A new hybrid approach based on the state-based peridynamic method and the material point method for numerical modeling of damage in ductile metals

This research introduces a new approach that integrates the state-based peridynamic method with the material point method to study the elastoplastic behavior of metals under large deformations and to model crack initiation and growth in a two-dimensional setting. In the proposed method, large elastoplastic deformations are calculated within the material point region, while the peridynamic component is automatically generated around points with potential for damage initiation and growth, optimally relocating along with the crack tip. The material domain is initially discretized using material point method particles. Subsequently, a new adaptive algorithm converts these material point particles into peridynamic particles to efficiently and rapidly model the damage region based on the distance from the crack tip. This process is reversible, allowing peridynamic points to revert to material point particles as needed. The main advantage of this method is the limited area of the peridynamic region during crack growth, coupled with the use of the state-based peridynamic method alongside classical mechanics. The proposed method's performance is evaluated through numerical examples and compared with similar numerical methods and experimental results in terms of speed and accuracy. This approach provides significant benefits in calculation cost and accuracy for modeling the behavior of ductile metals under large deformations and subsequent material failure.