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Application of Particle Methods to Static Fracture of Reinforced Concrete Structures

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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.

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References

  • Akkermann, J. (2000). Rotationsverhalten von Stahlbeton-Rahmenecken, Dissertation. Institut fuer Massivbau und Baustofftechnologie, Heft 39, Universitaet Karlsruhe.

  • M. Arrea A.R. Ingraffea (1982) Mixed-mode crack propagation in mortar and concrete Dept. of Struct. Eng. Cornell University Ithaka N.Y.

    Google Scholar 

  • 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.

  • Babuska, I. and Melenk, J.M. (1995). The partition of unity finite element method. University of Maryland, Technical Note BN-1185.

  • Z.P. Bažant T. Belytschko T.P. Chang (1984) ArticleTitleContinuum theory for strain softening Journal of Engineering Mechanics-ASCE 110 IssueID12 1666–1692

    Google Scholar 

  • Z.P. Bažant G. Pijaudier Cabot (1988) ArticleTitleNonlocal continuum damage, localization instabilities and convergence Journal of Engineering Mechanics 55 287–293

    Google Scholar 

  • Z.P. Bažant P. Prat (1988) ArticleTitleMicroplane model for brittle plastic materials I: Theory, II: verification Journal of Engineering Mechanics ASCE 114 1672–1702

    Google Scholar 

  • Bažant, Z.P. and Jirasek, M. (2002). Nonlocal integral formulations of plasticity and damage: survey of progress. Journal of Engineering Mechanics 128(11).

  • Bažant, Z.P. and Oh, B.H. (1983). Crack band theory for fracture of concrete. Materials and Structures (January-February), 155–177.

  • T. Belytschko Y. Guo W.K. Liu S.P. Xiao (2000) ArticleTitleA unified stability analysis of meshless particle methods International Journal for Numerical Methods in Engineering 48 1359–1400 Occurrence Handle10.1002/1097-0207(20000730)48:9<1359::AID-NME829>3.0.CO;2-U Occurrence Handle2001b:74057

    Article  MathSciNet  Google Scholar 

  • T. Belytschko D. Organ Y. Krongauz (1995) ArticleTitleA coupled finite element-element-free Galerkin method Computational Mechanics 17 186–195 Occurrence Handle1995CompM..17..186B Occurrence Handle96j:73081

    ADS  MathSciNet  Google Scholar 

  • T. Belytschko Y. Krongauz J. Dolbow C. Gerlach (1998) ArticleTitleOn the completeness of meshfree particle methods International Journal for Numerical Methods in Engineering 43 785–819 Occurrence Handle10.1002/(SICI)1097-0207(19981115)43:5<785::AID-NME420>3.0.CO;2-9 Occurrence Handle99h:73084

    Article  MathSciNet  Google Scholar 

  • T. Belytschko Y.Y. Lu et al. (1994) ArticleTitleElement-free Galerkin methods International Journal for Numerical Methods in Engineering 37 229–256 Occurrence Handle94h:73083

    MathSciNet  Google Scholar 

  • T. Belytschko (1995) ArticleTitleCrack propagation by element free Galerkin methods Engineering Fracture Mechanics 51 IssueID2 295–315 Occurrence Handle10.1016/0013-7944(94)00153-9 Occurrence Handle1995EnFM...51..295B Occurrence Handle96b:73102

    Article  ADS  MathSciNet  Google Scholar 

  • T. Belytschko Y.Y. Lu (1995) ArticleTitleElement-free Galerkin methods for static and dynamic fracture International Journal of Solids and Structures 32 2547–2570 Occurrence Handle10.1016/0020-7683(94)00282-2

    Article  Google Scholar 

  • T. Belytschko W.K. Liu B. Moran (2000) Nonlinear Finite Elements for Continua and Structures John Wiley and Sons Ltd. New York, USA

    Google Scholar 

  • T. Belytschko S.P. Xiao (2000) ArticleTitleStability analysis of particle methods with corrected derivatives Computers and Mathematics with Applications 43 329–350 Occurrence Handle1883571

    MathSciNet  Google Scholar 

  • T. Belytschko T. Black (1999) ArticleTitleElastic crack growth in finite elements with minimal remeshing International Journal for Numerical Methods in Engineering 45 IssueID5 601–620 Occurrence Handle10.1002/(SICI)1097-0207(19990620)45:5<601::AID-NME598>3.0.CO;2-S Occurrence Handle99j:65103

    Article  MathSciNet  Google Scholar 

  • T. Belytschko N. Moes S. Usui C. Parimi (2001) ArticleTitleArbitrary discontinuities in finite elements International Journal for Numerical Methods in Engineering 50 IssueID4 993–1013 Occurrence Handle10.1002/1097-0207(20010210)50:4<993::AID-NME164>3.0.CO;2-M

    Article  Google Scholar 

  • T.N. Bittencourt P.A. Wawrzynek A.R. Ingraffea (1996) ArticleTitleQuasi-automatic simulation of crack propagation for 2D LEFM problems Engineering Fracture Mechanics 55 IssueID2 321–334 Occurrence Handle10.1016/0013-7944(95)00247-2

    Article  Google Scholar 

  • 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.

