A virtual node algorithm for changing mesh topology during simulation

Abstract

We propose a virtual node algorithm that allows material to separate along arbitrary (possibly branched) piecewise linear 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 real material and empty regions. The missing material is contained in another copy (or copies) of this element. 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 in a fashion consistent with the embedded geometry. This approach enables 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 CFL time step restrictions since they are embedded in well shaped larger elements. To enable robust simulation of embedded geometry, we propose new algorithms for handling rigid body and self collisions. 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.

CPU–GPU mixed implementation of virtual node method for real-time interactive cutting of deformable objects using OpenCL

“…The virtual node method was first proposed by Molino et al [22] in 2004. It had a limitation of four maximum cut pieces per tetrahedron.…”

“…We choose virtual node method [22,23] for cutting because it is the simplest to implement and has the least computational cost of all the cutting methods that do not affect numerical stability of deformation.…”

“…Virtual node method [22,23] embeds cut fragments in virtual elements, and the former are used for collision and rendering, while the latter are used for deformation. It does not affect stability of deformation.…”

Procedural models for cartoon cracks and fractures animations

“…Beside mass-spring systems, finite elements have also been widely used to simulate brittle fracture [15,16], ductile fracture [17], elasto-plastic materials and interactive fracture [18], and the fracture and deformation of voxelized surface meshes [19]. Other algorithms include generating fracture on elastic and plastic materials with the virtual node algorithm [20], a membrane-bending model for thin shell objects [21], and a meshless framework [22].…”

GPU-based physical cut in interactive haptic simulations

“…Graphical results of the method are convincing but the time requirements are too high for interactive simulations. A method to handle changes in mesh topology during simulation is proposed in [6]. The method creates copies of cut elements and splits the mass of the original element between them.…”