Stable Anisotropic Materials

The Finite Element Method (FEM) is commonly used to simulate isotropic deformable objects in computer graphics. Several applications (wood, plants, muscles) require modeling the directional dependence of the material elastic properties in three orthogonal directions. We investigate linear orthotropic materials, a special class of linear anisotropic materials where the shear stresses are decoupled from normal stresses, as well as general linear (non-orthotropic) anisotropic materials. Orthotropic materials generalize transversely isotropic materials, by exhibiting different stiffnesses in three orthogonal directions. Orthotropic materials are, however, parameterized by nine values that are difficult to tune in practice, as poorly adjusted settings easily lead to simulation instabilities. We present a user-friendly approach to setting these parameters that is guaranteed to be stable. Our approach is intuitive as it extends the familiar intuition known from isotropic materials. Similarly to linear orthotropic materials, we also derive a stability condition for a subset of general linear anisotropic materials, and give intuitive approaches to tuning them. In order to simulate large deformations, we augment linear corotational FEM simulations with our orthotropic and general anisotropic materials.