Advertisement

International Journal of Fracture

, Volume 137, Issue 1–4, pp 19–49 | Cite as

Application of Particle Methods to Static Fracture of Reinforced Concrete Structures

  • T. Rabczuk
  • T. Belytschko
Article

Abstract

Particle methods for modeling reinforced concrete are described. The reinforcements are modeled by finite elements and are coupled to the particle method by Lagrange multipliers. The method is applicable to nonlinear problems, problems with moderate to severe cracking and deformable interfaces. Applications to the static response of reinforced concrete structures where the concrete is discretized with particles and the reinforcement with elements are described. The method is also tested for several static problems where no relative displacements between the concrete and the reinforcement are allowed.

Keywords

Bond EFG fracture meshfree particle methods particle-FEM coupling reinforced concrete 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Akkermann, J. (2000). Rotationsverhalten von Stahlbeton-Rahmenecken, Dissertation. Institut fuer Massivbau und Baustofftechnologie, Heft 39, Universitaet Karlsruhe.Google Scholar
  2. Arrea, M., Ingraffea, A.R. 1982Mixed-mode crack propagation in mortar and concreteDept. of Struct. Eng. Cornell University IthakaN.Y.Rep. No. 81-13Google Scholar
  3. Attaway, S.W., Heinstein, M.W. and Swegle, J.W. (1994). Coupling of Smoothed Particle Hydrodynamics with the Finite Element Method, Nuclear Engineering and Design 150, Post-SMIRT Impact IV Seminar Berlin.Google Scholar
  4. Babuska, I. and Melenk, J.M. (1995). The partition of unity finite element method. University of Maryland, Technical Note BN-1185.Google Scholar
  5. Bažant, Z.P., Belytschko, T., Chang, T.P. 1984Continuum theory for strain softeningJournal of Engineering Mechanics-ASCE11016661692Google Scholar
  6. Bažant, Z.P., Pijaudier Cabot, G. 1988Nonlocal continuum damage, localization instabilities and convergenceJournal of Engineering Mechanics55287293Google Scholar
  7. Bažant, Z.P., Prat, P. 1988Microplane model for brittle plastic materials I: Theory, II: verificationJournal of Engineering Mechanics ASCE11416721702Google Scholar
  8. Bažant, Z.P. and Jirasek, M. (2002). Nonlocal integral formulations of plasticity and damage: survey of progress. Journal of Engineering Mechanics 128(11).Google Scholar
  9. Bažant, Z.P. and Oh, B.H. (1983). Crack band theory for fracture of concrete. Materials and Structures (January-February), 155–177.Google Scholar
  10. Belytschko, T., Guo, Y., Liu, W.K., Xiao, S.P. 2000A unified stability analysis of meshless particle methodsInternational Journal for Numerical Methods in Engineering4813591400CrossRefMathSciNetGoogle Scholar
  11. Belytschko, T., Organ, D., Krongauz, Y. 1995A coupled finite element-element-free Galerkin methodComputational Mechanics17186195ADSMathSciNetGoogle Scholar
  12. Belytschko, T., Krongauz, Y., Dolbow, J., Gerlach, C. 1998On the completeness of meshfree particle methodsInternational Journal for Numerical Methods in Engineering43785819CrossRefMathSciNetGoogle Scholar
  13. Belytschko, T., Lu, Y.Y.,  et al. 1994Element-free Galerkin methodsInternational Journal for Numerical Methods in Engineering37229256MathSciNetGoogle Scholar
  14. Belytschko, T. 1995Crack propagation by element free Galerkin methodsEngineering Fracture Mechanics51295315CrossRefADSMathSciNetGoogle Scholar
  15. Belytschko, T., Lu, Y.Y. 1995Element-free Galerkin methods for static and dynamic fractureInternational Journal of Solids and Structures3225472570CrossRefGoogle Scholar
  16. Belytschko, T., Liu, W.K., Moran, B. 2000Nonlinear Finite Elements for Continua and StructuresJohn Wiley and Sons Ltd.New York, USAGoogle Scholar
  17. Belytschko, T., Xiao, S.P. 2000Stability analysis of particle methods with corrected derivativesComputers and Mathematics with Applications43329350MathSciNetGoogle Scholar
  18. Belytschko, T., Black, T. 1999Elastic crack growth in finite elements with minimal remeshingInternational Journal for Numerical Methods in Engineering45601620CrossRefMathSciNetGoogle Scholar
