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

Abstract

In the present work, we present an approach to handle transient flows of elastoviscoplastic 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 elastoviscoplastic 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.

The “avalanche effect” of an elasto-viscoplastic thixotropic material on an inclined plane

“…This investigation was conducted by using a finite difference formulation recently proposed in [28] . In summary, the incompressible unsteady Navier-Stokes equations were solved via projection method applying the Crank-Nicolson/Adam-Bashforth scheme to time-discretize the momentum equation while the constitutive equation for the non-Newtonian tensor was treated by the second order Runge-Kutta method.…”

“…The mathematical formulation is the same as the one presented in [28] and hence, we repeat here its dimensionless form for the purpose of being self-contained.…”

“…It is worth noticing that different functions could have been adopted in the place of the chosen one for ζ ( ˙ γ eq ) as discussed by Oishi et al [28] . This function transforms a model conceived to capture the behavior of a yield-stress material into a model for apparent-yield-stress fluids.…”

“…The finite difference numerical scheme employed to study the transient motions of an elasto-viscoplastic thixotropic material has been presented by Oishi et al [28] . Thus, the solution procedure, assuming that at time t = t n the total tensor σ, the structure parameter λ and the markers positions x are known, can be summarized using the following steps: In the first step of the algorithm, the non-linear equation 14is solved by a hybrid bisection and Newton-Raphson method.…”

“…In the present work we study the avalanche effect problem representing the material by an elasto-viscoplastic thixotropic model that was recently developed in a series of papers [11,[24][25][26][27] . The transient numerical solution is provided through the finite difference scheme, as recently performed by Oishi et al [28] . This numerical framework combines the MAC method with front-tracking for describing the free surface boundary condition in the presence of moving fluid interface.…”