Phase transition in granular systems

  • Vescovi, Dalila (Politecnico di Milano)

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Granular systems can behave like either fluids, meaning that they yield under shear stress, or like solids able to resist applied stresses without deforming. In the presence of force chains, the stress tensor has a rate-independent component, revealing a solid-like behaviour of jammed and shear-jammed granular systems. In the absence of a stable contact network spanning the entire domain, the granular material is unjammed and behaves like a fluid, with a rate-dependent stress tensor. Furthermore, if the anisotropy of the contact network is such that the force chains span the domain only along one direction, buckling is more likely and the granular material is termed to be in a fragile state. The goal of this work is to investigate the phase transition in unsteady, homogeneous flows of a collection of spheres, by discrete element numerical simulations. Two different unsteady problems are analysed: shearing and cooling. In a first set of simulations, constant-volume, homogeneous shear flows are considered, in which a constant shear rate is applied to static assemblies of spheres, previously compressed at given densities. Depending on its density, the granular system is expected to reach the final steady state in fluid, solid, or near-to-critical conditions. We observe that, during the transient, fluid-like and solid-like behaviour can be distinguished based on the fluctuations of the coordination number and the pressure: fluid-like systems are characterized by large fluctuations, due to the continuous destruction/re-building of multi-particles aggregations, whereas fluctuations are much smaller when a contact network spanning the entire domain develops in the granular material (solid-like behaviour). In the second set of simulations, after homogeneously shearing an initially marginally solid-like system, we stop shearing at different times and let the system relax and dissipate its fluctuation kinetic energy (cooling). We observe that, depending on the initial fraction of mechanically stable particles, the granular material at the beginning of cooling can be shear-jammed, fragile or unjammed. The initial state determines the subsequent evolution of the dense assembly into either an anisotropic solid, an isotropic or an anisotropic fluid, respectively. While anisotropic solids and isotropic fluids rapidly reach an apparent final steady configuration, the microstructure continues to evolve for anisotropic fluids.