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Chapter 8. Elasto-plastic microplane formulation for FRCCapplication of the virtual work principle over the unit hemisphere according to Eq.(8.3). However, the integration of Eq. (8.3) is transformed into a summation, whichis characterized by a finite number of considered orientations (equal to the adopteddiscretizing microplanes).load kN86422 microplanes 4 microplanes8f 5.0f 2.0f 0.0load kN642f 5.0f 2.0f 0.000.000 0.002 0.004 0.006 0.008 0.010displacement mm00.000 0.002 0.004 0.006 0.008 0.010displacement mmload kN86426 microplanes 8 microplanes8f 5.0f 2.0f 0.0load kN642f 5.0f 2.0f 0.000.000 0.002 0.004 0.006 0.008 0.010displacement mm00.000 0.002 0.004 0.006 0.008 0.010displacement mmload kN864221 microplanes 25 microplanes8f 5.0f 2.0f 0.0load kN642f 5.0f 2.0f 0.000.000 0.002 0.004 0.006 0.008 0.010displacement mm00.000 0.002 0.004 0.006 0.008 0.010displacement mmFigure 8.11: Lateral shear load - displacement by considering several integration points(varying from 2 to 25) and fiber percentages.The accuracy of the numerical response, based on the number of the considered inte-170
8.6. Numerical analyses about the material failure8plain concreteload kN6482542162200.000 0.002 0.004 0.006 0.008 0.0108displacement mm f = 2.0 %load kN64825421622load kN00.000 0.002 0.004 0.006 0.008 0.0108642displacement mm f = 5.0 %825 2164200.000 0.002 0.004 0.006 0.008 0.010displacement mmFigure 8.12: Lateral shear load - displacement comparisons when several microplane numbersand fiber contents are considered.171
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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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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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Chapter 6. Structural scale failure
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Page 169 and 170: 7.1. Basic assumptionsSection at no
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Page 175 and 176: 7.4. Numerical predictionsvertical
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Page 200 and 201: Chapter 9. Conclusionsof first-crac
Page 202 and 203: Chapter 9. Conclusionsfibers in con
Page 204 and 205: Chapter 9. Conclusions9.6 Future re
Page 206 and 207: BibliographyN. Banthia and N. Nanda
Page 208 and 209: BibliographyM. Butler, V. Mechtcher
Page 210 and 211: BibliographyCUR. Bepaling van de Bu
Page 212 and 213: BibliographyEN-12390-3. Testing of
Page 214 and 215: BibliographyT. Guttema. Ein Beitrag
Page 216 and 217: BibliographyE. Kuhl, P. Steinmann,
Page 218 and 219: BibliographyO. Manzoli, J. Oliver,
Page 220 and 221: BibliographyK. Park, G. Paulino, an
Page 222 and 223: BibliographyI. Singh, B. Mishra, an
Page 224: BibliographyG. Wells and L. Sluys.
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