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Chapter 4. Bond behavior of fibers in cementitious materials: a unifiedformulationsmooth” fibers has clearly been pointed out in experimental studies by Naaman andNajm [1991] and Laranjeira et al. [2010]. Further experimental evidence about such arole is available in Cunha et al. [2010], whereas the effect of fiber length on the pull-outmechanism of polypropylene fibers has been outlined in Singh et al. [2004]. However,the bond behavior of fibers embedded in cementitious matrix is not only affected bythe above mentioned fiber properties, but moreover by the matrix quality. For instance,experimental researches on smooth fibers embedded in concrete of Normal (N-) andHigh Strength Concretes (HSCs) by Shannag et al. [1997] point out the fact that bondbehavior can be enhanced as the matrix strength increases. Moreover, the inclusion ofnano-particles in cement matrices is one of the most recent solutions, with the twofoldobjective of enhancing the durability of the fiber-to-matrix interface [Butler et al., 2009]and improving the adhesion properties between fibers and matrix [Wang et al., 2009].Thus, since several parameters play a significant role in the fiber-matrix interaction inFRCC, the formulation of sound mechanical models for simulating the bond behaviorof fibers embedded in cementitious materials is a fairly challenging issue. As a matterof principle, two main families of such models can be recognized in the scientificliterature[Stang et al., 1990, Li and Chan, 1994]: the first one can be defined as stressbasedapproaches [Katz and Li, 1995, Ghavami et al., 2010], while the second one isrepresented by the so-called energy-based bond-slip models [Shah and Ouyang, 1991,Fantilli and Vallini, 2007].Besides the particular interest in simulating the mechanical response of single fibers,the above mentioned models should be intended as a key contribution towards thepossible modeling of the structural behavior of FRCC members based on the explicitsimulation of the fiber influence on cracking processes. As a matter of fact, the mostcommon mechanical models currently employed for simulating the behavior of FRCCare based on continuous smeared-crack approaches [Seow and Swaddiwudhipong,2005] and generally deriving by previous proposals originally formulated for plainconcrete [Folino et al., 2009, Folino and Etse, 2012]. Although such models are generallyaccepted for simulating the cracking behaviors of FRCC, it should be noted that theircalibration is necessarily based on experimental results directly obtained on the FRCCmaterial under consideration, as the fiber-matrix bond interaction deeply affects thepost-cracking regime and the corresponding material parameters (mainly related withthe fracture energy to be considered in smeared-crack approaches).To overcome this drawback, alternative models aimed at explicitly simulating the actualdiscrete nature of FRCC have recently been formulated within the framework of theso-called discontinuous-based approaches [Oliver et al., 2008, Caggiano et al., 2012b].68
4.2. Bond behavior of fibers in concrete matrix: Basic assumptionsThe discrete-crack approach and the consequent possibility of modeling the behaviorof FRCC starting from both their components (i.e., the bond-slip mechanisms), andthe interactions among them is the main issue of the proposal reported in Chapter 3.Therein, the accurate description of the fiber-matrix bond behavior is the key elementto formulate and identify such a meso-mechanical model.This chapter proposes a unified formulation for simulating the overall bond behaviorof fibers embedded in cementitious matrices, based on the fundamental assumptionsreported in section 4.2. Two alternative models are actually considered. The first one isbased on the simple elasto-plastic behavior with isotropic linear softening as outlinedin section 4.3. Conversely, the second one is founded on the fracture energy-basedcontact model outlined in section 4.4 and is employed in a numerical solution of thefiber-matrix interaction problem. Finally, section 4.5 presents the results of simulationsobtained through the two models considered in the presented unified formulation ofthe tensile response of fibers embedded in concrete matrices. Moreover, the theoreticalinvestigation about the influence of relevant parameters (such as fiber anchoragelength and diameter) is also outlined in the same section.4.2 Bond behavior of fibers in concrete matrix: Basic assumptionsThe basic assumptions for Finite Element (FE) simulation of bond behavior of fiberembedded in cementitious materials are presented in this section. Fiber reinforcementis modeled by one-dimensional two-nodes iso-parametric truss element. The interfaceslip between reinforcing steel and the surrounding concrete is simulated by means ofinterface elements as schematically shown in Figure 4.1.4.2.1 Behavior of steel fibersThe mechanical behavior of steel in fibers is modeled as a 1-D elastic-perfectly plasticmaterial. The incremental stress-strain law can be written asσ˙f = E ep ˙ε f (4.1)f69
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Dottorato di Ricercain Ingegneria d
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AcknowledgementsI would like to exp
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Abstractinclusion of fibers and the
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ContentsAcknowledgementsAbstractTab
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Contents8.6.1 Tensile tests . . . .
