Interaction and multiscale mechanics

  • 제6권2호
  • /
  • Pages.173-195
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  • 2013
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  • 1976-0426(pISSN)
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  • 2092-6200(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Concrete fragmentation modeling using coupled finite element - meshfree formulations

  • Wu, Youcai (Karagozian & Case (K&C)) ;
  • Choi, Hyung-Jin (Karagozian & Case (K&C)) ;
  • Crawford, John E. (Karagozian & Case (K&C))
  • 투고 : 2013.03.03
  • 심사 : 2013.05.07
  • 발행 : 2013.09.01
⟨ 이전 논문 다음 논문 ⟩

초록

Meshfree methods are known to have the capability to overcome the strict regularization requirements and numerical instabilities that encumber the finite element method (FEM) in large deformation problems. They are also more naturally suited for problems involving material perforation and fragmentation. To take advantage of the high efficiency of FEM and high accuracy of meshfree methods, a coupled finite element (FE) and reproducing kernel (RK, one of the meshfree approximations) formulation is described in this paper. The coupling of FE and RK approximation is implemented in an evolutionary fashion, where the extent and location of the evolution is dependent on a triggering criteria provided by the material constitutive laws. To enhance computational efficiency, Gauss quadrature is applied to integrate both FE and RK domains so that no state variable transfer is required when mesh conversion is performed. To control the hourglassing that might occur with 1-point integrated hexahedral grids, viscous type hourglass control is implemented. Meanwhile, the FEM version of the K&C concrete (KCC) model was modified to make it applicable in both FE and RK formulations. Results using this code and the KCC model are shown for the modeling of concrete responses under quasi-static, blast and impact loadings. These analyses demonstrate that fragmentation phenomena of the sort commonly observed under blast and impact loadings of concrete structures was able to be realistically captured by the coupled formulation.

