A Unified MPM Framework supporting Phase-field Models and Elastic-viscoplastic Phase Transition

Recent years have witnessed the rapid deployment of numerous physics-based modeling and simulation algorithms and techniques for fluids, solids, and their delicate coupling in computer animation. However, it still remains a challenging problem to model the complex elastic-viscoplastic (EVP) behaviors during fluid-solid phase transitions and facilitate their seamless interactions inside the same framework. In this paper, we propose a practical method capable of simulating granular flows, viscoplastic liquids, elastic-plastic solids, rigid bodies, and interacting with each other, to support novel phenomena all heavily involving realistic phase transitions, including dissolution, melting, cooling, expansion, shrinking, etc. At the physics level, we propose to combine and morph von Mises with Drucker-Prager and Cam-Clay yield models to establish a unified phase-field-driven EVP model, capable of describing the behaviors of granular, elastic, plastic, viscous materials, liquid, non-Newtonian fluids, and their smooth evolution. At the numerical level, we derive the discretization form of Cahn-Hilliard and Allen-Cahn equations with the material point method (MPM) to effectively track the phase-field evolution, so as to avoid explicit handling of the boundary conditions at the interface. At the application level, we design a novel heuristic strategy to control specialized behaviors via user-defined schemes, including chemical potential, density curve, etc. We exhibit a set of numerous experimental results consisting of challenging scenarios in order to validate the effectiveness and versatility of the new unified approach. This flexible and highly stable framework, founded upon the unified treatment and seamless coupling among various phases, and effective numerical discretization, has its unique advantage in animation creation towards novel phenomena heavily involving phase transitions with artistic creativity and guidance.