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Chapter 1. Introduction(Figure 1.4): no element connectivity is stated. The description of the geometry andthe numerical model formulation of the problem is only given on a set of nodes jointlywith a description of exterior and interior boundaries. Significant contributions tostatic elasticity and fracture mechanics have been proposed in Belytschko et al. [1995],Belytschko et al. [2000], Singh et al. [2011] and Zhang et al. [2008].Lattice models: within the framework of discontinuous crack approaches and fracturebehavior of concrete elements, the lattice-based model is a simple and effective toolfor understanding the physics of fracture processes in concrete members [Yip et al.,2006]. Lattice type models can be based on either truss [Schorn and Rode, 1987] orbeam elements as in Figure 1.5 [Lilliu and van Mier, 2003].(a) (b) (c)Figure 1.5: Meso-mechanical simulation by means of the beam lattice model [Lilliu and vanMier, 2003]: (a) geometry, (b) definition of matrix, interface and aggregates, (c) crack patternsimulations.Strong discontinuity approaches: they incorporate displacement discontinuities inthe finite element formulations for capturing arbitrary crack propagations within fixedFE mesh without loosing mesh objectivity. Particularly, new types of finite elements,essentially formulated by enriching the (continuous) displacement fields with additionaldiscontinuities, are proposed. It can be distinguished two families of strongdiscontinuity depending on the technique to enrich the displacement field:• the Embedded strong discontinuity Finite Elements (E-FEM), proposed amongothers by Dvorkin et al. [1990], Oliver [1996], Oliver et al. [2002] and Armeroand Linder [2009], which are able to reproduce displacement “jumps” through“elemental discontinuity enrichments” (Figure 1.6a), and• the eXtended Finite Element Method (X-FEM) in which the discontinuity of thedisplacement field is captured by means of “nodal enrichments” (Figure 1.6b) byWells and Sluys [2001] and Liu et al. [2011].12
1.2. Theoretical proposals for concrete-like materialsFigure 1.6: Elemental (E-FEM) and eXtended (X-FEM) enrichment approaches [Oliver et al.,2006].An interesting comparison between the E-FEM and X-FEM approaches, to model strongdiscontinuities in concrete materials, has been highlighted by Oliver et al. [2006].Figure 1.7: Unnotched specimens in tension of various sizes with randomly generated particlesby Bazant et al. [1990].Particle models: these models are based on the formulation of the microscopic inter-13
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 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
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Page 34 and 35: Chapter 1. Introduction[Vrech and E
Page 36 and 37: Chapter 1. IntroductionDespite the
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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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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