Transient motions of elasto-viscoplastic thixotropic materials subjected to an imposed stress field and to stress-based free-surface boundary conditions

In the present work, we present an approach to handle transient flows of elasto-viscoplastic thixotropic (EVPT) materials under the action of the gravity force field and subjected to free-surface boundary conditions that are stress-based. This kind of conditions are common in problems where the motion is unknown a priori, i.e. the motion is treated as a consequence while the forces are the cause. The model for the EVPT material employed is within the scope of a recently developed thermodynamic backbone for elasto-viscoplastic thixotropic materials. The finite difference Marker and Cell method is used to investigate effects of elasticity, thixotropy, and plasticity varying the Weissenberg number, the dimensionless thixotropic equilibrium time, and the yield number, respectively. The Cartesian Poiseuille flow is used to test the main features of the numerical scheme. The evolution in time of an initially square and fully-structured block is captured. The structure level and shape evolutions of the block reveal the capability of the present numerical approach to handle the complexity of the material and the free-surface motion.