Embedded Lagrangian Surfaces for Explicit Contact Interface Representation in the Material Point Method

ABSTRACT The Material Point Method (MPM) is widely used in simulating large‐deformation problems, but it suffers from inherent contact‐related issues, including premature contact, contact penetration, and poor adaptability to multi‐resolution object contact. To address these challenges, this paper proposes an easily implementable embedded Lagrangian surface (ELS) contact algorithm and establishes a complete ELS‐MPM solution framework. The core of the proposed method is the introduction of an ELS that moves synchronously with the boundary particles of deformable bodies. The contact interface is discretized using surface meshes; potential contact pairs are first filtered via a coarse search, and then accurate contact detection is achieved through fine distance calculation and penetration judgment. Contact forces are computed based on the penalty method and Coulomb friction model and integrated into MPM's grid‐particle dynamic update via a two‐step transfer process: “contact points to ELS nodes” and “ELS nodes to background grid.” Performance verification shows that ELS‐MPM effectively eliminates premature contact and penetration by precisely defining the contact interface with ELS. It supports independent background grids for multi‐resolution objects, breaking the resolution matching constraint of traditional MPM while maintaining compatibility with the traditional MPM core framework. A noted limitation is that the method cannot inherently handle material interface fracture, which requires integration with automatic surface mesh partitioning algorithms in future work. This study demonstrates the feasibility and advantages of ELS‐MPM through theoretical analysis, framework construction, and case verification, providing an efficient and stable solution for MPM to address complex contact problems.