Simulating deformable models with anisotropic materials - Cai, Jianping (2016)
This research work is on dynamics simulation of deformable objects. We focus on the simulation of anisotropic materials, which is less exploited in existing research. To do this, it is essential to improve the physical realism of simulation, since many real-world objects have complex mechanical rather than isotropic properties. Both physically-based and geometrically-based approaches are studied, and contributions are made in modeling and control of anisotropic dynamics deformations. First, we studied transversely isotropic materials for the simulation of deformable objects with fibrous structures. In existing work, direction-dependent behaviors of transversely isotropic materials can only be achieved with an additional energy function which incorporates the material preferred direction. Such an additional energy term increases the computational complexity. We propose a fiber-field incorporated corotational finite element model (CLFEM) that works directly with a constitutive model of transversely isotropic material. A smooth fiber-field is used to establish the local frames for each element. The orientation information of each element is incorporated into the CLFEM model by adding local transformations onto each element of the stiffness matrix. With pre-computation, it adds no additional computational cost on the existing model during dynamics simulation. We further introduce deformation simulation for orthotropic materials. Technical innovations are made in several aspects: 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 designed for propagating the user-defined sparsely distributed frames into the entire object. The orthotropic frame-field is coupled with the CLFEM model to complete an orthotropic deformable model. Finally, we present an integrated real-time system for animation of skeletal characters with anisotropic tissues. Existing geometrically-based skinning techniques suffer from obvious volume distortion artifact, and they cannot produce secondary dynamic motions, such as jiggling effects. Physically-based skinning with FEM models has high computational cost that restricts its practical applications. To solve these problems, we developed a novel strain-based PBD framework for skeletal animation. It bridges the gap between geometric models and physically-based models, and achieves both efficient and physically-plausible performance. Natural secondary motion of soft tissues is produced. Anisotropic deformations are made possible with separately defined stretch and shear properties of the material, using the user-designed frame-field. Owing to the efficiency and stability of our proposed layered constraint solving scheme, we can achieve real-time performance, and the system is robust with large deformations and degenerate cases. Limitations of our system and directions of future work, such as self-collision constraint and two-way coupling of rigid and soft bodies for locomotion control, are also discussed.