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

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 fi nite 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 orig inal one dimensional problem devised in Dufour et al . [4] is recovered as pro fi les of deformation orthog onal to the idealized crack direction are computed. An estimate of the crack opening and an error indicator are computed by comparing fi nite element deformation pro fi les and theoretical pro fi les corresponding to a displacement discontinuity. Two estimates have been considered: In the strong approach, the maxima of the pro fi les are assumed to be equal; in the weak approach, the integrals of each pro fi le are set equal. Two dimensional numerical calculations show that the weak estimates perform better than do the strong ones. Error indicators, de fi ned as the distance between the numerical and theoretical pro fi les, 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 ( > 40 m m )