An integrated cohesive/overlapping crack model for the analysis of flexural cracking and crushing in RC beams

In the present paper, a new fracture-mechanics based model is proposed for the analysis of reinforced concrete beams in bending describing both cracking and crushing growths taking place during the loading process by means of the concept of strain localization. In particular, the nonlinear behaviour of concrete in compression is modelled by the Overlapping Crack Model, which considers a material interpenetration when the elastic limit is overcome, in close analogy with the Cohesive Crack Model, routinely adopted for modelling the tensile behaviour of concrete. On the basis of different nonlinear contributions due to concrete and steel, a numerical finite element algorithm is proposed. According to this approach, the flexural behaviour of reinforced concrete structural elements is analyzed by varying the main geometrical and mechanical parameters. Particular regard is given to the role of the size-scale effects on the ductility of plastic hinges, which is available at the ultimate load conditions.

[1]  Alberto Carpinteri,et al.  Size Effects on Strength, Toughness, and Ductility , 1989 .

[2]  A. Hillerborg,et al.  Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements , 1976 .

[3]  J. P. Ulfkjær,et al.  Rotational Capacity of Reinforced Concrete Beams , 1995 .

[4]  A. Carpinteri,et al.  Softening and Snap-Through Behavior of Reinforced Elements , 1992 .

[5]  Jaime Planas,et al.  Size Effect and Bond-Slip Dependence of Lightly Reinforced Concrete Beams , 1999 .

[6]  V. Papanikolaou,et al.  Confinement-sensitive plasticity constitutive model for concrete in triaxial compression , 2007 .

[7]  Alberto Carpinteri,et al.  Numerical Simulation of Concrete Fracture Through a Bilinear Softening Stress-Crack Opening Displacement Law , 1989 .

[8]  Alberto Carpinteri,et al.  Double brittle-to-ductile transition in bending of fibre reinforced concrete beams with rebars , 2004 .

[9]  Alberto Carpinteri,et al.  Stability of Fracturing Process in RC Beams , 1984 .

[10]  Michael D. Kotsovos,et al.  Effect of testing techniques on the post-ultimate behaviour of concrete in compression , 1983 .

[11]  J. R. Carmona,et al.  Flexural to shear and crushing failure transitions in RC beams by the bridged crack model , 2007 .

[12]  Milan Jirásek,et al.  Damage-plastic model for concrete failure , 2006 .

[13]  Alberto Carpinteri,et al.  Effect of specimen size on the dissipated energy density in compression , 2008 .

[14]  R. de Borst,et al.  Non-linear analysis of frictional materials , 1986 .

[15]  Alberto Carpinteri,et al.  Continuous vs discontinuous bridged-crack model for fiber-reinforced materials in flexure , 1997 .

[16]  Kaspar Willam,et al.  Fracture Energy‐Based Plasticity Formulation of Plain Concrete , 1989 .

[17]  Antoine E. Naaman,et al.  Fracture Model for Fiber Reinforced Concrete , 1983 .

[18]  Surendra P. Shah,et al.  A model for predicting fracture resistance of fiber reinforced concrete , 1983 .

[19]  Alberto Carpinteri,et al.  Cohesive versus overlapping crack model for a size effect analysis of RC elements in bending , 2007 .

[20]  J. Balayssac,et al.  Strain-softening of concrete in uniaxial compression , 1997 .

[21]  C. Morley,et al.  WHEN PLASTICITY ? , 2007 .

[22]  Alberto Carpinteri,et al.  An extended (fractal) Overlapping Crack Model to describe crushing size-scale effects in compression , 2009 .

[23]  Satyendra K. Ghosh,et al.  Flexural Ductility of Ultra-High-Strength Concrete Members , 1989 .

[24]  Giovanni Fabbrocino,et al.  PLASTIC ROTATION CAPACITY OF BEAMS IN NORMAL AND HIGH-PERFORMANCE CONCRETE , 1999 .

[25]  Surendra P. Shah,et al.  Effect of Length on Compressive Strain Softening of Concrete , 1997 .

[26]  Alberto Carpinteri,et al.  Size-scale and slenderness influence on the compressive strain-softening behaviour of concrete: experimental and numerical analysis , 2001 .

[27]  Mitsuyoshi Akiyama,et al.  CONCENTRIC LOADING TEST OF RC COLUMNS WITH NORMAL- AND HIGH-STRENGTH MATERIALS AND STRESS-STRAIN MODEL FOR CONFINED CONCRETE CONSIDERING COMPRESSIVE FRACTURE ENERGY , 2005 .

[28]  M. A. Crisfield,et al.  Finite elements in plasticity—theory and practice, D. R. J. Owen and E. Hinton, Pineridge Press, Swansea , 1981 .

[29]  D. Owen,et al.  Finite elements in plasticity : theory and practice , 1980 .

[30]  P. Paramasivam,et al.  Modelling the fracture of cementitious materials , 1992 .

[31]  Joaquim Figueiras,et al.  Finite element analysis of reinforced and prestressed concrete structures including thermal loading , 1983 .

[32]  Giuseppe Mancini,et al.  The overlapping crack model for uniaxial and eccentric concrete compression tests , 2009 .

[33]  A. Carpinteri Minimum Reinforcement in Concrete Members , 1999 .

[34]  Alberto Carpinteri,et al.  An Analytical Model Based on Strain Localisation for the Study of Size‐Scale and Slenderness Effects in Uniaxial Compression Tests , 2011 .

[35]  C. Bosco,et al.  Influence of some basic parameters on the plastic rotation of reinforced concrete elements , 1993 .

[36]  Alberto Carpinteri,et al.  The effect of contact on the decohesion of laminated beams with multiple microcracks , 2008 .

[37]  Surendra P. Shah,et al.  Application of fracture mechanics to cementitious composites , 1985 .

[38]  Ned H. Burns,et al.  Plastic Hinging in Reinforced Concrete , 1966 .

[39]  Alessandro Pasquale Fantilli,et al.  Size effect of compressed concrete in four point bending RC beams , 2004 .

[40]  Alberto Carpinteri,et al.  Interpretation of the Griffith Instability as a Bifurcation of the Global Equilibrium , 1985 .

[41]  J. Červenka,et al.  Three dimensional combined fracture-plastic material model for concrete , 2008 .

[42]  J. C. Simo,et al.  Strain- and stress-based continuum damage models—II. Computational aspects , 1987 .

[43]  K. Willam,et al.  Triaxial failure criterion for concrete and its generalization , 1995 .

[44]  J.G.M. van Mier,et al.  Strain-softening of concrete under multiaxial loading conditions , 1984 .

[45]  V. Li,et al.  Fracture processes in concrete and fiber reinforced cementitious composites , 1986 .

[46]  J. G. Williams,et al.  Analytical solutions for cohesive zone models , 2002 .

[47]  Gabriel O. Ribeiro,et al.  Analysis Of Reinforced Concrete Structures Using Ansys , 2022 .

[48]  Juan José López Cela,et al.  Material Identification Procedure for Elastoplastic Drucker–Prager Model , 2002 .