How to extract the crack opening from a continuous damage finite-element computation?

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 https://www.w3.org/1998/Math/MathML" display="inline"> ε ~ ( [ U ] ) governing the damage variable in Mazars’ model. Besides, from a classical FE computation, we obtain a distribution of the state variable https://www.w3.org/1998/Math/MathML" display="inline"> ε ~ F E with the same shape due to the non local weight function. Finally the displacement jump is computed by setting https://www.w3.org/1998/Math/MathML" display="inline"> ε ( [ U ] ) = ε ~ F E 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.