Anisotropic Rheology of Non-spherical Grains

Abstract

The flow of granular materials is the subject of various academic research and industrial applications. The rheology of granular materials spans from packing, sorting and transportation of the pharmaceuticals to the study of avalanche dynamics. The rheology of shape isotropic (spherical) materials has been studied extensively and successful constitutive stress response models are present in the literature. In most real-life applications the grains are shape anisotropic (ellipsoidal), and their rheological and mechanical response is more complex than spherical grains. The shape anisotropy of the grains brings the effect of the grain orientation to their response. Isotropic granular rheology models neglect the effect of the grain orientation and shape on the mechanical response of the system. This report proposes a novel continuum stress response model based on isotropic granular rheology and utilizes a kinematic continuum model to capture the effect of the grain orientation. The representation theorem has been used to obtain the full description of the novel isotopic tensor valued function of the tensor variable. Dissipation inequality applied as a guide during the construction of the continuum model. The model predictions showed good agreement with the available experimental results of the simple shear flow at the steady-state. To reveal the complete capabilities of the model, the 2-D simple shear flow was studied. The results indicated that the model well captured the nonmonotonic behaviour of the effective viscosity of the flow caused by the effect of grain shape and the orientation with two material parameters. This study revealed the future application potential of the proposed phenomenological model, and concluded as a successful step forward in understanding and modelling the complex character of the shape anisotropic granular materials.