Mesh-independent discrete numerical representations of cohesive-zone models

The importance of the cohesive-zone approach to analyse localisation and fracture in engineering materials is emphasised and ways to incorporate the cohesive-zone methodology in computational methods are discussed. Until recently, numerical implementations of cohesive-zone models have suffered from a certain mesh bias. For discrete representations this is caused by the initial mesh design, while for smeared representations it is rooted in the ill-posedness of the rate boundary value problem that arises upon the introduction of decohesion. A proper representation of the discrete character of cohesive-zone formulations which avoids any mesh bias is obtained by exploiting the partition-of-unity property of finite element shape functions. The recently developed cohesive segments method, which is well-suited for simulating the entire process of crack nucleation, growth and coalescence is reviewed. The effectiveness of this approach is illustrated by some examples for crack nucleation and growth in heterogeneous materials and for fast crack growth.

[1]  D. Borst,et al.  A NON-LINEAR FINITE ELEMENT APPROACH FOR THE ANALYSIS OF MODE-I FREE EDGE DELAMINATION IN COMPOSITES , 1993 .

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

[3]  K. Ravi-Chandar.  On the failure mode transitions in polycarbonate under dynamic mixed-mode loading , 1995 .

[4]  T. Belytschko,et al.  Efficient large scale non‐linear transient analysis by finite elements , 1976 .

[5]  Esteban Samaniego,et al.  A study on nite elements for capturing strong discontinuities , 2020 .

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

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

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

[9]  L. J. Sluys,et al.  From continuous to discontinuous failure in a gradient-enhanced continuum damage model , 2003 .

[10]  P. Hansbo,et al.  A finite element method for the simulation of strong and weak discontinuities in solid mechanics , 2004 .

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

[12]  R. Borst,et al.  A Large Strain Discontinuous Finite Element Approach to Laminated Composites , 2003 .

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

[14]  Milan Jirásek,et al.  Comparative study on finite elements with embedded discontinuities , 2000 .

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

[16]  Stefano Mariani,et al.  Extended finite element method for quasi‐brittle fracture , 2003 .

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

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

[19]  Gerhard A. Holzapfel,et al.  Modeling 3D crack propagation in unreinforced concrete using PUFEM , 2005 .

[20]  N. Chandra,et al.  Some issues in the application of cohesive zone models for metal–ceramic interfaces , 2002 .

[21]  R. Borst.  Numerical aspects of cohesive-zone models , 2003 .

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

[23]  R. de Borst,et al.  Simulating the propagation of displacement discontinuities in a regularized strain‐softening medium , 2002 .

[24]  H.E.J.G. Schlangen,et al.  Experimental and numerical analysis of fracture processes in concrete : proefschrift , 1993 .

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

[26]  Jörn Mosler,et al.  Embedded crack vs. smeared crack models: a comparison of elementwise discontinuous crack path approaches with emphasis on mesh bias , 2004 .

[27]  T. Belytschko,et al.  Continuum–discontinuum modelling of shear bands , 2005 .

[28]  Alberto Corigliano,et al.  Geometrical and interfacial non-linearities in the analysis of delamination in composites , 1999 .

[29]  A. Rosakis,et al.  Full field measurements of the dynamic deformation field around a growing adiabatic shear band at the tip of a dynamically loaded crack or notch , 1994 .

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

[31]  Thomas J. R. Hughes,et al.  Encyclopedia of computational mechanics , 2004 .

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

[33]  T. Belytschko,et al.  Non‐linear analysis of shells with arbitrary evolving cracks using XFEM , 2005 .

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

[35]  R. Larsson.  A Discontinuous Shell-Interface Element for Delamination Analysis of Laminated Composite Structures , 2004 .

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

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

[38]  Ted Belytschko,et al.  Mesh-free Galerkin simulations of dynamic shear band propagation and failure mode transition , 2002 .

[39]  René de Borst,et al.  Damage, Material Instabilities, and Failure , 2004 .

[40]  Garth N. Wells,et al.  A solid‐like shell element allowing for arbitrary delaminations , 2003 .

[41]  René de Borst,et al.  Discrete vs smeared crack models for concrete fracture: bridging the gap , 2004 .

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

[43]  A. Needleman,et al.  Analysis of a brittle-ductile transition under dynamic shear loading , 1995 .

[44]  O. Allix,et al.  Interlaminar interface modelling for the prediction of delamination , 1992 .

[45]  Claude Bédard,et al.  Fracture Processes of Concrete for NLFEA Methods , 1986 .

[46]  J. Hutchinson,et al.  The relation between crack growth resistance and fracture process parameters in elastic-plastic solids , 1992 .

[47]  F. H. Wittmann,et al.  Fracture toughness and fracture energy of concrete , 1986 .

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

[49]  P. Steinmann,et al.  A finite element method for the computational modelling of cohesive cracks , 2005 .

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

[51]  Bert Sluys,et al.  Numerical simulation of quasi-brittle fracture using damaging cohesive surfaces , 2000 .

[52]  H. Reinhardt,et al.  Post-peak cyclic behaviour of concrete in uniaxial tensile and alternating tensile and compressive loading , 1984 .