Multi-material topology optimization of structures infilled with conformal metamaterials

Topology optimization is being widely employed in designing metamaterial unit cells which can be utilized as core materials for structural components. In this paper, we carried out multi-material topology optimization using orthotropic metamaterials. After topology optimization, the microstructures of the metamaterials are mapped to the resulted irregular domains for each material phase, acting as infill. Different from the existing work, we proposed an alternative way of mapping the metamaterial microstructures to irregular domains by employing the conformal mapping theory. Conformal mapping is an angle-preserving Riemann mapping that preserves the local shape and can efficiently transform a rectangular unit cell to an irregular quadrilateral domain. Each group of metamaterials is bounded by a thin layer of material to guarantee structural connectivity between different microstructures and smooth external boundaries.