Simulation and Visualization of Deformation with Anisotropic Materials

Physically based deformable models have been a hot topic in the computer graphics and visualization community. However, most of the implemented models work only for isotropic materials, leaving the more general anisotropic materials less studied. We look into the challenging issues in dynamics simulation and real time visualization for anisotropic materials, and present our theoretic and practical work along the way to provide an ultimate solution to deformation with such materials. First, our models are based on continuum mechanics and approximated by the Finite Element Method, and different approaches such as co rotated, invertible, and total Lagrangian explicit dynamics. Secondly, for controls of the deformation, we have focused on materials that have their own internal structures (fibers) that determine the dynamics behaviors. We propose a fibers incorporated deformable model that can approximate the anisotropic elastic material properties. The orientation information is combined into the existing deformable models by element transformations along the given directions, which provide a control of the desired deformation. Thirdly, constraints for the strain density in linear elastic models are analyzed, and a positive-definite elasticity tensor is derived for an anisotropic material. Fourthly, an orthotropic deformation controlling frame-field is conceptualized and the frame construction tool is developed for the user to define the desired material properties. A quaternion Laplacian smoothing algorithm is designed for propagating the rotation minimization frames into the entire object. And finally, the co rotational linear FEM model is coupled with the orthotropic frame-field to realize a dynamics system, which can deal with large anisotropic deformations.