A mortar segment-to-segment frictional contact approach in material point method

Handling contact problems in the Material Point Method (MPM) has long been a challenge. Traditional grid-based contact approaches often face issues with mesh dependency, while material point-based methods can be computationally intensive. To address these challenges, this study develops a novel mortar segment-to-segment frictional contact approach for MPM. We first introduce boundary vertices and propose an innovative kinematic update scheme for precise representation of the boundaries of the continuum media and their continuously evolving contact normals throughout the contact process. Then, we construct a weak form of contact constraints based on the mortar method to facilitate a stable segment-to-segment contact detection. To rigorously ensure the non-penetration condition, the energetic barrier method is further adopted and implemented in MPM for enforcing the contact constraints. The proposed kinematic update scheme for boundary vertices is first verified through a cantilever beam benchmark test. The verified framework is further examined through a wide range of contact scenarios, including rolling, sliding, collision of two rings, and multi-body contacts, in both small and finite deformations. The simulation results are thoroughly discussed, highlighting the significant improvements in accuracy and versatility. Potential limitations of the proposed method are also examined.