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Chapter 4. Bond behavior of fibers in cementitious materials: a unifiedformulationMPa 3.0Pi N 350z m m(b)300 7250 6200 5150 4 31008250 1019 00.0 0.1 0.2 0.3 0.4 0.5 0.6 0.72.572.0 5 61.54381.020.5 910.0 100 5 10 15 20 25 30 35si mm(a)0.8strain 1. E30.60.40.20.076543 8291100 5 10 15 20 25 30 35z mm(c)Figure 4.15: Pull-out simulation for a steel fiber diameter of 1.5mm and an embedded lengthof 27.1mm 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.throughout the bond length for the same forces labeled by the dots represented inFigures 4.14a, 4.15a and 4.16a for the three specimens under consideration. Figures4.14c, 4.15c and 4.16c report the axial strain distribution, namely ε s [z] = d sd z , throughoutthe fiber length: each curve refers to several force levels represented by the dots of theP i − s i curves.4.6 Closing remarksThis chapter presents a unified formulation for describing the overall bond-slip responseof fibers embedded in cementitious matrices. Following remarks can be drawnout related to both the model formulation and their applications:90• The proposed unified formulation has been intended as a key element to be
4.6. Closing remarksMPa3.02.5Pi N2.0 5 6 71.5 43 81.020.5 910.0 100 5 10 15 20 25z mm(b)500 7400 6 5300 4200 38100219 1000.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7si mm(a)0.8strain1.E30.60.47654380.2 291100.00 5 10 15 20 25z mm(c)Figure 4.16: Pull-out simulation for a steel fiber diameter of 2.0mm and an embedded lengthof 35.0mm 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.employed in the numerical model proposed in Chapter 3 to explicitly simulatethe mechanical behavior of FRCC by taking into account the discrete natureof such materials and the contributions of the various constituents within theframework of the so-called meso-mechanical approach;• Two alternative constitutive models have been proposed for obtaining the abovementioned formulation: i.e., the first one has been based on the simpler elastoplasticbehavior with isotropic linear softening, while, the second one has beenfounded on a more complex fracture energy-based contact model;• The limits derived by assuming a simplified bilinear τ− s relationship for simulatingthe response of fibers under tensile stresses emerge in the final comparativeanalysis: although such a relationship allows for a fully analytical solution ofthe problem under consideration, it lacks in simulating the highly non-linearresponse which develops in the post-peak stage;91
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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 66 and 67: Chapter 2. Experimental characteriz
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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
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Page 111 and 112: 4.5. Numerical results and experime
Page 113 and 114: 4.5. Numerical results and experime
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Page 119 and 120: 5 Model performance and numericalpr
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Page 127 and 128: 5.1. Numerical analysestic behavior
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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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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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