Stress based nonlocal interactions

The progressive degradation of quasi-brittle materials can be reproduced efficiently by means of damage models. The presence of microcracks in the media gives a nonlocal aspect to the evolution of damage. By interacting with each other under loading, it leads to stress amplification (singularity) or decrease (shield effect) at a given location. In the framework of damage models, the nonlocal integral method [1] or the gradient enhanced media [2] introduce this notion of interactions between points by means of an internal length. However, they are still some pending issues regarding these methods [3] (e.g., treatment of free boundaries, description of the damage state close to complete failure). In this paper, a modification of the nonlocal integral regularization method is proposed. The influence of a point on its neighbourhood is evolving during the loading and its intensity and direction depend on the stress state it encounters. Through several numerical simulations, we show that our proposition improves the treatment of free boundaries and gives physically sound damage and strain field in the fracture process zone up to complete failure. The latter being a key parameter of durability analysis