How to extract a crack opening from a continuous damage finite-element computation?
Abstract
Doubtlessly, for assessing the integrity and the strength of concrete structures to environmental attacks it would be ideal to model the transition between diffuse damage and a discontinuous description. We propose, in a first approach, to extract an equivalent crack opening using a non local Mazars’ damage model. We consider a discontinuous displacement field with a given jump $[U]$ from which we compute the equivalent non local strain $\tilde{ε}([U])$ governing the damage variable in Mazars’ model. Besides, from a classical FE computation, we obtain a distribution of the state variable $\tilde{ε}^{FE}$ with the same shape due to the non local weight function. Finally the displacement jump is computed by setting $\tilde{ε}([U]) = \tilde{ε}^{FE}$ at the discontinuity. The proposed approach is applied on a tension rod with an error measure between both solutions to evaluate how the non local solution approaches asymptotically the representation of a discontinuity. Results show good agreement for large damage.
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