Integral-Based Material Point Method and Peridynamics Model for Animating Elastoplastic Material

Abstract

This paper exploits the use of Material Point Method (MPM) for graphical animation of elastoplastic materials and fracture. Previous partial derivative based MPM studies face challenges of underlying instability issues of particle distribution and the complexity of modeling discontinuities. This paper incorporates the state-based peridynamics structure with the MPM to alleviate these problems, which outweighs differential-based methods in both accuracy and stability. The deviatoric flow theory and a simple yield function are incorporated to animate plasticity. To model viscoelastic material, the constitutive model is developed with the linearized peridynamics theory which regards the current configuration as equilibrated and is only influenced by current incremental deformation. The peridynamics theory doesn't involve the deformation gradient, thus it is straightforward to handle the problem of cracking in our hybrid framework. To ease the implementation of the fracture divergence under MPM, two time integration methods are adopted to update the crack interface and continuous parts separately. Our work can create a wide range of material phenomenon including elasticity, plasticity, viscoelasticity and fracture. Our framework provides an attractive method for producing a variety of elastoplastic materials and fracture with visual realism and high stability.