×

Two new three-dimensional contact algorithms for staggered Lagrangian hydrodynamics. (English) Zbl 1349.76482

Summary: This paper presents two new three-dimensional contact algorithms for staggered Lagrangian Hydrodynamics, named discrete accurate matching method and discrete Lagrangian multiplier method. These new contact algorithms utilize the unified contact algorithm for contact searching. Contact segments from all potential contact surfaces are treated as a single set. The basic idea of these new methods is to partition all contact segments into triangular facets firstly; then for each pair of two triangular facets which correspond to a hitting node and a target node respectively, these two triangular facets are projected to one plane and their intersection area is calculated; the nodal masses and nodal forces of the hitting node and the target node are distributed to the intersection portions of these two triangular facets respectively according to the proportion of the intersection area to corresponding nodal area. In the discrete accurate matching method, the masses and forces of the intersection portions of these two triangular facets are added to corresponding contact nodes of each other, and then the accelerations and velocities of the contact nodes are updated; while in the discrete Lagrangian multiplier method, the intersection portions of these two triangular facets are considered as a 1D contact pair in the normal direction for which the contact force is explicitly calculated by the Lagrangian multiplier method for a 1D contact pair of one hitting point and one target point, then the contact force being added to corresponding contact nodes. These new contact algorithms are assessed through several numerical tests performed on three-dimensional structured and unstructured meshes. The results of these tests show the accuracy and robustness of these new methods.

MSC:

76M20 Finite difference methods applied to problems in fluid mechanics
76Txx Multiphase and multicomponent flows
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Addessio, F. L.; Carroll, D. E.; Dukowicz, J. K.; Harlow, F. H.; Johnson, J. N.; Kashiwa, B. A.; Maltrud, M. E.; Ruppel, H. M., CAVEAT: A computer code for fluid dynamics problems with large distortion and internal slip (1988), Los Alamos National Laboratory UC-32
[2] Attaway, S. W.; Hendrickson, B. A.; Plimpton, S. J., A parallel contact detection algorithm for transient solid dynamics simulations using PRONTO3D, Comput. Mech., 22, 2, 143-159 (1998) · Zbl 0927.74064
[3] Barlow, A., A new Lagrangian scheme for multimaterial cells, (Proceedings of European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS Computational Fluid Dynamics Conference 2001. Proceedings of European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS Computational Fluid Dynamics Conference 2001, Swansea, Wales, U.K. (4-7 September 2001)), 235-294
[4] Belytschko, T.; Yeh, I. S., The splitting pinball method for contact-impact problems, Comput. Methods Appl. Mech. Eng., 105, 375-393 (1993) · Zbl 0774.73081
[5] Benson, D. J., Computational methods in Lagrangian and Eulerian hydrocodes, Comput. Methods Appl. Mech. Eng., 99, 235-394 (1992) · Zbl 0763.73052
[6] Benson, D. J.; Hallquist, J. O., A Single Surface Contact Algorithm for Post-Buckling Analysis of Shell Structures (1987), University of California: University of California San Diego · Zbl 0708.73079
[7] Berger, M. J.; Bokhari, S. H., A partitioning strategy for nonuniform problems on multi-processors, IEEE Trans. Comput., C-36, 570-580 (1987)
[8] Bertholf, L. D.; Benzley, S. E., TOODY II, A computer program for two-dimensional wave propagation (1968), Sandia National Laboratories, SC-RR-68-41
[9] Bourago, N. G.; Kukudzhanov, V. N., A review of contact algorithms, available at
[10] Bourago, N. G., A survey on contact algorithms, available at
[11] Burton, D. E.; Carney, T. C.; Morgan, N. R.; Sambasivan, S. K.; Shashkov, M. J., A cell-centered Lagrangian Godunov-like method for solid dynamics, Comput. Fluids, 83, 33-47 (2013) · Zbl 1290.76095
[12] Campbell, J. C.; Shashkov, M. J., A tensor artificial viscosity using a mimetic finite difference algorithm, J. Comput. Phys., 172, 739-765 (2001) · Zbl 1002.76082
