DOI QR코드

DOI QR Code

2D continuum viscodamage-embedded discontinuity model with second order mid-point scheme

  • Do, Xuan Nam (Universite de Technologie Compiegne / Sorbonne Universites, Laboratoire Roberval de Mecanique Centre de Recherche Royallieu, Rue Personne de Roberval) ;
  • Ibrahimbegovic, Adnan (Universite de Technologie Compiegne / Sorbonne Universites, Laboratoire Roberval de Mecanique Centre de Recherche Royallieu, Rue Personne de Roberval)
  • 투고 : 2018.08.01
  • 심사 : 2018.09.04
  • 발행 : 2018.12.25

초록

This paper deals with numerical modeling of dynamic failure phenomena in rate-sensitive brittle and/or ductile materials. To this end, a two-dimensional continuum viscodamage-embedded discontinuity model, which is based on our previous work (see Do et al. 2017), is developed. More specifically, the pre-peak nonlinear and rate-sensitive hardening response of the material behavior, representing the fracture-process zone creation, is described by a rate-dependent continuum damage model. Meanwhile, an embedded displacement discontinuity model is used to formulate the post-peak response, involving the macro-crack creation accompanied by exponential softening. The numerical implementation in the context of the finite element method exploiting the second-order mid-point scheme is discussed in detail. In order to show the performance of the model several numerical examples are included.