  • K. Brown S. Attaway S. Plimpton B. Hendrickson (2000) ArticleTitleParallel strategies for crash and impact simulations Computer Methods in Applied Mechanics and Engineering 184 375–390 Occurrence Handle10.1016/S0045-7825(99)00235-2

    Article  Google Scholar 

  • B.J. Carter P.A. Wawrzynek A.R. Ingraffea (2000) ArticleTitleAutomated 3-D crack growth simulation International Journal for Numerical Methods in Engineering 47 IssueID1–3 229–253

    Google Scholar 

  • J.S. Chen C. Pan C.T. Wu W.K. Liu (1996) ArticleTitleRepdroducing kernel particle methods for large deformation analysis of nonlinear structures Computer Methods in Applied Mechanics and Engineering 139 195–227 Occurrence Handle10.1016/S0045-7825(96)01083-3 Occurrence Handle97i:73109

    Article  MathSciNet  Google Scholar 

  • J.S. Chen C. Pan C.M.O.L. Roque H.P. Wang (1998) ArticleTitleA Lagrangian reproducing kernel particle method for metal forming analysis Computational Mechanics 22 289–307 Occurrence Handle10.1007/s004660050361 Occurrence Handle1998CompM..22..289C

    Article  ADS  Google Scholar 

  • W.F. Chen (1994) Constitutive Equations for Engineering Materials, Volume 2: Plasticity and Modeling Elsevier Amsterdam-London-New York-Tokyo

    Google Scholar 

  • J.V. Cox L.R. Herrmann (1998) ArticleTitleDevelopment of a plasticity bond model for steel reinforcement Mechanics of Cohesive-Frictional Materials 3 155–180 Occurrence Handle10.1002/(SICI)1099-1484(199804)3:2<155::AID-CFM45>3.0.CO;2-S

    Article  Google Scholar 

  • J.V. Cox L.R. Herrmann (1999) ArticleTitleValidation of a plasticity bond model for steel reinforcement Mechanics of Cohesive-Frictional Materials 4 361–389 Occurrence Handle10.1002/(SICI)1099-1484(199907)4:4<361::AID-CFM66>3.0.CO;2-F

    Article  Google Scholar 

  • Den Ujil, J. and Bigaj, A.J. (1996). A bondmodel for ribbed bars based on concrete loaded in compression. Heron 41 (3),.

  • Eibl, J., Stempniewski, L. and Rabczuk, T. (2001). Der Endbereich von im Werk vorgespannten Fertigteiltraegern-Hohlplatten, Abschlussbericht, Institut fuer Massivbau und Baustofftechnologie, Universitaet Karlsruhe.

  • 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.

  • A. Gravouil N. Moes T. Belytschko (2002) ArticleTitleNon-planar 3D crack growth by the extended finite element and level sets - Part II: Level set update International Journal for Numerical Methods in Engineering 53 2569–2586 Occurrence Handle10.1002/nme.430

    Article  Google Scholar 

  • 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.

  • D. Hegen (1996) ArticleTitleElement free Galerkin methods in combination with finite element approaches Computer Methods in Applied Mechanics and Engineering 135 143–166 Occurrence Handle10.1016/0045-7825(96)00994-2 Occurrence Handle0893.73063

    Article  MATH  Google Scholar 

  • 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.

  • Idda, K. (1999). Verbundverhalten von Betonrippenstaehlen bei Querzug, PhD-thesis, University of Karlsruhe, Institut fuer Massivbau und Baustofftechnologie.

  • A.R. Ingraffea W.H. Gerstle P. Gergely V. Saoma (1984) ArticleTitleFracture mechanics of bond in reinforced concrete Journal of Structural Engineering, ASCE 111 IssueID5 871–890

    Google Scholar 

  • M. Jirasek T. Zimmermann (1998) ArticleTitleRotating crack model with transition to scalar damage ASCE, Journal of Engineering Mechanics 124 IssueID3 277–284

    Google Scholar 

  • M. Jirasek (1993) Modeling of fracture and damage in quasibrittle materials Northwestern University USA

    Google Scholar 

  • M. Jirasek (2000) ArticleTitleComparative study on finite elements with embedded discontinuities Computer Methods in Applied Mechanics and Engineering 188 307–330 Occurrence Handle10.1016/S0045-7825(99)00154-1 Occurrence Handle01506871

    Article  MATH  Google Scholar 

  • 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.

