Modeling and dynamics simulation for deformable objects of orthotropic materials

摘要

Simulation of physically based deformable models is a hot topic in computer graphics. Most of the existing models focus on isotropic materials and some on transversely isotropic materials. We propose a modeling method for orthotropic materials, which exhibits different mechanical behaviors along three orthogonal directions. First, constraints for the strain energy density in linear elastic models are analyzed, and a positive-definite elasticity tensor is derived for an orthotropic material. Second, an orthotropic deformation controlling frame-field is conceptualized and a frame construction tool is developed for users to define the desired material properties. A quaternion Laplacian smoothing algorithm is proposed, and several user-defined rotation minimizing frames are propagated into the entire body of the deformable object, which forms a smooth frame-field. Third, the corotational linear FEM model coupled with the orthonormal frame-field is formulated to realize a dynamics system, which can deal with large deformations. All the algorithms have been implemented in a comprehensive modeling and simulation system, and a GUI is provided to design the orthotropic model. Experiments on real-time deformation simulation and analytical comparisons are presented.