Modeling and simulation of deformable objects using iterative updates of local positions

Abstract

This dissertation proposes modeling and simulation of deformable objects modeling using iterative updates of local positions. Green strain tensor is used to express the nonlinearity of the object and to control the desired behavior by material properties. The equation of the motion derived using the implicit Euler time integration method is converted into a governing equation that finds a solution that minimizes kinetic energy and strain energy. The governing equation is combined with a local iterative solver in a position-based dynamics framework. The Hessian matrix of the energy is approximated to use the information of the surrounding elements, which include the local node. A group computation is performed iteratively in one Newton iteration by setting a group of elements that do not share a node as a unit group. A group generation method is proposed in which energy can be monotonically reduced after every update to converge the local location solution efficiently. The proposed group generating method is performed before the simulation starts and creates a group until all nodes belong to a group. It is verified that the energy decreases monotonically whenever the local location solution is updated by the proposed group generating method. A modified Saint Venant-Kirchhoff model is used to handle large deformations, such as initial conditions with zero volume. Large deformations of the elastic body can be handled by detecting the inverted elements and computing the corresponding stresses of the modified Saint Venant-Kirchhoff model. The proposed method increases the computational efficiency by maintaining the size of the system matrix at 12 × 12 for the 3D volume model composed of tetrahedral elements. The difference in computational efficiency between the global method that does not approximate the Hessian matrix, and the proposed method is analyzed using floating-point operations. The proposed method has a computational efficiency of 126 and 2520 times compared to the global method when the number of nodes is 443 and 2087 for the bunny model, respectively. Parallel computation is implemented using the proposed group generating method. The parallel computation method is more efficient than the serial computation method when the number of nodes is more than 5000. Simulations are conducted to analyze the effect of approximation of the Hessian matrix and configuration of the group. The dynamic behaviors are compared using the proposed method with two different group ordering method, the global method and constraint-based method. The cube model is used to exclude the effect of the shape. The bunny model is used to evaluate performance when the model has an irregular arrangement of the element. Simulations are performed for each of the forces acting equally on all nodes, the forces causing axial deformation and moment. It is shown that the proposed method has more computational efficiency than the global method and the constraint-based method when the displacement of the node where the largest deformation occurs is used as an index and has the same accuracy. The simulation results show that the proposed method has higher stiffness than the global method regardless of the shape when the force acts on all nodes equally. The high frequency response is more prominent than the global method when the arbitrary force is applied.