Fracturing Rigid Materials

We propose a novel approach to fracturing (and denting) brittle materials. To avoid the computational burden imposed by the stringent time step restrictions of explicit methods or with solving nonlinear systems of equations for implicit methods, we treat the material as a fully rigid body in the limit of infinite stiffness. In addition to a triangulated surface mesh and level set volume for collisions, each rigid body is outfitted with a tetrahedral mesh upon which finite element analysis can be carried out to provide a stress map for fracture criteria. We demonstrate that the commonly used stress criteria can lead to arbitrary fracture (especially for stiff materials) and instead propose the notion of a time averaged stress directly into the FEM analysis. When objects fracture, the virtual node algorithm provides new triangle and tetrahedral meshes in a straightforward and robust fashion. Although each new rigid body can be rasterized to obtain a new level set, small shards can be difficult to accurately resolve. Therefore, we propose a novel collision handling technique for treating both rigid bodies and rigid body thin shells represented by only a triangle mesh.