# American Institute of Mathematical Sciences

December  2014, 9(4): 575-597. doi: 10.3934/nhm.2014.9.575

## A review of non local continuum damage: Modelling of failure?

 1 Laboratoire des Fluides Complexes et leurs Réservoirs - UMR 5150, Université de Pau et des Pays de l'Adour, Allée du Parc Montaury, Anglet, 64600, France, France

Received  October 2014 Revised  October 2014 Published  December 2014

Failure of quasi-brittle materials such as concrete needs a proper description of strain softening due to progressive micro-cracking and the introduction of an internal length in the constitutive model in order to achieve non zero energy dissipation. This paper reviews the main results obtained with the non local damage model, which has been among the precursors of such models. In most cases up to now, the internal length has been considered as a constant. There is today a consensus that it should not be the case as models possess severe shortcomings such as incorrect averaging near the boundaries of the solid considered and non local transmission across non convex boundaries. An interaction-based model in which the weight function is constructed from the analysis of interaction has been proposed. It avoids empirical descriptions of the evolution of the internal length. This model is also recalled and further documented. Additional results dealing with spalling failure are discussed. Finally, it is pointed out that this model provides an asymptotic description of complete failure, which is consistent with fracture mechanics.
Citation: Gilles Pijaudier-Cabot, David Grégoire. A review of non local continuum damage: Modelling of failure?. Networks and Heterogeneous Media, 2014, 9 (4) : 575-597. doi: 10.3934/nhm.2014.9.575
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