tesi A. Caggiano.pdf - EleA@UniSA - UniversitÃ degli Studi di Salerno

More documents

Recommendations

Info

$3Eterov e)ce(te/rou sofo\v to/ te pa/lai to/ te nu=n. Ou ... - EleA@UniSA$

Chapter 8. Elasto-plastic microplane formulation for FRCCthe influence of several parameters such as fiber types, strength criteria and the fractureenergy.8.1 IntroductionA large amount of theoretical works and numerical tools, based on elastic, plastic,damage, viscous or fracture principles, deal with the so-called Smeared Crack Approach(SCA). As largely outlined in the previous chapters, they are characterized by strongFinite Element (FE)-mesh size dependence of the localization band width (e.g., a finerdiscretization leads to a decreasing toughness of the analyzed numerical model) andloss of ellipticity of the constitutive differential equations [Willam et al., 1984, Oliver,1989, Etse and Willam, 1994, Jirasek and Zimmermann, 2001, Rabczuk et al., 2005,Folino and Etse, 2012]. Nevertheless, the main advantages of employing smeared crackmodels are due to their lower computational cost and the easier to be implementedin classical commercial or open-source codes. On the contrary, models based on theDiscrete Crack Approach (DCA) are more computationally expensive than SCA, andtheir main disadvantage resides on the low feasibility to be included in commercial FEcodes. These facts represent the main motivations for formulating the new continuumbasedapproach presented in this chapter.During the last decades, the well-known microplane theory has largely been used forpredicting the mechanical behavior of quasi-brittle materials, such as concrete or rocks.The pioneer works have been proposed by Bazant and Gambarova [1984], Bazant andOh [1985, 1992], Carol et al. [1992], Bazant et al. [1996b,a]. Further extensions includingdamage and plasticity concepts have been proposed by Carol and Bazant [1997], Kuhlet al. [2000], Kuhl and Ramm [2000], Leukart and Ramm [2003], Cervenka et al. [2005].A well-established thermodynamically consistent approach has been described in theworks by Carol et al. [2001] and Kuhl et al. [2001]. Other relevant microplane-basedcontributions can be found in several applications including concrete failure predictionunder cyclic loads Ozbolt et al. [2001], for studying the mechanical response ofpolycrystalline shape memory alloys Brocca et al. [2002], micropolar continua formulationin the spirit of the “Cosserat media” Etse et al. [2003], Etse and Nieto [2004],strain-softening nonlocal models Bazant and Luzio [2004], Di Luzio [2007], large strainsCarol et al. [2004], non-linear hardening-softening behavior of fiber reinforced concretesBeghini et al. [2007], quasi-brittle orthotropic composite laminates Cus, early agebehavior of concrete structures Lee and Kim [2009] and dynamic impact loads Ozboltand Sharma [2011].154
8.2. Basic assumptions of the microplane-based material model8.2 Basic assumptions of the microplane-based material modelAn elasto-plastic fracture energy-based microplane model is developed for simulatingthe FRCC macroscopic failure behavior in a smeared crack mode as shown in Figure8.1. The following formulation is based on the approach proposed by Carol et al. [2001]and Kuhl et al. [2001].22113 43 4(b)(c)n(a)(d)Figure 8.1: (a) Concrete specimen, (b) continuum discretization scale, (c) 4-node continuumFE and (d) spherical microplane region at gauss-point with a generalized normal direction.8.2.1 Kinematic assumptionsThe kinematic constraint assumes that the microplane normal and shear strains (ε Nand ε T , respectively) are calculated by means of the following relationsε N = n · ε · nε T = ε · n − ε N n(8.1)or in index notationε N = ε i j n i n jε T,k = ε k j n j − ε N n k(8.2)being ε the macroscopic strain tensor (ε i j in index notation) projected on the microplanedirection n (with n i in index notation).155
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
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 58 and 59:
Page 60 and 61:
Page 62 and 63:
Page 64 and 65:
Page 66 and 67:
Page 68 and 69:
Page 70 and 71:
Chapter 3. Zero-thickness interface
Page 72 and 73:
Page 74 and 75:
Page 76 and 77:
Page 78 and 79:
Page 80 and 81:
Page 82 and 83:
Page 84 and 85:
Page 86 and 87:
Page 88 and 89:
Page 90 and 91:
Page 93 and 94:
4 Bond behavior of fibers in cement
Page 95 and 96:
4.2. Bond behavior of fibers in con
Page 97 and 98:
4.3. Elasto-plastic joint/interface
Page 99 and 100:
Page 101 and 102:
Page 103 and 104:
Page 105 and 106:
Page 107 and 108:
4.4. Fracture energy-based interfac
Page 109 and 110:
4.4. Fracture energy-based interfac
Page 111 and 112:
4.5. Numerical results and experime
Page 113 and 114:
Page 115 and 116:
Page 117 and 118:
4.6. Closing remarksMPa3.02.5Pi N2.
Page 119 and 120:
5 Model performance and numericalpr
Page 121 and 122:
5.1. Numerical analysesones mention
Page 123 and 124:
5.1. Numerical analysesshown in Fig
Page 125 and 126:
5.1. Numerical analysesconsidered,
Page 127 and 128:
5.1. Numerical analysestic behavior
Page 129 and 130: 5.1. Numerical analysesσ MPa121086
Page 131 and 132: 5.2. Cracking analysis of the propo
Page 133 and 134: 4 03 02 01 001 0 09 08 07 06 05 04
Page 139: 5.3. Closing remarksconnecting node
Page 142 and 143: Chapter 6. Structural scale failure
Page 167 and 168: 7 Cracked hinge numerical modelfor
Page 169 and 170: 7.1. Basic assumptionsSection at no
Page 171 and 172: 7.1. Basic assumptions1997, Stankow
Page 173 and 174: 7.2. Bond-slip bridging of fibers o
Page 175 and 176: 7.4. Numerical predictionsvertical
Page 177: 7.5. Closing remarksthe experimenta
Page 182 and 183: Chapter 8. Elasto-plastic microplan
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.
show all

tesi A. Caggiano.pdf - EleA@UniSA - UniversitÃ degli Studi di Salerno

Create successful ePaper yourself

Delete template?

Save as template?