A fracture multiscale model for peridynamic enrichment within the partition of unity method

Partition of unity methods are of domain decomposition type and provide the opportunity for multiscale and multiphysics numerical modeling. Different physical models can exist within a partition of unity method scheme for handling problems with zones of linear elasticity and zones where fractures occur. Here, the peridynamic model is used in regions of fracture and smooth partition of unity methods is used in the surrounding linear elastic media. Our method is novel in that we evolve the crack path using peridynamics and apply the partition of unity method to compute the elastic fields in the neighborhood of the crack tip. Earlier work uses the peridynamic fields, e.g displacement, at the crack tip to approximate enrichment functions for the partition of unity methods. The method is a so-called global-local enrichment strategy. The elastic fields of the undamaged media provide appropriate boundary data for the localized peridynamic simulations. The geometry of the crack path in the damaged media is transferred to partition of unity method. Here, Heaviside and Westergaard functions are used to model the crack. We do not transfer information of the peridynamic fields to the partition of unity method, solely the crack geometry. The first steps for a combined peridynamic and partition of unity method simulator are presented. We show that the local peridynamic approximation can be utilized to enrich the global partition of unity method approximation to capture the true material response with high accuracy efficiently. Test problems are provided demonstrating the validity and potential of this numerical approach.