Finite elements for thixotropic elasto-viscoplastic flows

This work aims at performing finite element approximations for entry flows of thixo- tropic elasto-viscoplastic fluids, using the structured fluid model introduced in de Souza Mendes (2011). The constitutive equation is based on a modification of the Oldroyd-B viscoelastic equa- tion, with variable viscosity and relaxation time. According to this model, both the relaxation time and the viscosity are functions of a scalar parameter – denoted herein by structure parame- ter – that deals with microscopic changes in the material microstructure. All results are obtained using a four-field GLS-type method, aiming at determining the accurate morphology and position of the unyielded regions in entry flows of elasto-viscoplastic fluids through an one-to-four sudden expansion.