Numerical coarsening of inhomogeneous elastic materials

ABSTRACT

We propose an approach for efficiently simulating elastic objects made of non-homogeneous, non-isotropic materials. Based on recent developments in homogenization theory, a methodology is introduced to approximate a deformable object made of arbitrary fine structures of various linear elastic materials with a dynamicallysimilar coarse model. This numerical coarsening of the material properties allows for simulation of fine, heterogeneous structures on very coarse grids while capturing the proper dynamics of the original dynamical system, thus saving orders of magnitude in computational time. Examples including inhomogeneous and/or anisotropic materials can be realistically simulated in realtime with a numerically-coarsened model made of a few mesh elements.

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INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
      I.3.5 Computational Geometry and Object Modeling

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
        G.1.10 Applications
      G.1.8 Partial Differential Equations

  I. Computing Methodologies
  I.6 SIMULATION AND MODELING
      I.6.5 Model Development
          Subjects: Modeling methodologies

General Terms:
Algorithms, Design, Measurement, Theory

Keywords:
homogenization, model coarsening, model reduction