Modeling and simulation of elastoviscoplastic materials
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Date
2024-07-03
Authors
Μοσχόπουλος, Παντελής
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Abstract
In our everyday lives, we encounter groups of materials that do not obey the intuitive principles that we are familiar with based on our experience. One of these groups consists of “weird” fluids that do not flow spontaneously, as water or oil does, but only if we stress them sufficiently. Everybody squeezes the toothpaste from the tube or uses a knife to spread peanut butter evenly over their bread. 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. Thus, the property that differentiates them from common fluids, like water, is this stress threshold called 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. Moreover, numerous simulations using ideal viscoplastic models cannot capture the experiments. Thus, in this thesis, we instigate the effect of elasticity in modeling yield stress materials. Prior to that, we enhance the Penalized Augmented Lagrangian method, proposed by Dimakopoulos and coworkers, and develop a faster and stabler finite element formulation for the simulation of ideal viscoplastic material. Then, we embark on examining the difference in predictions between viscoplastic and elastoviscoplastic rheological models in two separate processes. In the first, we place a sample material between two coaxial disks, and suddenly, one is set into motion. The material stretches, creating a filament, which eventually thins and breaks because of capillarity. In the second, we place a bubble inside a yield stress fluid and monitor its steady-state shape, velocities, and induced stresses inside the material. We present novel numerical simulations of these processes and obtain good agreement with experiments in both cases when we introduce elasticity in the rheological modeling of yield stress materials. We stress that in the scenarios when elasticity is apparent, the ideal viscoplastic theory fails to give even qualitatively accurate predictions. In this thesis, we do not focus only on yield stress materials. 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. The bubble shape does not exhibit axial symmetry anymore. A sharp, two-dimensional, cusp-like tail forms in one view, but it changes and becomes a broad knife or a spade in the perpendicular one. 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.
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Keywords
Finite elements, Elastoviscoplastic materials, Filament stretching, Bubble rise