Collision response analysis and fracture simulation of deformable objects for computer graphics

Computer Animation is a sub-field of computer graphics with an emphasis on the timedependent description of events of interest. It has been used in many disciplines such as entertainment, scientific visualization, industrial design, multimedia, etc. Modeling of deformable objects in a dynamic interaction andfor fracture process has been an active research topic in the past decade. The main objective of this thesis is to provide a new effective approach to address dynamic interaction and fracture simulation. With respect to dynamic interaction between deformable objects. this thesis proposes a new semi-explicit local collision response analysis (CRA) algorithm which is better than most previous approaches in three aspects: computational efficiency, accuracy and generality. The computational cost of the semi-explicit local CRA algorithm is guaranteed to be O(n) for each time step, which is especially desirable for the collision response analysis of complex systems. With the use of the Lagrange multiplier method, the semi-explicit local CRA dgorithm avoids shortcomings associated with the penalty method and provides an accurate description of detailed local deformation during a collision process. The generic geometric constraint and the Gauss-Seidel iteration for enforcing a Loading constraint such as the Coulomb friction law make the semiexplicit local CRA algorithm general enough to handle arbitrary oblique collisions. The experimental results indicate that the semi-explicit local CRA approach is capable of capturing all the key features during a collision of deformable objects and matches closely with the theoretical solution of a classic collision problem in solid mechanics. For fracture simulation, a new element-split method is proposed, which has a sounder mechanical basis than previous approaches in computer graphics and is more flexible so as to accommodate different material fracture criteria such that different failure patterns are obtained accordingly. Quantitative simulation results show that the element-split approach is consistent with the theoretical Mohr's circle analysis and the slip-Iine theory in plasticity. while quaiimive results indicate its visual effectiveness.