Non-ordinary state-based peridynamic analysis of stationary crack problems

An implicit implementation of the non-ordinary state-based peridynamics formulation for quasi-static linearly elastic solids is presented. Emphasis is placed on assessing the accuracy of the numerical scheme in the vicinity of the crack front and other sources of stress concentration. We also present a comparative study of methods used to control the zero-energy modes inherent in the nonlocal definition of the strain tensor and reduce the spurious oscillations present particularly in regions of high strain gradients. The accuracy of the peridynamics scheme, including the impact of the lattice spacing and configuration, is assessed by performing an analysis of the near-tip stress and displacement fields (K-fields) for 2D problems. The manuscript also summarizes a verification study based on the classical 3D penny-shaped crack problem and a validation study of a 3D notched fracture specimen.