Estimation of crack opening from a two-dimensional continuum-based finite element computation

Author (s): Dufour, F.; Legrain, G.; Pijaudier-Cabot, G. and Huerta, A.
Journal: International Journal for Numerical and Analytical Methods in Geomechanics

Volume: 36, Iss. 16
Pages: 1813 – 1830
Date: 2012

Abstract:
Damage models are capable of representing crack initiation and mimicking crack propagation within a continuum framework. Thus, in principle, they do not describe crack openings. In durability analyses of concrete structures however, transfer properties are a key issue controlled by crack propagation and crack opening. We extend here a one-dimensional approach for estimating a crack opening from a continuum-based finite element calculation to two-dimensional cases. The technique operates in the case of mode I cracking described in a continuum setting by a nonlocal isotropic damage model. We used the global tracking method to compute the idealized crack location as a post-treatment procedure. The original one-dimensional problem devised in Dufour et al. is recovered as profiles of deformation orthogonal to the idealized crack direction are computed. An estimate of the crack opening and an error indicator are computed by comparing finite element deformation profiles and theoretical profiles corresponding to a displacement discontinuity. Two estimates have been considered: In the strong approach, the maxima of the profiles are assumed to be equal; in the weak approach, the integrals of each profile are set equal. Two-dimensional numerical calculations show that the weak estimates perform better than do the strong ones. Error indicators, defined as the distance between the numerical and theoretical profiles, are less than a few percentages. In the case of a three-point bending, test results are in good agreement with experimental data, with an error lower than 10% for widely opened crack (>?40µm).

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Bibtex:

@article{Dufour-DLPH:12,
  Author      = {Fr\'ed\'eric Dufour and Gr\'egory Legrain and Gilles Pijaudier-Cabot and Antonio Huerta},
  Title       = {Estimation of crack opening from a two-dimensional continuum-based finite element computation},
  Fjournal    = {International Journal for Numerical and Analytical Methods in Geomechanics},
  Journal     = {Int. J. Numer. Anal. Meth. Geomech.},
  Volume      = {36},
  Number      = {16},
  Pages       = {1813--1830},
  doi         = {10.1002/nag.1097},
  year        = {2012}
}