PhD Thesis Defence Presentations - Pantelis Moschopoulos

In everyday life, we encounter materials that behave differently compared to common fluids like water or oil. One intriguing group includes "weird" fluids that do not flow spontaneously but only if we stress them sufficiently. If we examine these materials carefully, we can identify two distinct kinds of behavior: a solid-like when we do not exert adequate stress and a fluid-like when we exceed the material-specific stress threshold., which is termed the yield stress. The earlier investigations of yield stress materials suggested that elasticity and plasticity are mutually exclusive behaviors. As a result, two distinct material groups emerged: viscoelastic and viscoplastic. However, excluding elasticity could not explain many experimental observations with yield-stress materials. Thus, in this thesis, we instigate the effect of elasticity in modeling yield stress materials. To begin, the Penalized Augmented Lagrangian method, originally proposed by Dimakopoulos and colleagues, is enhanced to develop a more efficient and stabler finite element formulation for simulating ideal viscoplastic materials. Then, the thesis embarks on examining two distinct processes to investigate the effect of elasticity in yield stress materials. Firstly, we investigate the stretching of a sample material between coaxial disks, which forms and breaks filaments due to capillary effects. Secondly, we study the motion of a bubble that translates in a yield stress fluid, where steady-state shapes, velocities, and induced stresses are monitored. Novel numerical simulations are conducted for both processes, demonstrating that incorporating elasticity significantly improves the agreement between simulations and experimental observations. Beyond yield stress materials, the thesis extends its scope to viscoelastic solutions and we model the motion of a bubble rising inside a viscoelastic solution without assuming axial symmetry to allow the development of three-dimensional disturbances. This allows us to capture numerically the peculiar knife-edge bubble shape for the first time which does not exhibit axial symmetry anymore. Finally, we propose a new finite element formulation when two materials interact through a moving interface, either fluids or solids. We remedy the interface constraints, namely the continuity of velocities and stresses, using a single-node approach and the same continuous basis functions for the velocities in both materials. We incorporate the XFEM method to overcome the pressure jump across the interface. We assess the robustness of the new FE formulation in numerous 2D and 3D problems and compare our results with those of the literature.