Remeshing-Free Graph-Based Finite Element Method for Ductile and Brittle Fracture

This paper presents a remeshing-free, graph-based finite element method (FEM) for simulating ductile and brittle fracture. Since fracture produces new mesh fragments and introduces additional degrees of freedom in the system dynamics, existing FEM based methods suffer from an explosion in computational cost as the system matrix size increases. Our model develops an algorithm for modelling fracture on the graph induced in a volumetric mesh with tetrahedral elements, by its vertices and edges. In order to initialize and propagate fracture, We simply relabel the edges of the graph using a damage variable, and control the diffusion of fracture inside the object by varying the support of a damage kernel. We present the reformulated system dynamics for this relabeled graph that allows us to simulate fracture in a FEM setting, without changing the size of system dynamics matrix of the mesh. This makes our computational method remeshing-free and scalable to high-resolution meshes. The fracture surface has to be reconstructed explicitly for visualization purposes only. We evaluate our algorithm extensively on a variety of brittle and ductile materials and compare its features with other state of the art methods. We simulate standard laboratory experiments from structural mechanics and compare the results visually and quantitatively with real-world experiments performed on physical material samples. We also present results evaluating the performance of our method, and show that our techniques offer stability and speed that is unmatched in current literature.