Spring-Bead Animation of Viscoelastic Materials

Nobuhiko Tamura, Norimichi Tsumura, Toshiya Nakaguchi, Yoichi Miyake
Chiba University, Chiba, Japan
IEEE Computer Graphics and Applications, 2007


   title={Spring-bead animation of viscoelastic materials},

   author={Tamura, N. and Nakaguchi, T. and Tsumura, N. and Miyake, Y.},

   journal={IEEE computer graphics and applications},



   publisher={IEEE Computer Society}


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In this article, we present a particle-based animation method for viscoelastic materials. All polymeric materials, such as proteins, fats, and plastics, have viscoelastic characteristics. Such materials are composed of intertwined polymer chains, which we modeled in the proposed simulation method as particle chains connected by a spring force based on Rouse’s spring-bead model. We modified Rouse’s spring-bead model by adding springs to form the connections between polymer chains for the simulation of various features of viscoelasticity. The collision force between particles is approximated by the gradient of the particles’ density field. Viscoelasticity is represented by the amount of twining between particle chains. We can change the viscoelasticity dynamically by cutting the connections or reducing the amount of twining between the polymer chains. We implemented our approach using Microsoft DirectX Shader Model 3.0. Although Goktekin, Bargteil, and O’Brien have previously proposed animation methods for viscoelastic fluids, the animation is based on continuous body calculation using the Navier-Stokes equation. Their method isn’t suitable for real-time computation. We propose an interactive animation scheme specifically for viscoelastic materials based on a particle system.
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