The Material Point Method for the Physics-Based Simulation of Solids and Fluids

OF THE DISSERTATION The Material Point Method for the Physics-Based Simulation of Solids and Fluids by Chenfanfu Jiang Doctor of Philosophy in Computer Science University of California, Los Angeles, 2015 Professor Demetri Terzopoulos, Co-chair Professor Joseph M. Teran, Co-chair Simulating fluids and solid materials undergoing large deformation remains an important and challenging problem in Computer Graphics. The dynamics of these materials usually involve dramatic topological changes and therefore require sophisticated numerical approaches to achieve sufficient accuracy and visual realism. This dissertation focuses on the Material Point Method (MPM) for simulating solids and fluids for use in computer animation, and it makes four major contributions: First, we introduce new MPM for simulating viscoelastic fluids, foams and sponges. We design our discretization from the upper convected derivative terms in the evolution of the left Cauchy-Green elastic strain tensor. We combine this with an Oldroyd-B model for plastic flow in a complex viscoelastic fluid. While the Oldroyd-B model is traditionally used for viscoelastic fluids, we show that its interpretation as a plastic flow naturally allows us to simulate a wide range of complex material behaviors. In order to do this, we provide a modification to the traditional Oldroyd-B model that guarantees volume preserving plastic flows. Our plasticity model is remarkably simple (foregoing the need for the singular value decomposition (SVD) of stresses or strains). We show that implicit time stepping can be achieved in a manner that enables high resolution