A Particle Method for Multiphase Mechanics Simulation

Author(s): Chang, Yi-Jui | Advisor(s): Eldredge, Jeff D | Abstract: Modeling the multiphase mechanics with coupled fluid and elastic material is important for many applications such as blood perfused soft tissues, wicking in porous medium. The liquid-solid interaction results in complicated effect on structure deformation and liquid transportation. The current study aims to develop high visual and physical fidelity simulations of multiphase mechanics, particularly within the context of soft tissue swelling, human injuries, medical treatments, the transport of blood through damaged tissue under bleeding or hemorrhaging conditions and droplet spreading on a fabric. The solid material is considered as a dynamic poro-hyperelastic material with liquid-filled voids. A biphasic formulation---effectively, a generalization of Darcy's law---is utilized, treating the phases as occupying fractions of the same volume. A Stokes-like friction force, a pressure that penalizes deviations from volume fractions summing to unity and the surface tension between multiphase interface, serve as the interaction force between solid and liquid phases. The resulting equations for both phases are discretized with the method of Smoothed Particle Hydrodynamics (SPH). The solver is validated separately on each phase and demonstrates good agreement with exact solutions in test problems. Simulations of oozing, hysteresis, swelling, drying and shrinkage, tissue fracturing and hemorrhage, liquid droplet spreading on a fabric are shown in this work. Besides the physical-based SPH solver, the technique called dynamic mode decomposition (DMD) from data science also applies on the results from SPH solver to extract the system features without any knowledge of governing equations, providing benefits such as data compression and efficient data manipulation, raising the potential of developing data-driven computational solver in the future.