Transition endommagement-fissuration par une formulation eikonale pour les modèles d'endommagement avec et sans plasticité

To properly handle material failure, one needs to be able to predict, for a given loading, the possible initiation and propagation of cracks.Aside from the Linear Elastic Fracture Mechanics, which only deals with existing cracks, this can be achieved through continuum damage mechanics, which also accounts for the associated progressive loss of stiffness. However, despite their advantages, those models suffer from a certain number of deficiencies, especially when handling strain localization. As it is, while local damage models suffer from spurious mesh dependency, the nonlocal ones, which were developed to address this issue, fail to make a highly damaged zone equivalent to a crack.A nonlocal Eikonal-based formulation with damage-dependent interactions has been shown to successfully address these issues, though it still suffers from the drawbacks inherent to integral-type formulations. After proposing a definition of what is called here a “good” damage model, this work focuses on a new gradient-type formulation that derives from this approach and can thus be expected to address the issues associated with both local and nonlocal models.This work first presents the non-intrusive implementation in Abaqus of the formulation associated with an isotropic damage model, which is used to study its properties in a one-dimensional setting. This formulation is shown to have properties similar to those of a phase-field-based formulation, both successfully addressing the damage-fracture transition though they exhibit a rather brittle behaviour.It then deals with the introduction of plasticity, i.e. using a damage-plastic model instead of a pure damage one, and how it could be used to address the brittleness issue while keeping the properties of the Eikonal-based approach. A one-dimensional study is thus conducted, focusing on the theoretical responses obtained with both models associated with either fixed or shrinking localization area. Based on its results, one can conclude that introducing permanent strains would reduce the brittleness linked to the shrinking of the localization area and the associated unloading.Both damage and damage-plastic formulations are then implemented in the finite element code OOFEM, which is used to confirm these preliminary observations in a three-point-bending setting. It is then shown that both formulations can be used to model structural failure by providing mesh-independent results where a highly damaged zone is equivalent to a crack. Moreover, while the response associated with the pure damage model remains somewhat brittle, the issue is addressed by the damage-plastic one.