Mixed discrete continuum modelling of dense granular flow

Abstract

Granular materials are central to many natural and industrial processes, yet faithfully simulating their behaviour at full scale remains challenging. The Discrete Element Method (DEM) resolves grain-scale physics but becomes costly for large assemblies, while the Finite Element Method (FEM) accelerates computation by treating the material as a continuum at the expense of particle level detail. Coupling DEM at the particle scale with FEM at the macro scale offers a practical route for large-scale problems. This thesis introduces a hybrid DEM–FEM framework implemented in the open-source KRATOS MULTIPHYSICS platform, in which the two descriptions overlap in a hybrid zone; displacement compatibility is enforced via a penalty, and smoothly varying weights enable seamless transfer of stress and strain across the interface.

Rather than focusing solely on bulk metrics, the verification campaign resolves the mechanics within the overlap and quantifies the influence of coupling parameters. The framework is first exercised on an analytically guided one-dimensional force-transfer problem, then on two benchmarks: uniaxial compression of a monodisperse column and compaction of a polydisperse assembly. A systematic study charts how penalty stiffness, weight-function shape, mesh-to-particle size ratio, and inter-particle friction affect stress/strain transfer and convergence, yielding practical guidelines for robust, resolution-aware coupling across a range of mesh–particle ratios and overlap thicknesses.

A compact, dimensionally consistent scaling for the penalty, ε =CE/(d Lc), is proposed, where E is an effective modulus, d a characteristic particle size, Lc the hybrid-zone thickness, and C accounts for nonidealities due to weighting, mapping, and engagement. Choosing C ≈ 10 reliably places the coupling in a high-fidelity regime over diverse mesh/particle ratios and overlap sizes. For the polydisperse system under cyclic loading, a calibrated elasto-plastic Drucker–Prager continuum reproduces DEM responses, capturing friction-dependent stiffening and the evolution of the lateral stress ratio K while maintaining stable overlap behaviour.

Industrial relevance is demonstrated through a large silo-discharge simulation in which flowing regions are resolved with DEM and quasi-static zones are represented by an elasto-plastic FEM. Hybrid predictions of vertical stress, lateral stress ratio, and grain-scale kinematics are benchmarked against a high-resolution DEM reference, confirming process-scale fidelity and indicating where continuum constitutive enrichment (e.g., dilatancy-evolving or nonlocal models) can further reduce residuals. By releasing the implementation through Kratos’s CoSimulation module, the work provides a flexible, open-source foundation for adaptive model switching, multi-rate co-simulation, uncertainty quantification, and multiphysics extensions, alongside new insight into the mechanics of DEM–FEM overlap zones.