Topological search of the crack pattern from a continuum mechanical computation

Abstract In this contribution, a method to track the crack path from a continuum finite element simulation using failure material models is presented. The work belongs to a larger project, aiming at extracting the crack opening a posteriori of a continuum finite element computation to deal with durability assessment of concrete structures. Cracking is modelled in a diffuse manner by a distribution of an appropriate scalar state variable associated to material degradation. With the proposed method, the crack path is found in the post-processing phase by means of a step-by-step procedure. At each step, a new location point is computed where the state variable is maximum in a given direction at a given distance. Furthermore a specific procedure is proposed to detect multiple cracks in an automatic way. The proposed method is successfully applied to two studies implying either a single crack or a multi-crack pattern, obtained with different continuum models to highlight the versatility of the proposed approach.

[1]  Antonio Huerta,et al.  Extraction of a crack opening from a continuous approach using regularized damage models , 2008 .

[2]  François Fleury,et al.  Containment Evaluation under Severe Accidents (CESA): synthesis of the predictive calculations and analysis of the first experimental results obtained on the Civaux mock-up , 2001 .

[3]  J. Lemaître.  How to use damage mechanics , 1984 .

[4]  Rhj Ron Peerlings,et al.  Some observations on localisation in non-local and gradient damage models , 1996 .

[5]  Alfredo Edmundo Huespe,et al.  Continuum approach to material failure in strong discontinuity settings , 2004 .

[6]  T. Belytschko,et al.  Non‐planar 3D crack growth by the extended finite element and level sets—Part I: Mechanical model , 2002 .

[7]  Jan Carmeliet,et al.  Three‐dimensional liquid transport in concrete cracks , 2004 .

[8]  N. Coulon,et al.  Air–steam leakage through cracks in concrete walls , 2007 .

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

[10]  Grégory Legrain,et al.  Estimation of crack opening from a two‐dimensional continuum‐based finite element computation , 2012 .

[11]  Sergio Oller,et al.  A general framework for continuum damage models. I. Infinitesimal plastic damage models in stress space , 2000 .

[12]  N. Chevaugeon,et al.  A level set based model for damage growth: The thick level set approach , 2011 .

[13]  S. H. Simmonds,et al.  Air Leakage Characteristics in Reinforced Concrete , 1984 .

[14]  Gilles Pijaudier-Cabot,et al.  Permeability due to the Increase of Damage in Concrete: From Diffuse to Localized Damage Distributions , 2009 .

[15]  L. J. Sluys,et al.  Remeshing strategies for adaptive ALE analysis of strain localisation , 2000 .

[16]  J. Mier,et al.  Crack Interaction in Concrete , 2005 .

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

[18]  Quoc Son Nguyen,et al.  Sur les matériaux standard généralisés , 1975 .

[19]  Fabrice Gatuingt,et al.  Nonlocal anisotropic damage model and related computational aspects for quasi-brittle materials , 2007 .

[20]  D. C. Tobutt,et al.  The reliability of earth slopes , 1979 .

[21]  A. Combescure,et al.  A cohesive zone model which is energetically equivalent to a gradient-enhanced coupled damage-plasticity model , 2010 .

[22]  Wieland Ramm,et al.  Air leakage characteristics in cracked concrete , 1995 .

[23]  S. Andrieux,et al.  A variational formulation for nonlocal damage models , 1999 .

[24]  M. Frémond,et al.  Damage, gradient of damage and principle of virtual power , 1996 .

[25]  Stefano Mariani,et al.  An extended FE strategy for transition from continuum damage to mode I cohesive crack propagation , 2007 .

[26]  L. J. Sluys,et al.  On the use of embedded discontinuity elements with crack path continuity for mode-I and mixed-mode fracture , 2002 .

[27]  Mgd Marc Geers,et al.  Strain-based transient-gradient damage model for failure analyses , 1998 .

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

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

[30]  Paolo Riva,et al.  Prediction of air and steam leak rate through cracked reinforced concrete panels , 1999 .

[31]  Rhj Ron Peerlings,et al.  Interpolation requirements for implicit gradient-enhanced continuum damage models , 2003 .

[32]  Kyrylo Kazymyrenko,et al.  Convergence of a gradient damage model toward a cohesive zone model , 2011 .

[33]  M. Matallah,et al.  A practical method to estimate crack openings in concrete structures , 2009 .

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

[35]  J. Lemaître,et al.  Engineering Damage Mechanics: Ductile, Creep, Fatigue and Brittle Failures , 2005 .

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

[37]  F. Dufour,et al.  Stress-based nonlocal damage model , 2011 .

[38]  Eric Lorentz,et al.  Gradient damage models: Toward full-scale computations , 2011 .

[39]  A. Huespe,et al.  Theoretical and computational issues in modelling material failure in strong discontinuity scenarios , 2004 .