Diehl P., Lipton R., Wick T., Tyagi M., A comparative review of peridynamics and phase-field models for engineering fracture mechanics, Comput Mech ( 2022) 1– 35, 10.1007/s00467-0.Bourdin B., Francfort G.A., Marigo J.-J., Numerical experiments in revisited brittle fracture, J Mech Phys Solids 48 ( 4) ( 2000) 797– 826.Diehl P., Prudhomme S., Lévesque M., A review of benchmark experiments for the validation of peridynamics models, J Peridynam Nonlocal Model 1 ( 1) ( 2019) 14– 35, 10.1007/s4210-x.Test problems are provided demonstrating the validity and potential of this numerical approach. 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. The first steps for a combined peridynamic and partition of unity method simulator are presented. We do not transfer information of the peridynamic fields to the partition of unity method, solely the crack geometry. Here, Heaviside and Westergaard functions are used to model the crack. The geometry of the crack path in the damaged media is transferred to partition of unity method. The elastic fields of the undamaged media provide appropriate boundary data for the localized peridynamic simulations. The method is a so-called global–local enrichment strategy. Earlier work uses the peridynamic fields, e.g displacement, at the crack tip to approximate enrichment functions for the partition of unity methods. 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. Here, the peridynamic model is used in regions of fracture and smooth partition of unity methods is used in the surrounding linear elastic media. 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. Partition of unity methods are of domain decomposition type and provide the opportunity for multiscale and multiphysics numerical modeling.

Meshfree particle methods