Modeling Cohesive Cracks with Meshless Method

We present a discrete rotating crack method embedded in the elementfree Galerkin method. The crack is represented by discrete cohesive crack segments only passing through nodes. The discrete crack segments are introduced when the tensile strength in the material is exceeded and the crack segments are oriented perpendicular to the direction of the maximum principal stress. The orientation of the crack segments are rotated when directional changes in the maximum principal stress occur. It will be shown that fixed crack models lead to over-smearing the crack and too stiff responses of the system. The advantage of this method is that no representation of the crack surface is needed.

[1]  T. Belytschko,et al.  Element-free galerkin methods for static and dynamic fracture , 1995 .

[2]  Noël Challamel,et al.  Creep Failure in Concrete as a Bifurcation Phenomenon , 2005 .

[3]  Ares J. Rosakis,et al.  Modeling and simulation of intersonic crack growth , 2004 .

[4]  Su Hao,et al.  Computer implementation of damage models by finite element and meshfree methods , 2000 .

[5]  Ted Belytschko,et al.  A vector level set method and new discontinuity approximations for crack growth by EFG , 2002 .

[6]  Su Hao,et al.  Moving particle finite element method with superconvergence: Nodal integration formulation and applications , 2006 .

[7]  T. Belytschko,et al.  Stable particle methods based on Lagrangian kernels , 2004 .

[8]  T. Rabczuk,et al.  A Meshfree Method based on the Local Partition of Unity for Cohesive Cracks , 2007 .

[9]  T. Belytschko,et al.  Adaptivity for structured meshfree particle methods in 2D and 3D , 2005 .

[10]  Shaofan Li,et al.  Meshfree Simulations of Ductile Crack Propagations , 2005 .

[11]  Mgd Marc Geers,et al.  Structural Damage Analysis of Masonry Walls using Computational Homogenization , 2007 .

[12]  Ted Belytschko,et al.  Wave propagation in a strain-softening bar: Exact solution , 1985 .

[13]  L. J. Malvar,et al.  A three dimensional application of the smeared crack approach , 1990 .

[14]  A. Khan,et al.  Elasto-damage Model for High Strength Concrete Subjected to Multiaxial Loading , 2007 .

[15]  T. Rabczuk,et al.  A meshfree thin shell method for non‐linear dynamic fracture , 2007 .

[16]  Dusan Krajcinovic,et al.  Statistical Damage Mechanics and Extreme Value Theory , 2007 .

[17]  Ziad N. Taqieddin,et al.  Continuum Approach to Damage Mechanics of Composite Materials with Fabric Tensors , 2007 .

[18]  G. Voyiadjis,et al.  A Mixed Finite Element Implementation of a Gradient-enhanced Coupled Damage—Plasticity Model , 2006 .

[19]  L. Chan,et al.  Damage-based Formability Analysis for TWBs , 2005 .

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

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

[22]  Ted Belytschko,et al.  Multiple scale meshfree methods for damage fracture and localization , 1999 .

[23]  K. Mattiasson,et al.  Oriented Damage in Ductile Sheets: Constitutive Modeling and Numerical Integration , 2007 .

[24]  M. Jie,et al.  Localized Necking Criterion for Strain-Softening Materials , 2005 .

[25]  René de Borst,et al.  Modern Domain-based Discretization Methods for Damage and Fracture , 2006 .

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

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

[28]  Su Hao,et al.  Localization-Induced Band and Cohesive Model , 2000 .

[29]  Mark A Fleming,et al.  Meshless methods: An overview and recent developments , 1996 .

[30]  I. Babuska,et al.  The partition of unity finite element method , 1996 .

[31]  T. Zimmermann.  Failure and fracturing analysis of concrete structures , 1986 .

[32]  C. L. Chow,et al.  An efficient explicit algorithm for damage-coupled viscoplastic fatigue model , 2007 .

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

[34]  Ted Belytschko,et al.  Cracking particles: a simplified meshfree method for arbitrary evolving cracks , 2004 .

[35]  T. Belytschko,et al.  Crack propagation by element-free Galerkin methods , 1995 .

[36]  Mark A Fleming,et al.  Continuous meshless approximations for nonconvex bodies by diffraction and transparency , 1996 .

[37]  I. Babuska,et al.  The partition of unity finite element method: Basic theory and applications , 1996 .

[38]  M. Jirásek,et al.  ANALYSIS OF ROTATING CRACK MODEL , 1998 .

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

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

[41]  Ted Belytschko,et al.  An introduction to programming the meshless Element F reeGalerkin method , 1998 .

[42]  M. Jie,et al.  A Damage-coupled Criterion of Localized Necking Based on Acoustic Tensor , 2007 .

[43]  René de Borst.  Modern Domain-based Discretization Methods for Damage and Fracture , 2006 .

[44]  Ted Belytschko,et al.  A method for dynamic crack and shear band propagation with phantom nodes , 2006 .

[45]  Rashid K. Abu Al-Rub,et al.  A Finite Strain Plastic-damage Model for High Velocity Impact using Combined Viscosity and Gradient Localization Limiters: Part I - Theoretical Formulation , 2006 .