  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.
