An implicit material point-to-rigid body contact approach for large deformation soil-structure interaction

Modelling the interaction between rigid and deformable bodies holds significant relevance in geotechnical engineering, particularly in scenarios involving stiff engineering objects interacting with highly deformable material such as soil. These processes are challenging due to the combined nonlinear mechanisms including large deformation, elasto-plasticity, and contact with friction. For highly deformable material, the Material Point Method is a natural choice over the Finite Element Method due to its ability to handle large deformations without remeshing by carrying material information at points. This paper uses the Implicit General Interpolation Material Point Method (GIMPM) to demonstrate a new approach for modelling this type of interaction, and exploits the GIMPM's inherent definition of the boundary of a deformable domain to formulate a consistent contact formulation, negating the need for boundary reconstruction. The formulation is demonstrated through validations and comparisons to alternative methods for simulating contact. The combination of the contact formulation with an implicit framework is shown to be an efficient method for modelling geotechnical problems. The proposed method exhibits optimal convergence for contact problems, accurately captures stick-slip Coulomb friction, and ensures consistent stress fields at the contact surface of a rigid body.