A Particle Finite Element Approach For Modeling Granular Flows With Phase Transition
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Natural hazards represent a major challenge for modern societies, with increasing impacts on infrastructure, ecosystems, and human safety. The protection of land has therefore become a critical factor in preventing environmental disasters. Landslides, in particular, can cause river overflows, posing serious threats to nearby areas. Computational mechanics offers effective tools to study these phenomena and to better understand their dynamics. In this work, an innovative model for the description of granular material is proposed. First, the μ(I)-rheology has been implemented, incorporating the regularization originally proposed in [1]. This approach is specifically designed to prevent abrupt transitions between rigid and visco-plastic behavior. A regularization technique is employed to limit the maximum viscosity at low shear rates. Numerical tests demonstrate that the model accurately reproduces the dynamics of free-surface granular flows. Then, since μ(I)-rheology is valid primarily in the inertial regime, it is most suitable for low-shear flows and collapse problems with small aspect ratios [2]. To capture solid-like behavior, the μ(I) model is enhanced treating the fluid as a Maxwell-type material with a Mohr-Coulomb failure criterion, providing an effective framework to describe the transition from solid to fluid in granular flows. The constitutive model has been implemented within a Particle Finite Element Method (PFEM) framework [3]. This method employs a Lagrangian approach, where the mesh moves with the particles, continuously updating node positions. A key challenge in PFEM is mesh degradation due to particle motion. To overcome this issue, a remeshing strategy is applied, changing the grid connectivity when needed. The proposed approach has been validated against experimental and numerical data. [1] Franci A., Cremonesi M., 3D regularized μ(I)-rheology for granular flows simulation, Journal of Computational Physics, 378, 257-277, 2018 [2] Barker T., Schaeffer D.G., Bohorquez P., Gray J.M.N.T., Well-posed and ill-posed behaviour of the μ(I)-rheology for granular flow, Journal of Fluid Mechanics, 779, 794-818, 2015 [3] Cremonesi M., Franci A., Idelsohn S. and O˜nate E., A State of the Art Review of the Particle Finite Element Method, Archives of Computational Methods in Engineering, 27, 1709-1735, 2020
