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List of Figures6.14 Crack paths of plain concrete and SFRC under three-point bending with centricalnotch by Carpinteri and Brighenti [2010]. . . . . . . . . . . . . . . . . . . . . . 1286.15 Load-deflection behavior of plain concrete and SFRC three point beams witheccentrical notch: comparison between numerical and experimental results[Carpinteri and Brighenti, 2010]. . . . . . . . . . . . . . . . . . . . . . . . . . 1296.16 Crack paths of plain concrete and SFRC three-point beams with eccentricalnotch at 0.25l (distance between the mid-length of the beam and the notchposition) by Carpinteri and Brighenti [2010]. . . . . . . . . . . . . . . . . . . . 1306.17 2-D FE discretization for concrete specimens with 6×6 aggregates: (a) geometry,(b) continuum elements and (c) interfaces. . . . . . . . . . . . . . . . . . . . . 1316.18 Results in uniaxial compression. . . . . . . . . . . . . . . . . . . . . . . . . . 1326.19 Sequence of micro- and macrocracks at various loading stages. . . . . . . . . . 1336.20 2-D FE discretization for concrete specimens at macro-level: (a) continuumelements and (b) interfaces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1346.21 Results in uniaxial compression. . . . . . . . . . . . . . . . . . . . . . . . . . 1356.22 Sequence of micro- and macrocracks at various loading stages. . . . . . . . . . 1356.23 Geometry, boundary conditions and discretization of the shear tests on plainand steel reinforced mortar specimens. . . . . . . . . . . . . . . . . . . . . . . 1376.24 Numerical simulations dealing with the lateral load vs. lateral displacements ofthe shear tests. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1386.25 Final pattern of the (a) plain mortar and (b) steel fiber reinforced mortar (ρ f =6.0% fiber content) specimens after the numerical analyses with the shear box. 1387.1 Geometrical description of the analyzed four-point bending scheme. . . . . . 1427.2 Stress distributions and fiber actions during the crack evolution. . . . . . . . . 1437.3 The three orientation zones for the square cross section beam: b × h × l (base ×height × length) having l ≥ b and l ≥ h. . . . . . . . . . . . . . . . . . . . . . . 1447.4 Cracked hinge: (a) stress-crack opening displacement of plain concrete and (b)main geometrical assumption under deformation. . . . . . . . . . . . . . . . 1457.5 Load-C T ODm numerical predictions against the experimental data on SFRCL100-type by Caggiano et al. [2012a]. . . . . . . . . . . . . . . . . . . . . . . . 1487.6 Load-C T ODm numerical predictions against the experimental data on SFRCL75-type by Caggiano et al. [2012a]. . . . . . . . . . . . . . . . . . . . . . . . . 1497.7 Load-C T ODm numerical predictions against the experimental data on SFRCLS50-type by Caggiano et al. [2012a]. . . . . . . . . . . . . . . . . . . . . . . . 1497.8 Load-C T ODm numerical predictions against the experimental data on SFRCS75-type by Caggiano et al. [2012a]. . . . . . . . . . . . . . . . . . . . . . . . . 150xviii
List of Figures7.9 Load-C T ODm numerical predictions against the experimental data on SFRCS100-type by Caggiano et al. [2012a]. . . . . . . . . . . . . . . . . . . . . . . . 1508.1 (a) Concrete specimen, (b) continuum discretization scale, (c) 4-node continuumFE and (d) spherical microplane region at gauss-point with a generalizednormal direction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1558.2 Strain and stress components at the microplane level. . . . . . . . . . . . . . . 1568.3 Maximum strength criteria and plastic flow rules. . . . . . . . . . . . . . . . . 1608.4 S[ξ # ] scaling function of the microplane model in terms of the ξ # parameter,where the # symbol = χ mi c ,c mi c , tan(α mi c ) or σ N ,C AP . . . . . . . . . . . . . . 1628.5 ξ # functions, with # = χ mi c ,c mi c , tan(α mi c ) or σ N ,C AP , depending on the workspent-to-fracture energy ratio, w cr /G I f or w cr /G I I a . . . . . . . . . . . . . . . . 163f8.6 Yielding criteria at different ratios between work spent values and fracture energies:(w crG I f, w crG I I af)= (0.0,0.0), (0.2,0.1), (0.4,0.2), (0.6,0.3), (0.8,0.4), (1.0,0.5),(1.0,0.6), (1.0,0.8) (from the biggest size up to smallest one). . . . . . . . . . . 1638.7 Microplane strain activating the fiber bridging effects. . . . . . . . . . . . . . . 1658.8 Load configurations and restraint conditions for uniaxial tension and simpleshear. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1668.9 Comparison between the numerical predictions and the experimental results(dotted curves) by Li and Li [2001] of SFRCs with “Dramix type I” and “type II”. 1678.10 Interface-based simulations vs. microplane ones under tensile load cases. . . . 1698.11 Lateral shear load - displacement by considering several integration points(varying from 2 to 25) and fiber percentages. . . . . . . . . . . . . . . . . . . . 1708.12 Lateral shear load - displacement comparisons when several microplane numbersand fiber contents are considered. . . . . . . . . . . . . . . . . . . . . . . 171xix
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 20 and 21: List of Figures4.16 Pull-out simula
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
Page 70 and 71: Chapter 3. Zero-thickness interface
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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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