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Application of particle methods to static fracture of reinforced concrete structures. (English) Zbl 1197.74175
Summary: 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.

MSC:
74R99 Fracture and damage
74S05 Finite element methods applied to problems in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
74E30 Composite and mixture properties
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[1] Akkermann, J. (2000). Rotationsverhalten von Stahlbeton-Rahmenecken, Dissertation. Institut fuer Massivbau und Baustofftechnologie, Heft 39, Universitaet Karlsruhe.
[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.
[4] Babuska, I. and Melenk, J.M. (1995). The partition of unity finite element method. University of Maryland, Technical Note BN-1185.
[8] Bažant, Z.P. and Jirasek, M. (2002). Nonlocal integral formulations of plasticity and damage: survey of progress. Journal of Engineering Mechanics 128(11).
[9] Bažant, Z.P. and Oh, B.H. (1983). Crack band theory for fracture of concrete. Materials and Structures (January-February), 155–177.
[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.
[29] Den Ujil, J. and Bigaj, A.J. (1996). A bondmodel for ribbed bars based on concrete loaded in compression. Heron 41 (3),.
[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.
[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.
[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.
[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.
[36] Idda, K. (1999). Verbundverhalten von Betonrippenstaehlen bei Querzug, PhD-thesis, University of Karlsruhe, Institut fuer Massivbau und Baustofftechnologie.
[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.
[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.
[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.
[47] Lemaitre, J. (1971). Evaluation of dissipation and damage in metal submitted to dynamic loading. Proceedings ICM 1.
[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. · Zbl 1060.74672
[59] Xiao, S.P. and Belytschko, T. (1996). Material Stability Analysis of Particle Methods, submitted. · Zbl 1060.74070
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