키워드

참고문헌

  1. Alfaiate, J., Wells, G.N. and Sluys, L.J. (2002), "On the use of embedded discontinuity elements with crack path continuity for mode-I and mixed-mode fracture", Eng. Fract. Mech., 69(6), 661-686. https://doi.org/10.1016/S0013-7944(01)00108-4
  2. Armero, F. and Garikipati, K. (1995), "Recent advances in the analysis and numerical simulation of strain localization in inelastic solids. In Owen, E., Onate, D.R.J., Hinton, E. (Eds)", Proceedings of the Computational Plasticity IV, CIMNE, Barcelona, 547-561.
  3. Armero, F. and Linder, C. (2009), "Numerical simulation of dynamic fracture using finite elements with embedded discontinuities", Int. J. Fract., 160(2), 119-141. https://doi.org/10.1007/s10704-009-9413-9
  4. Arrea, M. and Ingraffea, A.R. (1982), Mixed-Mode Crack Propagation in Mortar and Concrete, Report No. 81-13, Department of Structural Engineering, Cornell University, Ithaca, New York, U.S.A.
  5. Bazant, Z.P. (1976), "Instability, ductility, and size effect in strain-softening concrete", J. Eng. Mech. Div., 102, 331-344.
  6. Bazant, Z.P., Belytschko, T.B. and Chang, T.P. (1984), "Continuum theory for strain softening", J. Eng. Mech., 110(12), 1666-1691. https://doi.org/10.1061/(ASCE)0733-9399(1984)110:12(1666)
  7. Brancherie, D. and Ibrahimbegovic, A. (2009), "Novel anisotropic continuum-discrete damage model capable of representing localized failure of massive structures. Part I: Theoretical formulation and numerical implementation", Eng. Comput., 26(1/2), 100-127. https://doi.org/10.1108/02644400910924825
  8. Cervera, M., Oliver, J. and Manzoli, O. (1995), "A rate dependent isotropic damage model for the seismic analysis of concrete dams", Earthq. Eng. Struct. Dyn., 25, 987-1010.
  9. De Borst, R., Sluys, L.J., Muhlhaus, H.B. and Pamin, J. (1993), "Fundamental issues in finite element analyses of localization of deformation", Eng. Comput., 10, 99-121. https://doi.org/10.1108/eb023897
  10. Do, X.N., Ibrahimbegovic, A. and Brancherie, D. (2017), "Dynamics framework for 2D anisotropic continuum-discrete damage model for progressive localized failure of massive structures", Comput. Struct., 183, 14-26. https://doi.org/10.1016/j.compstruc.2017.01.011
  11. Dujc, J., Brank, B. and Ibrahimbegovic, A. (2013), "Stress-hybrid quadrilateral finite element with embedded strong discontinuity for failure analysis of plane stress solids", Int. J. Numer. Meth. Eng., 94(12), 1075-1098. https://doi.org/10.1002/nme.4475
  12. Fahrenthold, E.P. (1991), "A continuum damage for facture of brittle solids under dynamic loading", J. Appl. Mech., 58(4), 904-909. https://doi.org/10.1115/1.2897704
  13. Geuzaine, C. and Remacle, J.F. (2009), "Gmsh: A 3-d finite element mesh generator with built-in pre- and post-processing facilities", Int. J. Numer. Meth. Eng., 79(11), 1309-1331. https://doi.org/10.1002/nme.2579
  14. Grady, D.E. and Kipp, M.E. (1980), "Continuum modelling of explosive fracture in oil shale", Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 17(3), 147-157. https://doi.org/10.1016/0148-9062(80)91361-3
  15. Hamdi, E., Romdhane, N.B. and Le Cleac'h, J.M. (2011), "A tensile damage model for rocks: Application to blast induced damage assessment", Comput. Geotech., 38(2), 133-141. https://doi.org/10.1016/j.compgeo.2010.10.009
  16. Huespe, A.E., Oliver, J., Sanchez, P.J., Blanco, S. and Sonzogni, V. (2006), "Strong discontinuity approach in dynamic fracture simulations", Mecan. Comput., 25, 1997-2018.
  17. Ibrahimbegovic, A. and Melnyk, S. (2007), "Embedded discontinuity finite element method for modeling of localized failure in heterogeneous materials with structured mesh: an alternative to extended finite element method", Comput. Mech., 40(1), 149-155. https://doi.org/10.1007/s00466-006-0091-4
  18. Ibrahimbegovic, A. and Wilson, E.L. (1991), "A modified method of incompatible modes", Commun. Appl. Numer. Meth., 7(3), 187-194. https://doi.org/10.1002/cnm.1630070303
  19. Linder, C. and Armero, F. (2007), "Finite element with embedded strong discontinuities for the modeling of failure in solids", Numer. Meth. Eng., 72(12), 1391-1433. https://doi.org/10.1002/nme.2042
  20. Lu, Y. and Xu, K. (2004), "Modelling of dynamic behaviour of concrete materials under blast loading", Int. J. Sol. Struct., 41(1), 131-143. https://doi.org/10.1016/j.ijsolstr.2003.09.019
  21. Needleman, A. (1988), "Material rate dependence and mesh sensitivity in localization problems", Comput. Meth. Appl. Mech. Eng., 63(1), 69-85.
  22. Oliver, J. (1996), "Modelling strong discontinuities in solid mechanics via strain softening constitutive equations. Part I & Part II", Int. J. Numer. Meth. Eng., 39(21), 3575-3623. https://doi.org/10.1002/(SICI)1097-0207(19961115)39:21<3575::AID-NME65>3.0.CO;2-E
  23. Oliver, J. (2000), "On the discrete constitutive models induced by strong discontinuity kinematics and continuum constitutive equations", Int. J. Sol. Struct., 37(48-50), 7207-7229. https://doi.org/10.1016/S0020-7683(00)00196-7
  24. Petersson, P.E. (1981), Crack Growth and Development of Fracture Zones in Plain Concrete and Similar Materials, Report No. TVBM-1006, Division of Building Materials, University of Lund, Lund, Sweden.
  25. Radulovic, R., Bruhns, O.T. and Mosler, J. (2011), "Effective 3D failure simulations by combining the advantages of embedded strong discontinuity approaches and classical interface elements", Eng. Fract. Mech., 78(12), 2470-2485. https://doi.org/10.1016/j.engfracmech.2011.06.007
  26. Rots, J.G., Nauta, P., Kusters, G.M.A. and Blaauwendraad, J. (1985), "Smeared crack approach and fracture localization in concrete", Heron, 30(1), 1-48.
  27. Saksala, T., Brancherie, D., Harari, I. and Ibrahimbegovic, A. (2015), "Combined continuum damageembedded discontinuity model for explicit dynamic fracture analyses of quasi-brittle materials", Int. J. Numer. Meth. Eng., 101(3), 230-250. https://doi.org/10.1002/nme.4814
  28. Simo, J.C. and Rifai, M.S. (1990), "A class of mixed assumed strain methods and the method of incompatible modes", Int. J. Numer. Meth. Eng., 29(8), 1595-1638. https://doi.org/10.1002/nme.1620290802
  29. Simo, J.C., Oliver, J. and Armero, F. (1993), "An analysis of strong discontinuity induced by strain softening solutions in rate-independent solids", J. Comput. Mech., 12(5), 277-296. https://doi.org/10.1007/BF00372173
  30. Suaris, W. and Shah, S.P. (1984), "Rate-sensitive damage theory for brittle solids", J. Eng. Mech., 110(6), 985-997. https://doi.org/10.1061/(ASCE)0733-9399(1984)110:6(985)
  31. Taylor, L.M., Chen, E.P. and Kuszmaul, J.S. (1986), "Microcrack-induced damage accumulation in brittle rock under dynamic loading", Comput. Meth. Appl. Mech. Eng., 55(3), 301-320. https://doi.org/10.1016/0045-7825(86)90057-5
  32. Wang, Z., Li, Y. and Wang, J.G. (2008), "A method for evaluating dynamic tensile damage of rock", Eng. Fract. Mech., 75(10), 2812-2825. https://doi.org/10.1016/j.engfracmech.2008.01.005
  33. Yang, R., Bawden, W.F. and Katsabanis, P.D. (1996), "A new constitutive model for blast damage", Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 33(3), 245-254. https://doi.org/10.1016/0148-9062(95)00064-X
  34. Yazdchi, M., Valliappan, S. and Zhang, W. (1996), "Continuum model for dynamic damage evolution of anisotropic brittle materials", Int. J. Numer. Meth. Eng., 39(9), 1555-1583. https://doi.org/10.1002/(SICI)1097-0207(19960515)39:9<1555::AID-NME917>3.0.CO;2-J
  35. Zienkiewicz, O.C. and Taylor, R.L. (1989), The Finite Element Method: Basic Formulation and Linear Problems, McGraw-Hill, London, U.K.