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

• Applied computing

  • Physical sciences and engineering

    • Mathematics and statistics

• Computing methodologies

  • Computer graphics

    • Shape modeling

  • Modeling and simulation

    • Model development and analysis

      • Modeling methodologies

• Mathematics of computing

  • Mathematical analysis

    • Differential equations

      • Partial differential equations

    • Numerical analysis

• Theory of computation

  • Randomness, geometry and discrete structures

    • Computational geometry