  19. Belytschko, T., Moes, N., Usui, S., Parimi, C. 2001Arbitrary discontinuities in finite elementsInternational Journal for Numerical Methods in Engineering509931013CrossRefGoogle Scholar
  20. Bittencourt, T.N., Wawrzynek, P.A., Ingraffea, A.R. 1996Quasi-automatic simulation of crack propagation for 2D LEFM problemsEngineering Fracture Mechanics55321334CrossRefGoogle Scholar
  21. Bosco, C. and Debernardi, P.G. (1992). Experimental Investigations on the Ultimate Rotational Capacity of R.C. Beams. Dipartimento di Ingegneria Strutturale, Politecnico de Turin.Google Scholar
  22. Brown, K., Attaway, S., Plimpton, S., Hendrickson, B. 2000Parallel strategies for crash and impact simulationsComputer Methods in Applied Mechanics and Engineering184375390CrossRefGoogle Scholar
  23. Carter, B.J., Wawrzynek, P.A., Ingraffea, A.R. 2000Automated 3-D crack growth simulationInternational Journal for Numerical Methods in Engineering47229253Google Scholar
  24. Chen, J.S., Pan, C., Wu, C.T., Liu, W.K. 1996Repdroducing kernel particle methods for large deformation analysis of nonlinear structuresComputer Methods in Applied Mechanics and Engineering139195227CrossRefMathSciNetGoogle Scholar
  25. Chen, J.S., Pan, C., Roque, C.M.O.L., Wang, H.P. 1998A Lagrangian reproducing kernel particle method for metal forming analysisComputational Mechanics22289307CrossRefADSGoogle Scholar
  26. Chen, W.F. 1994Constitutive Equations for Engineering Materials, Volume 2: Plasticity and ModelingElsevierAmsterdam-London-New York-TokyoGoogle Scholar
  27. Cox, J.V., Herrmann, L.R. 1998Development of a plasticity bond model for steel reinforcementMechanics of Cohesive-Frictional Materials3155180CrossRefGoogle Scholar
  28. Cox, J.V., Herrmann, L.R. 1999Validation of a plasticity bond model for steel reinforcementMechanics of Cohesive-Frictional Materials4361389CrossRefGoogle Scholar
  29. Den Ujil, J. and Bigaj, A.J. (1996). A bondmodel for ribbed bars based on concrete loaded in compression. Heron 41 (3),.Google Scholar
  30. Eibl, J., Stempniewski, L. and Rabczuk, T. (2001). Der Endbereich von im Werk vorgespannten Fertigteiltraegern-Hohlplatten, Abschlussbericht, Institut fuer Massivbau und Baustofftechnologie, Universitaet Karlsruhe.Google Scholar
  31. Eligehausen, R. and Mayer, U. (1997). Parameterstudie zur Mitwirkung des Betons zwischen den Rissen unter Kurzzeitbelastung insbesondere in Abhaengigkeit von der Duktilitaet des Betonstahles, Forschungsbericht, Universitaet Stuttgart.Google Scholar
  32. Gravouil, A., Moes, N., Belytschko, T. 2002Non-planar 3D crack growth by the extended finite element and level sets - Part II: Level set updateInternational Journal for Numerical Methods in Engineering5325692586CrossRefGoogle Scholar
  33. De Groot, A.K., Kusters, G.M.A. and Monnier, T. (1981). Numerical Modeling of Bond-Slip Behavior, Heron, 26-1b, I.B.B.C., Institute Delft, Netherlands, 90 pp.Google Scholar
  34. Hegen, D. 1996Element free Galerkin methods in combination with finite element approachesComputer Methods in Applied Mechanics and Engineering135143166CrossRefzbMATHGoogle Scholar
  35. Hillerborg, A., Modeer, A. and Peterson, P.E. (1976). Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cement and Concrete Research (6), 773–782.Google Scholar
  36. Idda, K. (1999). Verbundverhalten von Betonrippenstaehlen bei Querzug, PhD-thesis, University of Karlsruhe, Institut fuer Massivbau und Baustofftechnologie.Google Scholar
  37. Ingraffea, A.R., Gerstle, W.H., Gergely, P., Saoma, V. 1984Fracture mechanics of bond in reinforced concreteJournal of Structural Engineering, ASCE111871890Google Scholar
  38. Jirasek, M., Zimmermann, T. 1998Rotating crack model with transition to scalar damageASCE, Journal of Engineering Mechanics124277284Google Scholar
  39. Jirasek, M. 1993Modeling of fracture and damage in quasibrittle materialsNorthwestern UniversityUSAPhD thesisGoogle Scholar
  40. Jirasek, M. 2000Comparative study on finite elements with embedded discontinuitiesComputer Methods in Applied Mechanics and Engineering188307330CrossRefzbMATHGoogle Scholar
