Evaluation of Material Models Used in Multi-Material Topology Optimization
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We evaluate the behavior of several interpolations to perform density-based topology optimization among many lattice structures. The relevance of different non-standard mappings is compared to interpolating ten orthotropic microstructures with similar costs and densities. More precisely, the lattices (materials) are distributed in two different interpolation domains, namely, over the edges of a square domain and at the vertices of a non-orthogonal decagonal prism. In addition, the material properties are interpolated by using either a Lagrange polynomial, or Wachspress shape-functions. The performances are evaluated on a standard benchmark problem, i.e., the compliance minimization problem over an MBB beam. The results show that the use of an elaborated interpolation function or domain seems unnecessary for conducting multi-material topology optimization when using one family of micro-structures with similar geometric features.
