Interaction-based non-local damage model for failure in quasi-brittle materials

•A new interaction-based non-local formulation has been proposed.•The interactions are computed explicitly from the dilation of circular inclusions.•Boundary effects and shielding effects are accounted for in the new formulation.•Non-local contributions close to a damage band do not exhibit spurious effects anymore.•The strain distribution computed at complete failure is very close to an ideal opening profile.

The purpose of this paper is to present a new macroscopic approach to describe the evolving non-local interactions which are produced at the mesoscale during damage and failure in quasi-brittle materials. A new-integral type non-local model is provided where the weight function is directly built from these interactions, and therefore takes into account their evolution during the material failure intrinsically.