  41. Johansson, M. (1995). New Reinforcement Detailing in Frame Corners in Civil Defence Shelters- Experiments and Fracture Mechanics Analyses, Chalmers University of Technology, Division of Concrete Structures, Report 95:2, Goeteborg.Google Scholar
  42. Johnson, G.R. (1994). Linking of Lagrangian Particle Methods to Standard Finite Element Methods for High Velocity Impact Copmutations, Nuclear Engineering and Design 150, Post-SMIRT Impact IV Seminar, Berlin.Google Scholar
  43. Johnson, G.R., Stryk, R.A., Beissel, S.R. 1996SPH for high velocity impact computationsComputer Methods in Applied Mechanics and Engineering139347374CrossRefGoogle Scholar
  44. Karutz, H. (2000). Adaptive Kopplung der Elementfreien Galerkin Methode mit der Methode der Finiten Elemente bei Rissfortschrittsproblemen, Dissertation, Institut fuer Statik und Dynamik der Ruhr Universitaet Bochum, VDI-Verlag, Reihe 18, Band 255.Google Scholar
  45. Keuser, M. 1985Verbundelemente fuer nichtlineare Finite-Element-Berechnungen von StahlbetonkonstruktionenVDI VerlagDuesseldorfGoogle Scholar
  46. Krysl, P., Belytschko, T. 1999The element free Galerkin method for dynamic propagation of arbitrary 3-D cracksInternational Journal for Numerical Methods in Engineering44767800CrossRefGoogle Scholar
  47. Lemaitre, J. (1971). Evaluation of dissipation and damage in metal submitted to dynamic loading. Proceedings ICM 1.Google Scholar
  48. Malvar, L.J. 1992Bond of reinforcement under controlled confinementACI Materials Journal89593601Google Scholar
  49. Oliver, J. 1996Modeling strong discontinuities in solid mechanics via strain softening constituitive equations, part 1: fundamentals part 2: numerical simulationInternational Journal for Numerical Methods in Engineering3935753624zbMATHGoogle Scholar
  50. Potyondy, D.O., Wawrzynek, P.A., Ingraffea, A.R. 1995An Algorithm to generate quadrilaterial or triangular element surface meshes in arbitrayr domains with applications to crack-propagationInternational Journal for Numerical Methods in Engineering3826772701CrossRefGoogle Scholar
  51. Simkins, D.C., Li, S., Lu, H., Liu, W.K. 2004Reproducing kernel element method Part IV: globally compatible Cn (n1) triangular hierarchyComputer Methods in Applied Mechanics and Engineering19310131034MathSciNetGoogle Scholar
  52. Lucy,  1977A numerical Approach to the testing of fission hypothesisAstronomical Journal8210131024CrossRefADSGoogle Scholar
  53. Rabczuk, T., Eibl, J. 2003Simulation of high velocity concrete fragmentation using SPH/MLSPHInternational Journal for Numerical Methods in Engineering5614211444CrossRefGoogle Scholar
  54. Rabczuk, T., Belytschko, T. and Xiao, S.P. Stable particle methods based on Lagrangian kernelss, accepted in Computer Methods in Applied Mechanics and Engineering.Google Scholar
  55. Rabczuk, T., Belytschko, T. 2004Cracking particles: a simplified meshfree methods for arbitrary evolving cracksInternational Journal for Numerical Methods in Engineering6123162343CrossRefGoogle Scholar
  56. Schaefer, K, Baumann, P. 1986Ausbreitung von Druckkraeften in Betonscheiben- Vergleichende Versuche mit Lasteinleitungen ueber Lastplatten, Bewehrungsstabumlenkungen und BewehrungsknotenInstitut fuer Massivbau, Universitaet StuttgartGermanyForschungsbericht DFGGoogle Scholar
  57. Stucki, D., Thuerlimann, B. 1990Versuche an Eckverbindungen aus StahlbetonInstitut fuer Baustatik und KonstruktionETH ZuerichGoogle Scholar
  58. Ventura, G., Xu, J., Belytschko, T. 2002A vector level set method and new discontinuity approximations for crack growth by EFGInternational Journal for Numerical Methods in Engineering54923944CrossRefGoogle Scholar
  59. Xiao, S.P. and Belytschko, T. (1996). Material Stability Analysis of Particle Methods, submitted.Google Scholar
  60. Xu, X.P., Needleman, A. 1996Numerical simulations of dynamic crack growth along an interfaceInternational Journal of Fracture74289324CrossRefGoogle Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringNorthwestern UniversityEvanstonUSA

Personalised recommendations