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Material interpolation schemes for unified topology and multi-material optimization


This paper presents two multi-material interpolation schemes as direct generalizations of the well-known SIMP and RAMP material interpolation schemes originally developed for isotropic mixtures of two isotropic material phases. The new interpolation schemes provide generally applicable interpolation schemes between an arbitrary number of pre-defined materials with given (anisotropic) properties. The method relies on a large number of sparse linear constraints to enforce the selection of at most one material in each design subdomain. Topology and multi-material optimization is formulated within a unified parametrization.

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This research is part of the project “Multimaterial design optimization of composite structures” sponsored by the Danish Research Council for Technology and Production Sciences (FTP), Grant no. 274-06-0443. This support is gratefully acknowledged.

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Correspondence to Christian Frier Hvejsel.

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Hvejsel, C.F., Lund, E. Material interpolation schemes for unified topology and multi-material optimization. Struct Multidisc Optim 43, 811–825 (2011).

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  • Material interpolation
  • Topology optimization
  • Multi-material parametrization
  • Composite materials