A coupled discrete element material point method for fluid–solid–particle interactions with large deformations

Fluid–solid–particle systems such as water–soil–rock mixtures are very common in many natural processes and engineering applications. However, modelling these complex interactions is still very challenging due to their multi-scale nature. Here, we present a hybrid model that combines the advantages of the two-phase (solid and liquid) Material Point Method (MPM) on handling continuum materials with large deformations and the capability of the Discrete Element Method (DEM) on simulating the mechanical behaviours of rigid particles. Moreover, in our model, the DEM has the ability to deal with non-spherical particles. A new collision detection approach is presented in detail, and a unified DEM style contact force model is proposed to couple MPM with DEM by considering momentum exchanges between particles and continuum phases. The proposed model is validated by several numerical benchmarks, including (1) flows around a cylinder, (2) a block sliding on an inclined plane, (3) projectile impacts a granular medium, and (4) sphere impacts and penetrates into wet granular material. The results match well with analytical solutions and experimental observations, demonstrating this model's capability to efficiently solve complex fluid–solid–particle interactions with large deformations. Finally, an example of column collapse is simulated to show future potential applications of the proposed method.