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Chapter 4. Bond behavior of fibers in cementitious materials: a unifiedformulation 300250 Fracture Based ModelPi N200 15010050ExperimentalData 27.1 mmd f 1.5 mmlemb00.0 0.2 0.4 0.6 0.8si mmFigure 4.12: Numerical prediction (continuous line) vs. experimental data (points) [Banholzeret al., 2006]: fiber diameter of 1.5mm and anchorage of 27.1mm. Pi N500400 300200100Fracture Based Modell emb 35.0 mmd f 2.0 mm Experimental Data00.0 0.2 0.4 0.6 0.8si mmFigure 4.13: Numerical prediction (continuous line) vs. experimental data (points) [Banholzeret al., 2006]: fiber diameter of 2.0mm and anchorage of 35.0mm.The following material parameters, dealing with an unified fracture energy-based τ − srule, are employed for all predictions in this section:• τ y,0 = 2.4 MPa (shear strength),• s u = 0.83mm (ultimate slip),• k E = 120 MPa/mm (initial elastic stiffness) and• G f = 0.80 N /mm (fracture energy under mode I I ).Figure 4.11 to 4.13 show as the numerical simulations are generally in good agreementwith the experimental results observed in pull-out tests. Load-slip curves are signifi-88
4.5. Numerical results and experimental validationcantly affected by both fiber diameter which varies from d f = 0.8 to 2.0mm, and theembedded lengths, varying from l emb = 22.1 to 35.0mm. The proposed procedure isable to realistically capture the influences of both parameters.MPa3.02.52.01.51.035 648Pi N71400.591100.00 5 10 15 20120 7100 680 5 460 3 840 220 19 1000.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7zmm(b)si mm(a)1.2strain 1.E31.0760.8540.60.43820.2 91100.00 5 10 15 20zmm(c)Figure 4.14: Pull-out simulation for a steel fiber diameter of 0.8mm and an embedded lengthof 22.1mm by Banholzer et al. [2006]: (a) load-slip curve P i − s i , (b) interface shear stressdistributions τ − z and (c) axial strain distributions ε s − z.Only the numerical results based on the fracture energy modeling are outlined and compared against the experimental evidence in this section. The bilinear bond-sliprelationship posses, as demonstrated in subsection 4.5.1, a limited prediction capabilityfor pull-out tests, compared to the fracture energy-based proposal. For this reason thebilinear bond-slip behavior is neglected in this section.Finally, the discussion focuses on the detailed simulation of the complete debondingprocesses developing in the three cases whose overall response is described in Figure4.11 to 4.13. To this end, fiber-to-concrete bond stresses and fiber strain distributionsthroughout the bond length are obtained by means of numerical simulations. Figure 4.14 to 4.16 show such results for different bond lengths and diameters. In particular,Figures 4.14b, 4.15b and 4.16b report the distribution of interface shear stresses89
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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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Chapter 1. Introductioncracking beh
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Chapter 1. Introduction• "c" if 0
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Chapter 1. Introductionsumed due to
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Chapter 1. Introductionaleatoric na
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Chapter 1. IntroductionFigure 1.13:
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Chapter 1. IntroductionElement Meth
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Chapter 2. Experimental characteriz
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Page 64 and 65: Chapter 2. Experimental characteriz
Page 70 and 71: Chapter 3. Zero-thickness interface
Page 93 and 94: 4 Bond behavior of fibers in cement
Page 95 and 96: 4.2. Bond behavior of fibers in con
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 113: 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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