Stable Simulations of Deformable Objects Using Explicit Integration

We present a new approach that deals with the stability limit of explicit integration schemes in simulations of deformable objects based on the finite element method. The underlying idea consists of using a large time step of a coarse tetrahedral mesh in any volumetric mesh that can be extracted from this initial mesh. This is performed by computing the intersection between two meshes: the volumetric mesh with a large time step (a tetrahedralized cube) and a triangular mesh that is the object to simulate. The mesh intersection is observed as cutting or dissecting the coarse mesh based on a given object´s surface mesh. This task can be performed by the co rotational extended Finite Element Method (XFEM) in a stable manner. The XFEM handles the dissections as discontinuities while maintaining the original mesh intact. Hence, the magnitude order of the largest time step is preserved. Elements lying outside the surface mesh are treated as fixed and thus are not considered in the simulation. The intersection method is computed only once before starting the simulation. Our approach is suitable for interactive applications with/without topological changes. Furthermore, our approach can be directly switched to implicit solvers. The proposed method is an important contribution for designing simulations of deformable objects without meshing techniques.