A Robust Lagrangian Implicit Material Point Method for Accurate Large-Deformation Analysis

The material point method (MPM) has shown significant potential for simulating problems involving large deformations. However, many implicit MPM formulations based on the traditional Updated Lagrangian (UL) scheme still face challenges in terms of computational stability. In this study, we propose a novel Lagrangian equilibrium formulation for an implicit MPM that is tailored to large-deformation problems. (1) The previously converged state is utilized to simplify stiffness matrix computations, thereby improving the stability of the algorithm. (2) The framework supports a variety of high-order interpolation functions, which effectively mitigate numerical artifacts such as cell-crossing errors. (3) The B-bar technique is further incorporated to suppress spurious stress oscillations in the incompressible limit. The proposed method is validated through two classical benchmark tests, the simple shear of a single element and the cantilever beam problem, by comparing the simulation results with analytical solutions and alternative numerical approaches. Finally, its capability is demonstrated in slope stability and strip footing analyses, confirming the superior accuracy, stability, and robustness of the method for large-deformation elastoplastic problems.