A mixed-formulated total Lagrangian material point method for dynamic interaction between structure and soil

In this study, we develop a novel framework by coupling the Updated Lagrangian Material Point Method (ULMPM) and the Total Lagrangian Material Point Method (TLMPM) to simulate the dynamic interaction between large-deformation soils and solid structures. The key contribution lies in enhancing the stabilized performance of TLMPM under nearly incompressible conditions through the implementation of a mixed-formulation scheme. Within the mixed-formulation scheme, linear momentum and the deformation gradient are treated as the primary unknowns, and the Petrov-Galerkin method is employed to derive the weak form of the governing equations. To explicitly characterize the contact behavior between ULMPM and TLMPM, a particle-based contact algorithm is introduced, where the contact forces are treated as external forces acting on different particle pairs. The accuracy and robustness of the proposed scheme are validated through the modeling of various quasi-static and dynamic benchmarks. By comparing the numerical results with those obtained from other methods and experimental data, the effectiveness of the framework in addressing nearly incompressible materials and soil-structure interaction problems is demonstrated.