Efficient FEM simulation techniques for thixoviscoplastic flow problems

Abstract

This thesis is concerned with the numerical simulations of thixoviscoplastic (TVP) flow problems. As a nonlinear multifield two-way coupled problem, the analysis of thixoviscoplasticity in complex fluid processes would present a great challenge. Numerical simulations are conceived as economic and credible tools to replicate thixoviscoplastic phenomena in different flow circumstances. This thesis proceeds to provide efficient numerical methods and corresponding algorithmic tools to fulfil this goal. To start with, we generalized the standard FEM settings of Stokes equations, and proceeded with the well-posedness study of the problem to set the foundation for the approximate problem, and for the efficient solver. In the context of solver, we advantageously use the delicate symbiosis aspects of the problem settings for FEM approximations, and the algorithmic tools to develop a monolithic Newton-multigrid TVP solver. Most importantly, we used the numerical simulations of thixoviscoplastic flow problems to understand the complex phenomena of interplay between plasticity and thixotropy. We incorporated thixotropy in well-established academical benchmarks, namely channel flow and lid-driven cavity flow. In addition, we analyzed type of transitions, namely shear localization and shear banding in Couette devices. In the end, we used thixotropy in contraction configuration to highlight the importance of taking in consideration thixotropy of material rheology for an accurate flow simulations.