[13] Caramana, E. J.; Burton, D. E.; Shashkov, M. J.; Whalen, P. P., The construction of compatible hydrodynamics algorithms utilizing conservation of total energy, J. Comput. Phys., 146, 227-262 (1998) · Zbl 0931.76080
[14] Caramana, E. J.; Rousculp, C. L.; Burton, D. E., A compatible, energy and symmetry preserving Lagrangian hydrodynamics algorithm in three-dimensional Cartesian geometry, J. Comput. Phys., 157, 89-119 (2000) · Zbl 0961.76049
[15] Caramana, E. J.; Shashkov, M. J.; Whalen, P. P., Formulations of artificial viscosity for multidimensional shock wave computations, J. Comput. Phys., 144, 70-97 (1998) · Zbl 1392.76041
[16] Caramana, E. J.; Shashkov, M. J., Elimination of artificial grid distortion and hourglass-type motions by means of Lagrangian subzonal masses and pressures, J. Comput. Phys., 142, 521-561 (1998) · Zbl 0932.76068
[17] Caramana, E. J.; Loubère, R., “Curl-q”: A vorticity damping artificial viscosity for essentially irrotational Lagrangian hydrodynamics calculations, J. Comput. Phys., 215, 385-391 (2006) · Zbl 1173.76380
[18] Caramana, E. J., The implementation of slide lines as a combined force and velocity boundary condition, J. Comput. Phys., 228, 3911-3916 (2009) · Zbl 1273.76258
[19] Carpenter, N. J.; Taylor, R. L.; Katona, M. G., Lagrange constraints for transient finite element surface contact, Int. J. Numer. Methods Eng., 32, 1, 103-128 (1991) · Zbl 0763.73053
[20] Chaudhary, A. B.; Bathe, K. J., A Lagrange multiplier segment procedure for solution of three dimensional contact problems (1985), U.S. Army Ballistic Research Laboratory BRL-CR-544
[21] Cooper, P., Explosive Engineering, 206-207 (1996), Wiley, VCH
[22] Després, B.; Mazeran, C., Lagrangian gas dynamics in two-dimensions and Lagrangian systems, Arch. Ration. Mech. Anal., 178, 327-372 (2005) · Zbl 1096.76046
[23] Eakins, D.; Thadani, N., Instrumented Taylor anvil-on-rod impact tests for validating applicability of standard strength models to transient deformation states, J. Appl. Phys., 100, 073503 (2006)
[24] Franke, R., Scattered data interpolation: tests of some methods, Math. Comput., 38, 181-199 (1982) · Zbl 0476.65005
[25] Godunov, S. K.; Zabrodine, A.; Ivanov, M.; Kraiko, A.; Prokopov, G., Résolution numérique des problèmes multidimensionnels de la dynamique des gaz (1979), Mir · Zbl 0421.65056
[26] Gonzalez, J. A.; Park, K. C.; Felippa, C. A.; Abascal, R., A formulation based on localized Lagrange multipliers for BEM-FEM coupling in contact problems, Comput. Methods Appl. Mech. Eng., 197, 623-640 (2008) · Zbl 1169.74639
[27] Hallquist, J. O., Nike2D-a vectorized, implicit, finite deformation, finite element code for analyzing the static and dynamic response of two-dimensional solids (1979), LLNL: LLNL Livermore, Rept. UCRL-52678
[28] Hallquist, J. O., LS-DYNA3D Theoretical Manual (1991), Livermore Software Technology Corporation: Livermore Software Technology Corporation Livermore
[29] Hallquist, J.; Goudreau, G.; Benson, D., Sliding interfaces with contact-impact in large scale Lagrangian computations, Comput. Methods Appl. Mech. Eng., 51, 3, 107-137 (1985) · Zbl 0567.73120
[30] Hardy, R. L., Multiquadric equations of topography and other irregular surfaces, J. Geophys. Res., 176, 1905-1915 (1971)
[31] Howell, B. P.; Ball, G. J., A free-Lagrange augmented Godunov method for the simulation of elastic-plastic solids, J. Comput. Phys., 175, 128-167 (2002) · Zbl 1043.74048
[32] Kenamond, M.; Bement, M., Slideline modeling in the FLAG hydrocode, (MultiMat Conference. MultiMat Conference, Arcachon, France, September 5-9 (2011))
[33] Kolev, Tz. V.; Rieben, R. N., A tensor artificial viscosity using a finite element approach, J. Comput. Phys., 228, 8336-8366 (2009) · Zbl 1287.76166
[34] Kuchařík, M.; Loubère, R.; Bednárik, L.; Liska, R., Enhancement of Lagrangian slide lines as a combined force and velocity boundary condition, Comput. Fluids, 83, 3-14 (2013) · Zbl 1290.76137
[35] Lipnikov, K.; Shashkov, M., A mimetic tensor artificial viscosity method for arbitrary polyhedral meshes, Proc. Comput. Sci., 1, 1921-1929 (2012)
