Tensile effects in peridynamic plates with circular holes

Microstructures are often responsible of the mechanical behavior at the macroscale level, governing damage processes and fractures. A suitable choice for modeling these kind of phenomena is a nonlocal theory, which considers microscale behaviors by defining an internal length scale. Thanks to this intrinsic property and to their ability to naturally handle discontinuities and singularities, nonlocal models are succeeding in analyzing onset of damage and fracture development in both previously unexplored fields and in well-known classical problems. Among these, this work aims to investigate the influence of a particular choice of nonlocal microstructure on a classical (local) problem of fracture propagation, namely that of a plate with a circular hole placed under tension. The selected microstructure corresponds to the discrete lattice representation of bond-based peridynamics, the theory on which this study is based. In particular, a recently proposed nonlocal dimensionally reduced model, crucial for minimizing the significant computational efforts associated with nonlocal settings, has been employed. The holed nonlocal plate has been analyzed for two different microstructures, each one corresponding to a proper choice of the horizon, a specific parameter representing the internal length scale of the medium. The analyses have been performed by keeping the same overall elastic stiffness, by computing the "peridynamic stress", and by using a stress-based bonds' failure criterion. The outcomes of this research highlight the shift of the stress peak, which becomes more distal when the internal length scale increases. In addition, the stress concentration area becomes more diffuse when the horizon rises, and the actual value of the stress concentration factor decreases. These results are in agreement with the development of the delamination surface, which is more diffuse when the horizon is higher.