Geoffrey Irving, Craig Schroeder, Ronald Fedkiw
We propose a numerical method for modeling highly deformable nonlinear
incompressible solids that conserves the volume locally near
each node in a finite element mesh. Our method works with
arbitrary constitutive models, is applicable to both passive
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.
We correct errors in volume without introducing oscillations
by treating position and velocity in separate implicit solves.
Finally, we propose a novel method for treating both object
contact and self-contact as linear constraints during the
incompressible solve, alleviating issues in enforcing multiple
possibly conflicting constraints.
Available in the proceedings of SIGGRAPH 2007.