A Method for Physics-based Dynamic Deformation with St. Venant Kirchhoff Elasticity and Implicit Newmark Integrator

摘要

In this paper, we present a method for physics-based dynamic deformation simulation of 3D object. In interactive large deformation, linear elasticity model would typically suffer from linear exaggeration distortion, and the divergence of explicit integrator always makes the dynamic deformation completely collapse as simulation time moves forward. We use St. Venant Kirchhoff elasticity to define a linear relationship between second Piola-Kirchhoff stress tensor and Green-Lagrange strain tensor, further to derive quadratic internal elastic force with respect to deformation vector. Under specified constrained conditions and initial conditions of 3D deformable object, a motion equilibrium equation system is built with Finite Element Method discretization between the internal forces and typically interactive external force. Implicit Newmark integrator is employed to solve for deformation vector in the dynamic motion equilibrium equation. Contrastive experiments with deformable models demonstrate the superiority and effectiveness of the method in realistically rendering the interactive deformation of 3D object.