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List of Figures2.1 Fine and coarse
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List of Figures4.16 Pull-out simula
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List of Figures6.14 Crack paths of
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List of Tables2.1 Mix design per cu
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Chapter 1. Introduction1.1.1 Fiber
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Chapter 1. Introductionthe fiber ad
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Chapter 1. Introductionand mechanic
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Chapter 1. Introduction[Vrech and E
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Chapter 1. IntroductionDespite the
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Chapter 1. Introduction(Figure 1.4)
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Chapter 1. IntroductionFigure 1.8:
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Chapter 1. Introductionfor structur
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Page 46 and 47: Chapter 1. Introduction• "c" if 0
Page 48 and 49: Chapter 1. Introductionsumed due to
Page 50 and 51: Chapter 1. Introductionaleatoric na
Page 52 and 53: Chapter 1. IntroductionFigure 1.13:
Page 54 and 55: Chapter 1. IntroductionElement Meth
Page 56 and 57: Chapter 2. Experimental characteriz
Page 70 and 71: Chapter 3. Zero-thickness interface
Page 93: 4 Bond behavior of fibers in cement
Page 97 and 98: 4.3. Elasto-plastic joint/interface
Page 107 and 108: 4.4. Fracture energy-based interfac
Page 109 and 110: 4.4. Fracture energy-based interfac
Page 111 and 112: 4.5. Numerical results and experime
Page 117 and 118: 4.6. Closing remarksMPa3.02.5Pi N2.
Page 119 and 120: 5 Model performance and numericalpr
Page 121 and 122: 5.1. Numerical analysesones mention
Page 123 and 124: 5.1. Numerical analysesshown in Fig
Page 125 and 126: 5.1. Numerical analysesconsidered,
Page 127 and 128: 5.1. Numerical analysestic behavior
Page 129 and 130: 5.1. Numerical analysesσ MPa121086
Page 131 and 132: 5.2. Cracking analysis of the propo
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Page 139: 5.3. Closing remarksconnecting node
Page 142 and 143: Chapter 6. Structural scale failure
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Chapter 6. Structural scale failure
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7 Cracked hinge numerical modelfor
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7.1. Basic assumptionsSection at no
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7.1. Basic assumptions1997, Stankow
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7.2. Bond-slip bridging of fibers o
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7.4. Numerical predictionsvertical
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7.5. Closing remarksthe experimenta
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Chapter 8. Elasto-plastic microplan
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Chapter 9. Conclusionsof first-crac
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Chapter 9. Conclusionsfibers in con
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Chapter 9. Conclusions9.6 Future re
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BibliographyN. Banthia and N. Nanda
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BibliographyM. Butler, V. Mechtcher
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BibliographyCUR. Bepaling van de Bu
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BibliographyEN-12390-3. Testing of
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BibliographyT. Guttema. Ein Beitrag
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BibliographyE. Kuhl, P. Steinmann,
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BibliographyO. Manzoli, J. Oliver,
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BibliographyK. Park, G. Paulino, an
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BibliographyI. Singh, B. Mishra, an
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BibliographyG. Wells and L. Sluys.
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