Continuous-discontinuous formulation for ductile fracture

In this contribution, a continuum-discontinuum model for ductile failure is presented. The degradation of material properties through deformation is described by a Continuum Damage Mechanics model, which uses a non-local integral formulation to avoid mesh dependence. In the final stage of failure, the damaged zone is replaced by a macro crack for a more realistic representation of the phenomenon. The inclusion of the discontinuity surfaces is performed by the XFEM and Level Set Method to avoid the spurious damage growth typical of this class of models.

[1]  J. Mediavilla Varas,et al.  Continuous and discontinuous modelling of ductile fracture , 2005 .

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

[3]  Jean Lemaitre,et al.  A Course on Damage Mechanics , 1992 .

[4]  E. A. de Souza Neto,et al.  A fast, one-equation integration algorithm for the Lemaitre ductile damage model , 2002 .

[5]  T. Hughes Generalization of selective integration procedures to anisotropic and nonlinear media , 1980 .

[6]  Renato Natal Jorge,et al.  Quadrilateral elements for the solution of elasto‐plastic finite strain problems , 2001 .

[7]  J. M. A. César de Sá,et al.  Damage modelling in metal forming problems using an implicit non-local gradient model , 2006 .

[8]  D. Krajcinovic,et al.  Introduction to Damage Mechanics , 2000 .

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

[10]  T. Belytschko,et al.  Vector level sets for description of propagating cracks in finite elements , 2003 .

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

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

[13]  Gilles Pijaudier-Cabot,et al.  From damage to fracture mechanics and conversely: A combined approach , 1996 .

[14]  E. Verron,et al.  Stress analysis around crack tips in finite strain problems using the eXtended finite element method , 2005 .

[15]  Cv Clemens Verhoosel,et al.  Non-Linear Finite Element Analysis of Solids and Structures , 1991 .

[16]  A. Combescure,et al.  A thermodynamic method for the construction of a cohesive law from a nonlocal damage model , 2009 .

[17]  Ted Belytschko,et al.  Modelling crack growth by level sets in the extended finite element method , 2001 .

[18]  G. Irwin ANALYSIS OF STRESS AND STRAINS NEAR THE END OF A CRACK TRAVERSING A PLATE , 1957 .

[19]  Ted Belytschko,et al.  Discontinuous enrichment in finite elements with a partition of unity method , 2000 .

[20]  F. M. Andrade Pires,et al.  Improvement of the numerical prediction of ductile failure with an integral nonlocal damage model , 2009 .

[21]  J. Z. Zhu,et al.  The finite element method , 1977 .

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

[23]  J. Dolbow,et al.  Enrichment of enhanced assumed strain approximations for representing strong discontinuities: addressing volumetric incompressibility and the discontinuous patch test , 2004 .

[24]  J. Chaboche,et al.  Mechanics of Solid Materials , 1990 .

[25]  J. Prévost,et al.  Modeling quasi-static crack growth with the extended finite element method Part I: Computer implementation , 2003 .

[26]  David R. Owen,et al.  FINITE ELEMENT PROGRAMMING , 1980, The Finite Element Method Using MATLAB.