  • 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.

  • G.R. Johnson R.A. Stryk S.R. Beissel (1996) ArticleTitleSPH for high velocity impact computations Computer Methods in Applied Mechanics and Engineering 139 347–374 Occurrence Handle10.1016/S0045-7825(96)01089-4

    Article  Google Scholar 

  • 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.

  • M. Keuser (1985) Verbundelemente fuer nichtlineare Finite-Element-Berechnungen von Stahlbetonkonstruktionen VDI Verlag Duesseldorf

    Google Scholar 

  • P. Krysl T. Belytschko (1999) ArticleTitleThe element free Galerkin method for dynamic propagation of arbitrary 3-D cracks International Journal for Numerical Methods in Engineering 44 IssueID6 767–800 Occurrence Handle10.1002/(SICI)1097-0207(19990228)44:6<767::AID-NME524>3.0.CO;2-G

    Article  Google Scholar 

  • Lemaitre, J. (1971). Evaluation of dissipation and damage in metal submitted to dynamic loading. Proceedings ICM 1.

  • L.J. Malvar (1992) ArticleTitleBond of reinforcement under controlled confinement ACI Materials Journal 89 IssueID6 593–601

    Google Scholar 

  • J. Oliver (1996) ArticleTitleModeling strong discontinuities in solid mechanics via strain softening constituitive equations, part 1: fundamentals part 2: numerical simulation International Journal for Numerical Methods in Engineering 39 3575–3624 Occurrence Handle0888.73018

    MATH  Google Scholar 

  • D.O. Potyondy P.A. Wawrzynek A.R. Ingraffea (1995) ArticleTitleAn Algorithm to generate quadrilaterial or triangular element surface meshes in arbitrayr domains with applications to crack-propagation International Journal for Numerical Methods in Engineering 38 IssueID16 2677–2701 Occurrence Handle10.1002/nme.1620381603

    Article  Google Scholar 

  • D.C. Simkins S. Li H. Lu W.K. Liu (2004) ArticleTitleReproducing kernel element method Part IV: globally compatible Cn (n1) triangular hierarchy Computer Methods in Applied Mechanics and Engineering 193 IssueID12–14 1013–1034 Occurrence Handle2005a:65139

    MathSciNet  Google Scholar 

  • Lucy (1977) ArticleTitleA numerical Approach to the testing of fission hypothesis Astronomical Journal 82 1013–1024 Occurrence Handle10.1086/112164 Occurrence Handle1977AJ.....82.1013L

    Article  ADS  Google Scholar 

  • T. Rabczuk J. Eibl (2003) ArticleTitleSimulation of high velocity concrete fragmentation using SPH/MLSPH International Journal for Numerical Methods in Engineering 56 1421–1444 Occurrence Handle10.1002/nme.617

    Article  Google Scholar 

  • Rabczuk, T., Belytschko, T. and Xiao, S.P. Stable particle methods based on Lagrangian kernelss, accepted in Computer Methods in Applied Mechanics and Engineering.

  • T. Rabczuk T. Belytschko (2004) ArticleTitleCracking particles: a simplified meshfree methods for arbitrary evolving cracks International Journal for Numerical Methods in Engineering 61 IssueID13 2316–2343 Occurrence Handle10.1002/nme.1151

    Article  Google Scholar 

  • K Schaefer P. Baumann (1986) Ausbreitung von Druckkraeften in Betonscheiben- Vergleichende Versuche mit Lasteinleitungen ueber Lastplatten, Bewehrungsstabumlenkungen und Bewehrungsknoten Institut fuer Massivbau, Universitaet Stuttgart Germany

    Google Scholar 

  • D. Stucki B. Thuerlimann (1990) Versuche an Eckverbindungen aus Stahlbeton Institut fuer Baustatik und Konstruktion ETH Zuerich

    Google Scholar 

  • G. Ventura J. Xu T. Belytschko (2002) ArticleTitleA vector level set method and new discontinuity approximations for crack growth by EFG International Journal for Numerical Methods in Engineering 54 IssueID6 923–944 Occurrence Handle10.1002/nme.471

    Article  Google Scholar 

  • Xiao, S.P. and Belytschko, T. (1996). Material Stability Analysis of Particle Methods, submitted.

  • X.P. Xu A. Needleman (1996) ArticleTitleNumerical simulations of dynamic crack growth along an interface International Journal of Fracture 74 IssueID4 289–324 Occurrence Handle10.1007/BF00035845

    Article  Google Scholar 

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Rabczuk, T., Belytschko, T. Application of Particle Methods to Static Fracture of Reinforced Concrete Structures. Int J Fract 137, 19–49 (2006). https://doi.org/10.1007/s10704-005-3075-z

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