Quasi-static non-ordinary state-based peridynamics for the modeling of 3D fracture

A majority of the efforts in modeling crack propagation have used continuum models built upon partial derivatives with respect to the spatial coordinates in the force and displacement relationship. These methods are inherently incompatible for modeling cracks because the partial derivatives are undefined at crack faces due to the discontinous displacement field. Furthermore, these methods fall short on robustness and computational complexity when involving heterogeneous materials, crack initiation and crack branching, especially in a 3D setting. A recent addition to the list of numerical methods used in fracture mechanics, peridynamics is a particle-based continuum model that addresses some shortcomings of other methods. In this work, a quasi-static linearly elastic implicit parallel implementation of the non-ordinary state-based peridynamics formulation is presented for both stationary and propagating cracks. Emphasis is placed on assessing the accuracy of the numerical scheme in the vicinity of the crack front and other sources of stress concentration. The near-tip solution is affected by the presence of zero-energy modes, particularly in regions of high strain gradients, caused by the nonlocal definition of the strains. A systematic comparative study is presented between the various methods introduced to address this numerical instability. The accuracy of the peridynamics scheme, including the impact of the grid spacing and configuration, is assessed through a detailed analysis of the near-tip stress and displacement fields and the extraction of key fracture parameters such as stress intensity factors and conservation integrals. This assessment includes a verification study based on the classical 3D penny-shaped crack problem and a validation study of a 3D notched fracture specimen. For the modeling of propagating cracks, the emphasis of the assessment study is placed on the ability of the method to predict crack path. To that effect, a variety of verification and validation problems corresponding to classical test geometries (double cantilever beam, four-point bend specimen and V-notched Brazilian disc) are simulated. Lastly, an analytical and numerical study linking peridynamics and cohesive zone modeling under Mode I, Mode II and mixed-mode loading is developed