키워드

참고문헌

  1. Bardenhagen, S.G. and Kober, E.M. (2004), "The meneralized interpolation material point method", Comput. Modeling Eng. Sci., 5(6), 477-496.
  2. Batra, R.C. and Lear, M.H. (2004), "Simulation of brittle and ductile fracture in an impact loaded prenotched plate", Int. J. Fracture, 126(2), 179-203. https://doi.org/10.1023/B:FRAC.0000026364.13365.71
  3. Belytschko, T. and Tabbara, M. (1996), "Dynamic fracture using element free Galerkin methods", Int. J. Numer. Meth. Eng., 39(6), 923-938. https://doi.org/10.1002/(SICI)1097-0207(19960330)39:6<923::AID-NME887>3.0.CO;2-W
  4. Belytschko, T., Lu, Y.Y. and Gu, L. (1994), "Element-free Galerkin methods", Int. J. Numer. Meth. Eng., 37(2), 229-256. https://doi.org/10.1002/nme.1620370205
  5. Belytschko, T., Lu, Y.Y. and Gu, L. (1995), "Element-free Galerkin methods for static and dynamic fracture0", Int. J. Solids Struct., 32(17-18), 2547-2570. https://doi.org/10.1016/0020-7683(94)00282-2
  6. Chen, J.S. and Wang, D. (2006), "A constrained reproducing kernel particle formulation for shear deformable shell in Cartesian coordinates", Int. J. Numer. Meth. Eng., 68(2), 151-172. https://doi.org/10.1002/nme.1701
  7. Chen, J.S. and Wu, Y. (2007), "Stability in Lagrangian and semi-Lagrangian reproducing kernel discretizations using nodal integration in nonlinear solid mechanics", Compu.Meth. Appl. Mech. Eng., (Eds. V. M. A. Leitao, C.J.S. Alves, C. A. Duarte), Springer, 55-77
  8. Chen, J.S., Crawford, J.E. and Wu, Y. (2006), "Development of meshfree methods for fragment impact problems", TR 06 58.1, Karagozian & Case, Burbank, CA.
  9. Chen, J.S., Han, W., You, Y. and Meng, X. (2003), "A reproducing kernel method with nodal interpolation property", Int. J. Numer. Meth. Eng., 56, 935-960. https://doi.org/10.1002/nme.592
  10. Chen, J.S., Pan, C. and Wu, C.T. (1998c), "Application of reproducing kernel particle method to large deformation contact analysis of elastomers", Rubber Chem. Tech., 71, 191-213. https://doi.org/10.5254/1.3538479
  11. Chen, J.S., Pan, C. and Wu, C.T. (1998b), "Large deformation analysis of rubber based on a reproducing kernel particle method", Comput. Mech., 22, 289-307. https://doi.org/10.1007/s004660050361
  12. Chen, J.S., Pan, C., Roque, C.M.O.L. and Wang, H. (1998a), "A Lagrangian reproducing kernel particle method for metal forming analysis", Comput. Mech., 22, 289-307. https://doi.org/10.1007/s004660050361
  13. Chen, J.S., Pan, C., Wu, C.T. and Liu, W.K. (1996), "Reproducing kernel particle methods for large deformation analysis of nonlinear structures", Compu.Meth. Appl. Mech. Eng., 139, 195-227 https://doi.org/10.1016/S0045-7825(96)01083-3
  14. Chen, J.S., Wu, C.T., Chi, L.C. and Huck, F. (2001b), "A Lagrangian meshfree formulation for geotechnical material", J. Eng. Mech., 127, 440-449. https://doi.org/10.1061/(ASCE)0733-9399(2001)127:5(440)
  15. Chen, J.S., Wu, C.T., Yoon, S. and You, Y. (2001a), "A stabilized conforming nodal integration for Galerkin meshfree methods", Int. J. Numer. Meth. Eng., 50, 435-466, 2001. https://doi.org/10.1002/1097-0207(20010120)50:2<435::AID-NME32>3.0.CO;2-A
  16. Chen, J.S., Wu, C.T., Yoon, S. and You, Y. (2002), "Nonlinear version of stabilized conforming nodal integration for Galerkin meshfree methods", Int. J. Numer. Meth. Eng., 53, 2587-2615. https://doi.org/10.1002/nme.338
  17. Chen, W.F. (1982), "Plasticity in Reinforced Concrete", McGraw Hill, New York
  18. Courant, R. (1942), "Variational methods for the solution of problems of equilibrium and vibrations", Transaction of American Mathematical Society, 1-23.
  19. Crawford, J.E., Chen, J.S., Choi, H.J. and Wu, Y. (2005), "Description of meshfree methods developed for fragment impact, penetrations and other problems", TR-05-71.1, Karagozian & Case, Burbank, CA.
  20. Crawford, J.E., Magallanes, J.M., Lan, S. and Wu, Y. (2011), User's manual and documentation for release III of the K&C concrete material model in LS-DYNA, TR-11-36-1, Technical report, Karagozian & Case, Burbank, CA.
  21. Fernandez-Mendez, S. and Huerta, A. (2004), "Imposing essential boundary conditions in mesh-free methods", Compu.Meth. Appl. Mech. Eng., 193, 1257-1275. https://doi.org/10.1016/j.cma.2003.12.019
  22. Flanagan, D.P. and Belytshcko, T. (1981), "A uniform strain hexahedron and quadrilateral with orthogonal hourglass control", Int. J. Numer. Meth. Eng., 17, 679-706. https://doi.org/10.1002/nme.1620170504
  23. Gingold, R.A. and Monaghan, J.J. (1972), "Smooth particle hydrodynamics: theory and application to non-spherical stars", Monthly Notices of the Royal Astronomical Society, 181, 375-389.
  24. Guan, P.C., Chen, J.S., Wu, Y., Teng, H., Gaido,s J., Hofstetter, K. and Alsaleh, M. (2009), "Semi-Lagrangian reproducing kernel formulation and application to modeling earth moving operations", Mech. Mater., 41, 670-683. https://doi.org/10.1016/j.mechmat.2009.01.030
  25. Guan, P.C., Chi, S.W., Chen, J.S., Slawson, T.R. and Roth, M.J. (2011), "Semi-Lagrangian reproducing kernel particle method for fragment-impact problems", Int. J. Impact Eng., 38, 1033-1047. https://doi.org/10.1016/j.ijimpeng.2011.08.001
