Modelling of Bingham-like fluids with deformable core

We present here two extensions of the usual Bingham model in which we account for deformations in the region where the shear is below the threshold τo. In particular, we present two models that consider the material in the above region as a neo-Hookean solid or as a visco-elastic upper convected fluid. Both models are developed in the general 3-D framework of the natural configurations theory. After formulating the basic constitutive equations we focus on two 1-D problems: Shear flow driven by a constant stress and flow in a channel driven by a constant pressure gradient. For both the models, the resulting mathematical problems are free boundary problems involving parabolic and hyperbolic equations.