Abstract
Two nonlocal approaches are applied to the borehole geometry, herein simply modelled as a circular hole in an infinite elastic medium, subjected to remote biaxial loading and/or internal pressure. The former approach lies within the framework of Gradient Elasticity (GE). Its characteristic is nonlocal in the elastic material behaviour and local in the failure criterion, hence simply related to the stress concentration factor. The latter approach is the Finite Fracture Mechanics (FFM), a well-consolidated model within the framework of brittle fracture. Its characteristic is local in the elastic material behaviour and non-local in the fracture criterion, since crack onset occurs when two (stress and energy) conditions in front of the stress concentration point are simultaneously met. Although the two approaches have a completely different origin, they present some similarities, both involving a characteristic length. Notably, they lead to almost identical critical load predictions as far as the two internal lengths are properly related. A comparison with experimental data available in the literature is also provided.
Highlights
Engineers and scientists have used classical continuum solid mechanics along with strength-based failure criteria since the middle of the nineteenth century, usually successfully
The development of Linear Elastic Fracture Mechanics (LEFM), i.e. the theory based on Griffith infinitesimal energy balance during crack growth, allowed a first insight in the size effect explanation
The originality of the present analysis lies in the solution to the inner pressure loading, a novelty for both approaches, as well as in the comparison between them, since, at the authors’ best knowledge, it is the first time that Gradient Elasticity and Finite Fracture Mechanics are directly compared
Summary
Engineers and scientists have used classical continuum solid mechanics along with strength-based failure criteria since the middle of the nineteenth century, usually successfully. Among the different theories developed in the last decades to address the size effect issue (e.g. the fractal approach [2]), let us mention two main research directions, both falling within the framework of nonlocal models The former one is non-local elasticity: the stress at a point depends on the strain in a region surrounding that point (strong non-locality or integral models) or on the strain at that point plus its derivatives (weak non-locality or gradient models). Such a distance is the intrinsic length of the model, depending only on the material These approaches fail in predicting the failure stress of a cracked or notched structure having size comparable to the critical distance. To overcome these incongruences, the coupled criterion of Finite Fracture Mechanics (FFM) was introduced [19, 20]. The originality of the present analysis lies in the solution to the inner pressure loading, a novelty for both approaches, as well as in Meccanica
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
