Phenomenological nonlocal approaches based on implicit gradient-enhanced damage

The present paper focusses on five phenomenological approaches in gradient-enhanced damage, several of which have been proposed in the literature to simulate material degradation. These different gradient-damage based nonlocal models are examined with respect to their ability to describe crack initiation and crack propagation. The models are applied to identical mechanical benchmark tests, where the material damage evolution law is taken as good as possible equal for each model. Interesting differences between the different models arise, and it is shown that care must be taken in the interpretation and application of these models. One-dimensional results cannot be extrapolated in a straightforward fashion to two dimensions, and the physical relevance of some results is in some cases debatable. Furthermore, it is shown that the response of some models is strongly influenced by small differences in the applied damage evolution law. A discussion is made on the use of two different types of such evolution laws, which are frequently applied in the literature.