Fracturing deformable and rigid materials
Ronald P. Fedkiw, Zhaosheng Bao · 2006
In this thesis we have developed efficient methods for fracturing both deformable and stiff objects. They can be either volumetric bodies or infinitely thin shells. First, we propose a virtual node algorithm that allows material to separate along arbitrary paths through a mesh. The material within an element is fragmented by creating several replicas of the element and assigning a portion of real material to each replica. This results in elements that contain both some real material and empty regions. Our new virtual node algorithm automatically determines the number of replicas and the assignment of material to each. Moreover, it provides the degrees of freedom required to simulate the partially or fully fragmented material. This approach provides for the efficient simulation of complex geometry with a simple mesh, i.e. the geometry need not align itself with element boundaries. It also alleviates many shortcomings of traditional Lagrangian simulation techniques for meshes with changing topology. For example, slivers do not require small time step restrictions since they are embedded in well shaped larger elements. Consequently, using the virtual node algorithm, we are able to fracture deformable bodies without compromising stability. In addition, we present several mechanisms for influencing and controlling fracture with grain boundaries, prescoring, etc. We illustrate our method for both volumetric and thin-shell simulations. To enable robust simulation of embedded geometry, we also propose new algorithms for handling self collisions. Finally, we propose a novel approach to fracturing, denting and bending of 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.