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List of Figures4.16 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) interfaceshear stress distributions τ − z and (c) axial strain distributions ε s − z. . . . . . 915.1 Test set-up of tensile tests performed by Li et al. [1998] and the correspondinganalysis model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 945.2 Experimental data [Li et al., 1998] and numerical simulation for SFRC withDramix fibers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 965.3 Experimental data [Li et al., 1998] and numerical simulation for SFRC with Harexfibers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 965.4 Test set-up by Hassanzadeh [1990]: (a) concrete sample, (b) tensile state and (c)mixed fracture displacements. . . . . . . . . . . . . . . . . . . . . . . . . . . . 975.5 Boundary conditions and FE-discretization with one single interface crossed byshort fibers for Hassanzadeh [1990] tests on SFRC panels. . . . . . . . . . . . . 985.6 Normal stress vs. relative vertical displacement performed with different amountof fibers and θ = 90 o . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 985.7 Hassanzadeh [1990] tests with different number of fibers and θ = 75 o : a) normalstress vs. relative normal displacement and b) shear stress vs. relative tangentialdisplacement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 995.8 Hassanzadeh [1990] tests with different number of fibers and θ = 60 o : a) normalstress vs. relative normal displacement and b) shear stress vs. relative tangentialdisplacement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 995.9 Hassanzadeh [1990] tests with different number of fibers and θ = 30 o : a) normalstress vs. relative normal displacement and b) shear stress vs. relative tangentialdisplacement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1005.10 Comparison between numerical predictions and experimental results by Li andLi [2001]: SFRC with “Dramix type II” fibers. . . . . . . . . . . . . . . . . . . . 1025.11 Comparison between numerical predictions and experimental results by Li andLi [2001]: SFRC with “Dramix type I” fibers. . . . . . . . . . . . . . . . . . . . 1025.12 Comparison between numerical predictions of the test by Li and Li [2001] onSFRC with “Dramix type II” fibers: (a) full debonding vs. 50% of the debondingstrength and (b) full fracture energy, G I f , vs. 50% of G I f . . . . . . . . . . . . . . 1035.13 (a) Experimental test by Hassanzadeh [1990] and numerical predictions for SFRCwith “Dramix type I” fibers with ρ f = 5.0% and (b) effect of the dowel strengthon the stress-opening displacements in mixed-modes of fracture. . . . . . . . 1045.14 ρ and θ angles defined in the interface stress space. . . . . . . . . . . . . . . . 1065.15 Schematic interface stress states selected for the post-cracking analysis. . . . . 107xvi
List of Figures5.16 Post-cracking analysis at peak stress for different concrete types: plain concreteand SFRC with “Dramix type I” fibers having fiber contents of 3.0% and 6.0%. . 1085.17 Polar plots of post-cracking analysis of TS5 and TS6 for different concrete types:plain concrete and SFRC with “Dramix type I” fibers having fiber contents of3.0% and 6.0%. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1095.18 Polar plots of post-cracking analysis of TS3 and TS4 for different concrete types:plain concrete and SFRC with “Dramix type I” fibers having fiber contents of3.0% and 6.0%. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1105.19 Polar plots of post-cracking analysis of TS2 and UT for different concrete types:plain concrete and SFRC with “Dramix type I” fibers having fiber contents of3.0% and 6.0%. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1116.1 FE discretization including the cases of: (a) one, (b) four and (c) eight interfaces. 1166.2 Boundary conditions of (a) uniaxial tensile and (b) compressive cases, (c) shearwith unconstrained dilatancy and (d) shear with constrained dilatancy. . . . . 1166.3 Vertical load-displacement behavior of plain concrete and SFRCs under tension(left side) and crack paths (right side). . . . . . . . . . . . . . . . . . . . . . . 1176.4 Vertical load-displacement behavior of plain concrete and SFRCs under compression(left side) and crack paths (right side). . . . . . . . . . . . . . . . . . 1186.5 Lateral load-displacement behavior of plain concrete and SFRCs in direct shearwith free dilatancy in the vertical direction (left side) and crack paths (right side). 1196.6 Lateral load-displacement behavior of plain concrete and SFRCs in direct shearwith blocked dilatancy in the vertical direction (left side) and crack paths (rightside). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1206.7 Three-point bending test discretization on a notched beam for discrete failureanalyses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1226.8 Numerical results vs. experimental data by Rots et al. [1985] on a three-pointbeam. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1226.9 Failure configuration in terms of (a) vertical displacement mesh informationsand (b) work spent to available energy ratio of w cr /G I f . . . . . . . . . . . . . . 1236.10 FE discretization including Fiber Reinforced concrete and mortar, coarse aggregatesand interfaces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1246.11 (a) Initial regular 2D distribution, (b) randomly perturbed positions, (c) superpositionof the points and (d) Voronoi/Delaunay tessellation. . . . . . . . . . . 1256.12 Geometry and boundary conditions of the three-point bending problem of fiberreinforced concrete beam according to Carpinteri and Brighenti [2010]. . . . . 1266.13 Load-deflection behavior of three-point beam with central notch: numericalsimulation vs. experimental results by Carpinteri and Brighenti [2010]. . . . . 127xvii
Page 1 and 2: Dottorato di Ricercain Ingegneria d
Page 7: AcknowledgementsI would like to exp
Page 10 and 11: Abstractinclusion of fibers and the
Page 13: ContentsAcknowledgementsAbstractTab
Page 16 and 17: Contents8.6.1 Tensile tests . . . .
Page 18 and 19: List of Figures2.1 Fine and coarse
Page 22 and 23: List of Figures6.14 Crack paths of
Page 25: List of Tables2.1 Mix design per cu
Page 28 and 29: Chapter 1. Introduction1.1.1 Fiber
Page 30 and 31: Chapter 1. Introductionthe fiber ad
Page 32 and 33: Chapter 1. Introductionand mechanic
Page 34 and 35: Chapter 1. Introduction[Vrech and E
Page 36 and 37: Chapter 1. IntroductionDespite the
Page 38 and 39: Chapter 1. Introduction(Figure 1.4)
Page 40 and 41: Chapter 1. IntroductionFigure 1.8:
Page 42 and 43: Chapter 1. Introductionfor structur
Page 44 and 45: Chapter 1. Introductioncracking beh
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
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Chapter 3. Zero-thickness interface
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4 Bond behavior of fibers in cement
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4.2. Bond behavior of fibers in con
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4.3. Elasto-plastic joint/interface
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4.4. Fracture energy-based interfac
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4.4. Fracture energy-based interfac
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4.5. Numerical results and experime
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4.6. Closing remarksMPa3.02.5Pi N2.
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5 Model performance and numericalpr
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5.1. Numerical analysesones mention
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5.1. Numerical analysesshown in Fig
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5.1. Numerical analysesconsidered,
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5.1. Numerical analysestic behavior
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5.1. Numerical analysesσ MPa121086
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5.2. Cracking analysis of the propo
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4 03 02 01 001 0 09 08 07 06 05 04
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5.3. Closing remarksconnecting node
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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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