Phenomenological models of viscoplastic, thixotropic, and granular materials

Abstract

A simple constitutive framework is used to review some phenomenological models for solid-fluid mixtures. Several successful descriptions of viscoplasticity assume that stress is proportional to a normalized deformation rate. The modulus in this constitutive equation evolves with time for thixotropic materials. This approach is used in most models based on scalar measures of structure. Such measures are determined by an evolution equation that is insensitive to rate reversals during shear flow. This behavior appears to be characteristic of inelastic materials such as an aqueous solution of bentonite. However, the same solution with guargum does not exhibit this response due to elasticity induced by the polymer. Models for granular media extend this constitutive framework by including compressibility effects and a scalar measure of particle interactions. The effect of fluid viscosity on particle interactions is incorporated using a mixture theory approach. Pipe flow of viscoplastic materials and shear flow of granular media are analyzed using boundary conditions that allow slip at solid surfaces.