[36] Maire, P.-H.; Abgrall, R.; Breil, J.; Ovadia, J., A cell-centered Lagrangian scheme for two-dimensional compressible flow problems, SIAM J. Sci. Comput., 29, 1781-1824 (2007) · Zbl 1251.76028
[37] Morgan, N. R.; Kenamond, M. A.; Burton, D. E.; Carney, T. C., An approach for treating contact surfaces in Lagrangian cell-centered hydrodynamics, J. Comput. Phys., 250, 527-554 (2013)
[38] Nilsson, L.; Zhong, Z. H.; Oldenburg, M., Analysis of shell structures subjected to contact-impacts, (Proc. Symposium on Analytical and Computational Models for Shells. Proc. Symposium on Analytical and Computational Models for Shells, ASME Annual Winter Meet, San Francisco, U.S.A. (1989)), 457-482
[39] Noh, W., Errors for calculations of strong shocks using an artificial viscosity and an artificial heat flux, J. Appl. Phys., 72, 78-120 (1987) · Zbl 0619.76091
[40] Papadopoulos, P.; Taylor, R. L., A simple algorithm for three-dimensional finite element analysis of contact problems, Comput. Struct., 46, 6, 1107-1118 (1993) · Zbl 0773.73089
[41] Papadopoulos, P.; Solberg, J., A Lagrange multiplier method for the finite element solution of frictionless contact problems, Math. Comput. Model., 28, 373-384 (1998) · Zbl 1002.74590
[42] Samarskii, A. A.; Tishkin, V. F.; Favorskii, A. P.; Shashkov, M. J., Operational finite difference schemes, Differ. Equ., 17, 854-862 (1981) · Zbl 0485.65060
[43] Sambasivan, S. K.; Shashkov, M. J.; Burton, D. E., A cell-centered Lagrangian finite volume approach for computing elasto-plastic response of solids in cylindrical axisymmetric geometries, J. Comput. Phys., 237, 251-288 (2013) · Zbl 1286.74113
[44] Sedov, L. I., Similarity and Dimensional Methods in Mechanics (1959), Academic Press: Academic Press New York · Zbl 0121.18504
[45] Shashkov, M. J., Conservative Finite-Difference Methods on General Grids (1996), CRC Press: CRC Press Boca Raton, FL · Zbl 0844.65067
[46] Shashkov, M. J., Closure models for multimaterial cells in arbitrary Lagrangian-Eulerian hydrocodes, Int. J. Numer. Methods Fluids, 56, 1497-1504 (2007) · Zbl 1151.76026
[47] Taylor, G., Proc. R. Soc. Lond. Ser. A, 194, 289-299 (1948)
[48] Taylor, L. M.; Flanagan, D. P., PRONTO2D: A two-dimensional transient solid dynamics program (1987), Sandia National Laboratories SAND86-0594
[49] Verney, D., Évaluation de la Limite Élastique du Cuivre et de l’Uranium par des Expèriences d’Implosion Lente, (Behavior of Dense Media under High Dynamic Pressures, Symposium. Behavior of Dense Media under High Dynamic Pressures, Symposium, H.D.P., IUTAM, Paris, 1967 (1968), Gordon & Breach: Gordon & Breach New York), 293-303
[50] Jihai, Wang, Polynomial form of Mie-Grüneisen equation of state and its isentropes, Explos. Shock Waves, 12, 1, 1-10 (1992), (in Chinese)
[51] Wang, Fujun; Cheng, Jiangang; Yao, Zhenhan, FFS contact searching algorithm for dynamic finite element analysis, Int. J. Numer. Methods Eng., 52, 655-672 (2001) · Zbl 1055.74042
[52] Wang, Fujun; Wang, Liping; Cheng, Jiangang; Yao, Zhenhan, Contact force algorithm in explicit transient analysis using finite-element method, Finite Elem. Anal. Des., 43, 580-587 (2007)
[53] Wilkins, M. L., Calculations of elastic-plastic flow, Methods Comput. Phys.. Methods Comput. Phys., Computer Simulation of Dynamic Phenomena, 3, 211-262 (1999), Springer-Verlag, (Ch. 5) · Zbl 0926.76001
[54] Wilkins, M. L., HEMP3D—A finite difference program for calculating elastic-plastic flow (1993), LLNL UCRI-ID-114993
[55] Zhong, Z. H., On contact-impact problems (1988), Linköping University, Dissertation No. 178
[56] Zhong, Z. H., Finite Element Procedures for Contact-Impact Problems (1993), Oxford University Press: Oxford University Press Oxford
[57] Zhong, Z. H.; Nilsson, L., A unified contact algorithm based on the territory concept, Comput. Methods Appl. Mech. Eng., 130, 1-16 (1996) · Zbl 0860.73062
[58] Zukas, J.; Walters, W., Explosive Effects and Applications, 91-93 (1998), Springer
[59] Jia, Zupeng; Liu, Jun; Zhang, Shudao, An effective integration of methods for second-order three-dimensional multi-material ALE method on unstructured hexahedral meshes using MOF interface reconstruction, J. Comput. Phys., 236, 513-562 (2013) · Zbl 1286.65036
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.