Average Vector Field Integration for St. Venant-Kirchhoff Deformable Models

We propose Average Vector Field (AVF) integration for simulation of deformable solids in physics-based animation. Our method achieves exact energy conservation for the St. Venant-Kirchhoff material without any correction steps or extra parameters. Exact energy conservation implies that our resulting animations 1) cannot explode and 2) do not suffer from numerical damping, which are two common problems with previous numerical integration techniques. Our method produces lively motion even with large time steps as typically used in physics-based animation. Our implicit update rules can be formulated as a minimization problem and solved in a similar way as optimization-based backward Euler, with only a mild computing overhead. Our approach also supports damping and collision response models, making it easy to deploy in practical computer animation pipelines.