Fast and Stable Deformations Using the Mesh Intersection Algorithm

Abstract

In this research, the stability problem of explicit integration schemes in simulations of deformable objects is addressed. We present a method that makes it possible to simulate a volumetric mesh using the magnitude order of the limit time step provided by another optimal mesh. The volumetric object to simulate, represented by a surface mesh (made up of triangles), is extracted from an optimal volumetric mesh (e.g. a tetrahedralized cube). The optimal mesh is easily tetrahedralized and thus the overall quality can rarely be surpassed. The simulation of the intersection can be performed in a stable manner using the eXtended Finite Element Method (XFEM) which introduces discontinuities (e.g. cutting and dissection) while it maintains the original mesh configuration. The elements (tetrahedra) are classified and those that lie outside the surface mesh are fixed and neglected in the simulation. Interface elements (those that lie inside and outside the surface mesh) are dissected and only the volume part lying inside the surface mesh is simulated. The intersection is performed only once before starting the simulation. Using our approach, the meshing methods and mesh optimization strategies are avoided. Furthermore, our approach can be directly switched to implicit solvers. The proposed method is useful for designing simulations of deformable objects without meshing techniques.