Comparison between two nonlocal criteria: A case study on pressurized holes

Two nonlocal approaches are applied to the borehole geometry, i.e. a circular hole in an infinite elastic medium subjected to internal pressure. The former approach lays in the framework of Gradient Elasticity (GE), which results nonlocal in the strict sense, being based on a nonlocal constitutive relationship. Changing the stress field as the geometry (i.e., the radius of the hole) varies, the related stress concentration factor can be thought as the critical failure parameter. The latter approach is the Finite Fracture Mechanics (FFM), well-consolidated in the framework of brittle fracture. Whereas the model belongs to classical linear elasticity, it reveals nonlocal in a loose sense: the failure condition is no more punctual, but achieved when two average requirements on the stress and the energy ahead of the notch tip are simultaneously fulfilled. Τhe two approaches, although different, present some similarities, both involving a characteristic length. It will be shown that the GE and FFM predictions are in excellent agreement when the two lengths are properly defined.