The elastic perfectly plastic constitutive equation for yield stress fluids

We explore the use of an Elastic Perfectly Plastic (EPP) constitutive equation for the modelling of yield stress fluids. Contrary to many other models, stresses in the EPP model arise from elastic deformation rather than as a viscous effect. In this paper, the EPP model is coupled to a standard viscous treatment of the post-yield flow stresses to produce Bingham-like behaviour, and the timescale associated with the yielding mechanism is linked to material parameters. We also show that when the yield stress is much smaller than the elastic modulus, EPP and Bingham models can produce very similar flow fields in channel and contraction geometries. The EPP model is found to be significantly cheaper computationally in both geometries. Additionally, in the case of channel flow where analytical solutions exist, the EPP model is associated with a much smaller error than the regularised Bingham model.