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Chapter 8. Elasto-plastic microplane formulation for FRCCComparison with the interface model under uniaxial tensionThis section addresses the effect of assuming a continuous based model like the oneproposed in this chapter instead of the interface discontinuous formulation given inChapters 3-6.The simulations of 1.0cm-edge cubic samples, as proposed in discontinuous schemesof Figures 6.1 and 6.2b reported in section 6.1, are reanalyzed according to a continuumapproach in this section. Plane stress hypothesis and displacement-based control areassumed. Then, two material types are considered:• plain concrete and• steel fiber reinforced concrete with fiber percentage ρ f = 5.0%.The same material parameters used in the tensile problems of the previous section6.1 are adopted. To compare the response of the two mentioned approaches in termsof load-displacement laws (result of the structural response achieved by employingthe discontinuous-based formulation of Figure 6.1), the load is now measured bymultiplying the vertical stress by the cross section of the specimen (1 × 1 cm 2 in case ofplane stress), while the vertical displacement is intended as the tensile strain whichmultiplies the specimen height (1 cm).Three comparisons are reported:• 1 horizontal interface vs. 1 microplane over the unit hemisphere,• 2 horizontal interfaces vs. 2 microplanes over the unit hemisphere and• 4 horizontal interfaces vs. 4 microplanes over the unit hemisphere,as schematized in Figure 8.10.The comparison in terms of tensile load-displacement law is shown in Figure 8.10.Based on such simulations, it can be observed that at least 2 microplanes over the unithemisphere must be considered to achieve an acceptable accuracy of the numericalintegration in case of pure tensile stress. The numerical responses of the tests involving4 horizontal interfaces and 4 microplanes highlight that greater number of interfaces isresponsable of a less ductile structural response in post-cracking regime.168
8.6. Numerical analyses about the material failure8f 5.06Microplanesn mic1Microplanenumberload kNf 5.04Interfaces2Plain00.000 0.002 0.004 0.006 0.008 0.010displacement mm(a)4f 5.0n mic1Microplanenumbern mic2Interfaceschemeload kN32Microplanes and Interfaces1Plain00.000 0.002 0.004 0.006 0.008 0.010displacement mm(b)4f 5.0n mic1 n mic3load kN32MicroplanesInterfacesnmic2n mic4 InterfaceMicroplanenumberscheme(c)1Plain00.000 0.002 0.004 0.006 0.008 0.010displacement mmFigure 8.10: Interface-based simulations vs. microplane ones under tensile load cases.8.6.2 Shear test results: influence of the integration approximation overthe unit hemisphereThe macroscopic stress tensor (in components σ i j ) can be theoretically evaluated byimposing the equilibrium between micro- and macroscopic stress tensor through the169
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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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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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