On damage regularity defect nucleation modelling

The purpose of this article is to model defect nucleation. The defect is considered as a small volume which evolves as a damaged zone. The damage is described by a transition zone which can be sharp or continuous. In the first case, discontinuities occur and the initiation of defect is based on bifurcation of an equilibrium state. When the transition is continuous, the initiation of the defect is continuous.The analysis is based on considering different models of damage, depending on the regularity imposed on mechanical field. For each model, the presence of discontinuities on mechanical fields is investigated. Consequences of each model on defect nucleation are illustrated on particular structures: bars under extension and spheres under radial loading.