On the role of bond-associated stabilization and discretization on deformation and fracture in non-ordinary state-based peridynamics

As it is well known, non-ordinary state-based peridynamic (NOSB PD) models suffer from inherent instability issues, which can severely affect deformation and fracture predictions. These issues have been identified and tackled through the years using stabilization methods that work by introducing additional terms in the formulation or by disturbing the radial symmetry of the horizon, leading to stabilized solutions. A popular and effective method is the bond-associated correspondence formulation. In this work, we make an in-depth investigation on the role of bond-associated stabilization and discretization on the deformation and fracture behaviour in NOSB PD by considering three different comprehensive and detailed numerical studies. Firstly, the convergence of the NOSB PD linear elastic formulation is investigated under both the L2 and H1 error norms. The role of the influence function is also considered and analysed. Different combinations of bond-associated horizon and point-associated horizon values are used to determine the role of these parameters in obtaining accurate solutions. Secondly, we consider a static analysis example where we compare PD with the finite element method (FEM), in order to verify the accuracy of the PD models for stress analysis. Lastly, a quasi-static crack propagation analysis benchmark example is presented to assess the accuracy of fracture predictions and the effect of varying the discretization parameters is studied for both load–displacement curves and crack paths.