Faculty / Organisational entity
- Continuum Mechanical Modeling of Dry Granular Systems: From Dilute Flow to Solid-Like Behavior (2014)
- In this thesis, we develop a granular hydrodynamic model which covers the three principal regimes observed in granular systems, i.e. the dilute flow, the dense flow and the solid-like regime. We start from a kinetic model valid at low density and extend its validity to the granular solid-like behavior. Analytical and numerical results show that this model reproduces a lot of complex phenomena like for instance slow viscoplastic motion, critical states and the pressure dip in sand piles. Finally we formulate a 1D version of the full model and develop a numerical method to solve it. We present two numerical examples, a filling simulation and the flow on an inclined plane where the three regimes are included.
- Constitutive models for static granular systems and focus to the Jiang-Liu hyperelastic law (2012)
- Granular systems in solid-like state exhibit properties like stiffness dependence on stress, dilatancy, yield or incremental non-linearity that can be described within the continuum mechanical framework. Different constitutive models have been proposed in the literature either based on relations between some components of the stress tensor or on a quasi-elastic description. After a brief description of these models, the hyperelastic law recently proposed by Jiang and Liu  will be investigated. In this framework, the stress-strain relation is derived from an elastic strain energy density where the stable proper- ties are linked to a Drucker-Prager yield criteria. Further, a numerical method based on the finite element discretization and Newton- Raphson iterations is presented to solve the force balance equation. The 2D numerical examples presented in this work show that the stress distributions can be computed not only for triangular domains, as previoulsy done in the literature, but also for more complex geometries. If the slope of the heap is greater than a critical value, numerical instabilities appear and no elastic solution can be found, as predicted by the theory. As main result, the dependence of the material parameter Xi on the maximum angle of repose is established.