impact Eng, 38, 238-246, (2011) |

[20] | Wang, Y; Beom, HG; Sun, M; Lin, S, Numerical simulation of explosive welding using the material point method, Int J Impact Eng, 38, 51-60, (2011) |

[21] | Gingold, RA; Monaghan, JJ, Smoothed particle hydrodynamics: theory and application to non-spherical stars, Mon Not R Astron Soc, 181, 375-389, (1977) · Zbl 0421.76032 |

[22] | Liu GR, Liu MB (2003) Smoothed particle hydrodynamics: a meshfree particle method. World Scientific, Singapore · Zbl 1046.76001 |

[23] | Lucy, LB, A numerical approach to the testing of the fission hypothesis, Astron J, 82, 1013-1024, (1977) |

[24] | Feng, DL; Liu, MB; Li, HQ; Liu, GR, Smoothed particle hydrodynamics modeling of linear shaped charge with jet formation and penetration effects, Comput Fluids, 86, 77-85, (2013) · Zbl 1290.76121 |

[25] | Liu, MB; Liu, GR; Lam, KY, Adaptive smoothed particle hydrodynamics for high strain hydrodynamics with material strength, Shock Waves, 15, 21-29, (2006) · Zbl 1195.76328 |

[26] | Liu, MB; Liu, GR; Lam, KY; Zong, Z, Smoothed particle hydrodynamics for numerical simulation of underwater explosion, Comput Mech, 30, 106-118, (2003) · Zbl 1128.76352 |

[27] | Liu, MB; Liu, GR; Zong, Z; Lam, KY, Computer simulation of high explosive explosion using smoothed particle hydrodynamics methodology, Comput Fluids, 32, 305-322, (2003) · Zbl 1009.76525 |

[28] | Randles, PW; Libersky, LD, Smoothed particle hydrodynamics: some recent improvements and applications, Comput Methods Appl Mech Eng, 139, 375-408, (1996) · Zbl 0896.73075 |

[29] | Swegle, JW; Attaway, SW, On the feasibility of using smoothed particle hydrodynamics for underwater explosion calculations, Comput Mech, 17, 151-168, (1995) · Zbl 0841.76073 |

[30] | Li, XJ; Mo, F; Wang, XH; Wang, B; Liu, KX, Numerical study on mechanism of explosive welding, Sci Technol Weld Join, 17, 36-41, (2012) |

[31] | Nassiri A, Kinsey B (2016) Numerical studies on high-velocity impact welding: smoothed particle hydrodynamics (SPH) and arbitrary Lagrangian-Eulerian (ALE). J Manuf Process 24 |

[32] | Shao, JR; Li, HQ; Liu, GR; Liu, MB, An improved SPH method for modeling liquid sloshing dynamics, Comput Struct, 100-101, 18-26, (2012) |

[33] | Liu, MB; Li, SM, On the modeling of viscous incompressible flows with smoothed particle hydrodynamics, J Hydrodyn, 28, 731-745, (2016) |

[34] | Zukas JA (1990) High velocity impact dynamics. Wiley, London |

[35] | Lee EL, Hornig HC, Kury JW (1967) Adiabatic expansion of high explosive detonation products. Livermore Lawrence Radiation Lab, California University, Livermore |

[36] | Johnson GR, Cook WH (1983) A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. In: Proceedings of seventh international symposium on ballistics, The Hague, Netherlands |

[37] | Zhou, CE; Liu, GR; Lou, KY, Three-dimensional penetration simulation using smoothed particle hydrodynamics, Int J Comput Methods, 4, 671-691, (2007) · Zbl 1257.74117 |

[38] | Liu, MB; Liu, GR, Restoring particle consistency in smoothed particle hydrodynamics, Appl Numer Math, 56, 19-36, (2006) · Zbl 1329.76285 |

[39] | Ren, B; Fan, H; Bergel, GL; Regueiro, RA; Lai, X; Li, S, A peridynamics-SPH coupling approach to simulate soil fragmentation induced by shock waves, Comput Mech, 55, 287-302, (2015) · Zbl 1398.74395 |

[40] | Chen, JK; Beraun, JE, A generalized smoothed particle hydrodynamics method for nonlinear dynamic problems, Comput Methods Appl Mech Eng, 190, 225-239, (2000) · Zbl 0967.76077 |

[41] | Liu, MB; Xie, WP; Liu, GR, Modeling incompressible flows using a finite particle method, Appl Math Model, 29, 1252-1270, (2005) · Zbl 1163.76404 |

[42] | Hu, XY; Adams, NA, An incompressible multi-phase SPH method, J Comput Phys, 227, 264-278, (2007) · Zbl 1126.76045 |

[43] | Zhang, MY; Deng, XL, A sharp interface method for SPH, J Comput Phys, 302, 469-484, (2015) · Zbl 1349.76755 |

[44] | Colagrossi A (2003) A meshless Lagrangian method for free-surface and interface flows with fragmentation. Universita di Roma, La Sapienza |

[45] | Monaghan JJ (2005) Smoothed particle hydrodynamics. World Scientific, Singapore · Zbl 1160.76399 |

[46] | Benz W (1990) Smooth particle hydrodynamics—a review. In: Buchler JR (ed) Numerical modelling of nonlinear stellar pulsations: problems and prospects. Kluwer Academic, Boston |

[47] | Mader CL (1979) Numerical modeling of detonation. University of California Press, Berkeley · Zbl 0646.73018 |

[48] | Carpenter SH, Wittman RH (1967) Relationships of explosive welding parameters to material properties and geometry factors. University of Denver, Denver |

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