Dynamic local remeshing for elastoplastic simulation

Abstract

Figure 1: An elastoplastic substance slowly drips from a horizontal surface. A dynamic meshing algorithm refines the drop while maintaining high-quality tetrahedra. At the narrowest part of the tendril, the mesher creates small, anisotropic tetrahedra where the strain gradient is anisotropic, so that a modest number are adequate. Work hardening causes the tendril to become brittle, whereupon it fractures. At right, we animate a fine triangulated surface embedded in the mesh. AbstractWe propose a finite element simulation method that addresses the full range of material behavior, from purely elastic to highly plastic, for physical domains that are substantially reshaped by plastic flow, fracture, or large elastic deformations. To mitigate artificial plasticity, we maintain a simulation mesh in both the current state and the rest shape, and store plastic offsets only to represent the nonembeddable portion of the plastic deformation. To maintain high element quality in a tetrahedral mesh undergoing gross changes, we use a dynamic meshing algorithm that attempts to replace as few tetrahedra as possible, and thereby limits the visual artifacts and artificial diffusion that would otherwise be introduced by repeatedly remeshing the domain from scratch. Our dynamic mesher also locally refines and coarsens a mesh, and even creates anisotropic tetrahedra, wherever a simulation requests it. We illustrate these features with animations of elastic and plastic behavior, extreme deformations, and fracture.

Optimizing Voronoi Diagrams for Polygonal Finite Element Computations

“…These conventional elements are well established and allow for simple and efficient implementations. However, they require complex remeshing when it comes to adaptive refinement, merging, cutting, or fracturing, i.e., general topological changes of the simulation domain [26,27,46,45,8,44].…”

Resolution Scaling for Mass Spring Model Simulations

“…More information regarding surface remeshing can be found in the survey by Alliez et al [20]. Examples of using mesh refinement for volumetric objects include Debunne et al [9] or Wicke et al [8]. In this study, we also consider three-dimensional (3D) volumetric objects; however, our techniques are not adaptive.…”

“…FEM is used in a majority of applications where either physical correctness or clear error handling is required. Consequently, the attention of researchers dealing with model simplification of elastic objects has been focused on FEM based representations [4], [5], [8], [9]. To the best of our knowledge, this is the first study that addresses the simplification of volumetric MSMs.…”

Energy Conservation for the Simulation of Deformable Bodies

“…P Eres = P E new altitude − P E total This ensures that energy is conserved when altitude springs are added and removed from the simulation. As future work, it would be interesting to try to adapt this scheme to a method that handles remeshing, such as [28]. Figure 10 shows a simulation with energy conserving triangle altitude springs, and Figure 8 shows the extension of this method to energy conserving tetrahedron altitude springs.…”