Fast Remeshing-Free Methods for Complex Cutting and Fracture Simulation

Simulating complex cuts and fractures robustly and accurately benefits a broad spectrum of researchers. This includes rendering realistic and spectacular animations in computer graphics and interactive techniques, as well as conducting material strength analysis in industrial design and mechanical engineering. In this thesis, we develop a graph-based Finite Element Method (FEM) model that reformulates the hyper-elastic strain energy for fracture simulation and thus adds negligible computational overhead over a regular FEM. Our algorithm models fracture on the graph induced in a volumetric mesh with tetrahedral elements. We relabel the edges of the graph using a computed damage variable to initialize and propagate the fracture. Following that, we extend graph-based FEM to simulate dynamic fracture in anisotropic materials. We further enhance this model by developing novel probabilistic damage mechanics for modelling materials with impurities using a random graph-based formulation. We demonstrate how this formulation can be used by artists for directing and controlling fracture. Finally, we combine graph-based FEM with a Galerkin multigrid method to run fracture and cutting simulation at a real-time, interactive rate even for high-resolution meshes.