Volume Conserving Finite Element Simulations of Deformable Models

We propose a numerical method for modeling highly deformable nonlinear incompressible solids that conserves the volume locally near each node in a finite element simulation. Our method works with arbitrary constitutive models, is applicable to both passive materials and active materials (e.g. muscles), and works with simple tetrahedra without the need for multiple quadrature points or stabilization techniques. Although simple linear tetrahedra typically suffer from locking when modeling incompressible materials, our method enforces incompressibility per node (in a one-ring), and we demonstrate that it is free from locking. Finally, we propose a novel method for treating both collisions and self-collisions as linear constraints during the incompressible solve, alleviating issues in enforcing multiple possibly conflicting constraints. CR Categories: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Physically based modeling