Discrete vs smeared crack models for concrete fracture: bridging the gap

Discrete and smeared crack models for concrete fracture are discussed in a historical perspective. It is argued that these two computational approaches, originally conceived as very different, can be brought together by exploiting the partition-of-unity property of finite element shape functions. The cohesive segments method, which exploits this partition-of-unity property, exhibits advantages of both the discrete and smeared crack approaches, and is capable of describing the transition from distributed micro-cracking to a dominant crack. The versatility of the cohesive methodology is shown by incorporating water diffusion and ion transport into the formulation.

[1]  Z. Bažant,et al.  Nonlocal damage theory , 1987 .

[2]  Rhj Ron Peerlings,et al.  Gradient‐enhanced damage modelling of concrete fracture , 1998 .

[3]  Xiaopeng Xu,et al.  Numerical simulations of fast crack growth in brittle solids , 1994 .

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

[5]  Ted Belytschko,et al.  A finite element method for crack growth without remeshing , 1999 .

[6]  Xiaopeng Xu,et al.  Void nucleation by inclusion debonding in a crystal matrix , 1993 .

[7]  G. I. Barenblatt.  THE MATHEMATICAL THEORY OF EQUILIBRIUM CRACKS IN BRITTLE FRACTURE , 1962 .

[8]  M. Ortiz,et al.  A finite element method for localized failure analysis , 1987 .

[9]  Ted Belytschko,et al.  Arbitrary discontinuities in finite elements , 2001 .

[10]  A. Needleman,et al.  A cohesive segments method for the simulation of crack growth , 2003 .

[11]  P. Jouanna,et al.  A generalized approach to heterogeneous media , 1996 .

[12]  Ronaldo I. Borja,et al.  A finite element model for strain localization analysis of strongly discontinuous fields based on standard Galerkin approximation , 2000 .

[13]  R. de Borst,et al.  A consistent geometrically non‐linear approach for delamination , 2002 .

[14]  Ekkehard Ramm,et al.  An anisotropic gradient damage model for quasi-brittle materials , 2000 .

[15]  M. Ortiz,et al.  Computational modelling of impact damage in brittle materials , 1996 .

[16]  L. J. Sluys,et al.  A new method for modelling cohesive cracks using finite elements , 2001 .

[17]  Ted Belytschko,et al.  Elastic crack growth in finite elements with minimal remeshing , 1999 .

[18]  T. Belytschko,et al.  Extended finite element method for cohesive crack growth , 2002 .

[19]  de R René Borst,et al.  On the numerical integration of interface elements , 1993 .

[20]  I. Babuska,et al.  The Partition of Unity Method , 1997 .

[21]  R. de Borst,et al.  Some observations on embedded discontinuity models , 2001 .

[22]  Francisco Armero,et al.  An analysis of strong discontinuities in a saturated poro-plastic solid , 1999 .

[23]  J. Mier.  Fracture Processes of Concrete , 1997 .

[24]  Rhj Ron Peerlings,et al.  Gradient enhanced damage for quasi-brittle materials , 1996 .

[25]  de R René Borst,et al.  Free edge delamination in carbon-epoxy laminates: a novel numerical/experimental approach , 1994 .

[26]  J. Rots.  Smeared and discrete representations of localized fracture , 1991 .

[27]  W. C. Schnobrich,et al.  Finite Element Analysis of Reinforced Concrete , 1973 .

[28]  B. Schrefler,et al.  The Finite Element Method in the Static and Dynamic Deformation and Consolidation of Porous Media , 1998 .

[29]  A. Ingraffea,et al.  Numerical modeling of discrete crack propagation in reinforced and plain concrete , 1985 .

[30]  Mgd Marc Geers,et al.  Localisation issues in local and nonlocal continuum approaches to fracture , 2002 .

[31]  Gilles Pijaudier-Cabot,et al.  CONTINUUM DAMAGE THEORY - APPLICATION TO CONCRETE , 1989 .

[32]  D. S. Dugdale.  Yielding of steel sheets containing slits , 1960 .

[33]  Zenon Mróz,et al.  Finite element analysis of deformation of strain‐softening materials , 1981 .

[34]  T. Belytschko,et al.  Arbitrary branched and intersecting cracks with the eXtended Finite Element Method , 2000 .

[35]  T. Belytschko,et al.  Element‐free Galerkin methods , 1994 .

[36]  A. Needleman.  A Continuum Model for Void Nucleation by Inclusion Debonding , 1987 .

[37]  Jonas Larsson,et al.  Localization Analysis of a Fluid Saturated Elastoplastic Porous Medium Using Regularized Discontinuities , 2000 .

[38]  D. Ngo,et al.  Finite Element Analysis of Reinforced Concrete Beams , 1967 .

[39]  Anthony G. Evans,et al.  MECHANICS OF MATERIALS: TOP-DOWN APPROACHES TO FRACTURE , 2000 .

[40]  Z. Bažant,et al.  Crack band theory for fracture of concrete , 1983 .

[41]  J. Mazars.  APPLICATION DE LA MECANIQUE DE L'ENDOMMAGEMENT AU COMPORTEMENT NON LINEAIRE ET A LA RUPTURE DU BETON DE STRUCTURE , 1984 .

[42]  T. Belytschko,et al.  A finite element with embedded localization zones , 1988 .

[43]  Stephen A. Vavasis,et al.  Time continuity in cohesive finite element modeling , 2003 .

[44]  John R. Rice,et al.  A Critical Evaluation of Cohesive Zone Models of Dynamic Fracture , 2001 .

[45]  Garth N. Wells,et al.  Discontinuous modelling of strain localisation and failure , 2001 .

[46]  D Dries Hegen,et al.  Element-free Galerkin methods in combination with finite element approaches , 1996 .

[47]  J. C. Simo,et al.  An analysis of strong discontinuities induced by strain-softening in rate-independent inelastic solids , 1993 .

[48]  R. de Borst,et al.  A numerical framework for continuum damage - discontinuum transition , 2002 .