Simulating Viscoelastic & Elastoplastic Solids

Yu Fang, Minchen Li, Ming Gao, Chenfanfu Jiang from the University of Pennsylvania gave a little talk about their research on Simulation of Non-Equilibrated Viscoelastic and Elastoplastic Solids presented at SIGGRAPH 2019.

Introduction

Hi! We are from the Computer Graphics Group at the University of Pennsylvania:

• Yu Fang, UPenn 1st-year PhD student
• Minchen Li, UPenn 1st-year PhD student
• Ming Gao, UPenn Postdoc
• Chenfanfu Jiang, UPenn Assistant Professor

We devise new technologies in physics-based simulation for computer graphics, computational solid and fluid mechanics, and scientific computing to reform the visual effects, animation, and fabrication industry.

Here’re our recent projects (four technical papers that were presented on SIGGRAPH 2019):

• CD-MPM: Continuum Damage Material Point Methods for Dynamic Fracture Animation
• Silly Rubber: An Implicit Material Point Method for Simulating Non-equilibrated Viscoelastic and Elastoplastic Solids
• Decomposed Optimization Time Integrator for Large-Step Elastodynamics
• Efficient and Conservative Fluids Using Bidirectional Mapping

Research Paper

In this article, we’ll talk about the subject researched in the second paper (Silly Rubber).

By tuning parameters of the physical characteristics, we can produce both fluid-like and solid-like materials. For solid-like material, the object is able to slowly revert to the rest shape after large deformation.

ADMM & ADMM-MPM

ADMM has been explored in simulating pure elasticity phenomena. However, the convergence of ADMM is still a challenging problem that has not been solved perfectly yet, especially when we try to apply it on visco-plasticity effects, which is more difficult than the pure elasticity setting. Based on our observation, the convergence of ADMM highly depends on what constraint weighting is used in the solver. Thus, we come up with a stiffness enhanced weighting scheme that is aware of the evolution of the animation and succeeded to improve the convergence in many cases.

ADMM-MPM is an alternative formulation of the implicit MPM algorithm. It is more flexible compared to the traditional Newton method since the nonlinear elasticity and visco-plasticity return mappings are separated from global inertia updates into independent local updates, making the iteration process more efficient and tractable. In addition, ADMM-MPM only requires a few iterations to obtain visually realistic results.

The damping scheme can be easily implemented from existing MPM particle-grid transfer schemes to provide both numerically stable and physically realistic damping effects in MPM simulation.

Material Point Method

Material point method has already shown its versatile ability to simulate plenty of materials, like snow, sand, rigid, jello. It is promising to simulate all kinds of materials in one single unified scheme. For visco-plasticity effects that we are targeting in this paper, the hybrid particle-grid discretization already enables a simple and intuitive implementation based on return mapping. Combining with the ADMM operator splitting technique, we further simplify the complex coupling into multiple simple and concise algorithm substeps.

Where Can It Help?

This technology could be widely used in the film and game industry. It will likely to be integrated into 3D animation software like Houdini, Maya, Blender, etc.

Yu Fang, Minchen Li, Ming Gao, Chenfanfu Jiang, University of Pennsylvania

Interview conducted by Kirill Tokarev