Explicit‐Implicit Material Point Method for Dense Granular Flows With a Novel Regularized µ ( I ) Model

ABSTRACT The material point method (MPM) is widely employed to simulate granular flows. Although explicit time integration is favored in most current MPM implementations for its simplicity, it cannot rigorously incorporate the incompressible µ ( I )‐rheology, an efficient model ubiquitously adopted in other particle‐based numerical methods. While operator‐splitting‐based explicit‐implicit MPM can overcome this limitation for incompressible fluids, its extension to dense granular flows governed by µ ( I )‐rheology remains unexplored. To bridge this gap, this study proposes an explicit‐implicit MPM framework specifically for incompressible dense granular flows governed by the µ ( I ) rheology, augmented by a novel regularization technique that eliminates pathological viscosity divergence inherent to the original µ ( I ). The explicit‐implicit MPM framework comprises two steps: (i) an explicit predictor for velocity estimation, and (ii) an implicit corrector for solving the Pressure Poisson equation and updating velocity. In particular, a staggered grid is adopted for both steps to improve pressure stability and computational efficiency, and the Multigrid Preconditioned Conjugate Gradient method (MGPCG) is utilized for efficient pressure solution. The framework is further rigorously validated against a series of experimental benchmarks. Analysis of the regularization method is also conducted, revealing that: (i) decreasing the regularization parameter λ increases viscosity at low strain rates, reducing the runout; (ii) L1 regularization produces a longer runout than the higher‐order formulations (L2–L4), while L2–L4 generate similar deposition patterns, indicating negligible benefit from the added mathematical complexity, and (iii) Unlike PFEM, where decreasing λ severely increases computational cost, the explicit‐implicit MPM computes regularization explicitly in the predictor step, maintaining λ ‐invariant efficiency.