  26. Guo, Y., Wu, C.T., Botkin, M.E. and Wang, H.P. (2004), "Coupled FEM/Meshfree shear-deformable shells for nonlinear analysis of shell structures", Proceedings of WCCM VI in conjunction with APCOM 04, September, Beijing, China.
  27. Hu, W., Wu, C.T. and Saito, K. (2010), "LS-DYNA meshfree interactive adaptivity and its application", 11th international LS-DYNA Users Conference, Detroit, MI.
  28. Lin, J.I. (2005), DYNA3D: a nonlinear, explicit, three-dimensional finite element code for solid and structural mechanics, User Manual, UCRL-MA-107254, Methods Development Group, Lawrence Livermore National Laboratory.
  29. Liu, W.K., Jun, S. and Zhang, Y.F. (1995), "Reproducing kernel particle methods", Int. J. Numer. Meth. Fluids, 20, 1081-1106. https://doi.org/10.1002/fld.1650200824
  30. Liu, W.K., Jun, S., Sihling, D.T., Chen, Y. and Hao, W. (1997), "Multiresolution reproducing kernel particle method for computational fluid dynamics", Int. J. Numer. Meth. Fluids, 24(12), 1391-1415. https://doi.org/10.1002/(SICI)1097-0363(199706)24:12<1391::AID-FLD566>3.0.CO;2-2
  31. Lu, H. and Chen, J.S. (2002), "Adaptive meshfree particle method", Lecture Notes Comput. Sci. Eng., 26, 251-267.
  32. Lu. Y.Y., Belytschko, T. and Gu, L. (1994), "A new implementation of the element free galerkin methods", Compu. Meth. Appl. Mech. Eng., 113, 397-414. https://doi.org/10.1016/0045-7825(94)90056-6
  33. Malvar, L.J., Crawford, J.E., Wesevich, J.W. and Simons, D. (1997), "A plasticity concrete material model for DYNA3D", Int. J. Impact Eng., 19, 847-873. https://doi.org/10.1016/S0734-743X(97)00023-7
  34. Monaghan, J.J. (1988), "An introduction to SPH", Comput. Physic. Commun., 48, 89-96. https://doi.org/10.1016/0010-4655(88)90026-4
  35. Puso, M.A., Chen, J.S., Zywicz, E. and Elmer, W. (2008), "Meshfree and finite element nodal integration method", Int. J. Numer. Meth. Eng., 74, 416-446. https://doi.org/10.1002/nme.2181
  36. Rabczuk, T. and Eibl, J. (2003), "Simulation of high velocity concrete fragmentation using SPH/MLSPH", Int. J. Numer. Meth. Eng., 56, 1421-1444. https://doi.org/10.1002/nme.617
  37. Wagner, G.J. and Liu, W.K. (2000), "Application of essential boundary conditions in mesh-free methods: a corrected collocation method", Int. J. Numer. Meth. Eng., 47, 1367-1379. https://doi.org/10.1002/(SICI)1097-0207(20000320)47:8<1367::AID-NME822>3.0.CO;2-Y
  38. Wang, D. and Chen, J.S. (2008), "A Hermite reproducing kernel approximation for thin plate analysis with sub-domain stabilized conforming integration", Int. J. Numer. Meth. Eng., 74, 368-390 https://doi.org/10.1002/nme.2175
  39. Wang, D. and Lin, Z. (2011), "Dispersion and transient analyses of Hermite reproducing kernel Galerkin meshfree method with sub-domain stabilized conforming integration for thin beam and plate structures", Comput. Mech., 48, 47-63. https://doi.org/10.1007/s00466-011-0580-y
  40. Wang, D. and Sun, Y. (2011), "A Galerkin meshfree formulation with stabilized conforming nodal integration for geometrically nonlinear analysis of shear deformable plates", Int. J. Comput. Meth., 8, 685-703. https://doi.org/10.1142/S0219876211002769
  41. Wang, D. and Wu, Y. (2008), "An efficient Galerkin meshfree analysis of shear deformable cylindrical panels", Interact. Multiscale Mech., 1, 339-355. https://doi.org/10.12989/imm.2008.1.3.339
  42. Wang, D. and Chen, J.S. (2004), "Locking-free stabilized conforming nodal integration for meshfree Mindlin-Reissner plate formulation", comput. Meth. Appl. Mech. Eng., 193, 1065-1083. https://doi.org/10.1016/j.cma.2003.12.006
  43. Wang, D. and Chen, J.S. (2006), "A locking-free meshfree curved beam formulation with the stabilized conforming nodal integration", Comput. Mech., 39(1), 83-90. https://doi.org/10.1007/s00466-005-0010-0
  44. Wang, D., Li, Z., Li, L. and Wu, Y. (2011), "Three dimensional efficient meshfree simulation of large deformation failure evolution in soil medium", Sic. China-Tech. Sci., 54, 573-580. https://doi.org/10.1007/s11431-010-4287-7
  45. Wang, H.P., Wu, C.T., Botkin, M. and Guo, Y. (2009), "A coupled meshfree/finite element method for automotive crashworthiness simulations", Int. J. Impact Eng., 36(10-11), 1210-1222. https://doi.org/10.1016/j.ijimpeng.2009.03.004
  46. Wu, Y. (2005) "A stabilized semi-Lagrangian Galerkin meshfree formulation for extremely large deformation analysis", Ph.D. Dissertation, UCLA.
  47. Wu, Y., Magallanes, J.M., Choi, H.J. and Crawford, J.E. (2013), "An evolutionarily coupled finite element - meshfree formulation for modeling concrete behaviors under blast and impact loadings", ASCE J. Eng. Mech., 139(4), 525-536. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000497
  48. Zhou, M., Ravichandran, G. and Rosakis, A.J. (1996), "Dynamically propagating shear bands in impact-loaded prenotched plates - 2. Numerical Simulations", J. Mech. Physic Solid, 44(6), 1007-1032. https://doi.org/10.1016/0022-5096(96)00004-X
  49. Zhu, T., Zhang, J.D. and Atluri, S.N. (1998), "A meshless local boundary integral equation (LBIE) method for solving nonlinear problems", Comput. Mech., 22, 174-186. https://doi.org/10.1007/s004660050351

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