Physically-based invertible deformation simulation of solid objects

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Xiang Feng and Wanggen Wan

Shanghai University, China

: J Comput Eng Inf Technol

Abstract

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With an increased computing capacity of computer, physically based simulation of deformable objects has gradually evolved into an important tool in many applications of computer graphics, including haptic, computer games, and virtual surgery. Among physically based simulation, large deformation simulation of solid objects has attracted many attentions. During large deformation simulation, especially interactive simulation, element inversion may arise. In this case, standard finite element methods and mass-spring systems are not suitable because they are not able to generate elastic internal forces to recover from the inversion. This presentation will describe a method for invertible deformation of solid objects. We derive internal forces and stiffness matrix of invertible isotropic hyper-elastic material from the energy density function. This method can be applied to arbitrary isotropic hyper-elastic material when the energy density function of deformable model is given in terms of strain invariants. In order to achieve realistic deformation, volume preservation capacity is always pursued as an important property in physically based deformation simulation. We will discuss about the volume preservation capacity of three popular invertible materials: Saint-Venant Kirchhoff material, Neo-Hookean material and Mooney-Rivlin material from the perspective of the volume term in the energy density function. We will demonstrate how the volume preservation capacity of these three materials changes with their material parameters, such as Lame coefficients and Poisson’s ratio. Since the process of solving the new positions of mesh object can be transferred to independently solving the displacement of each vertex from the motion equilibrium equation at each time step, it enables us to utilize CPU multithread method to speed up the calculations. We will also present a CPU multithread implementation of internal forces and stiffness matrix.

Biography

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