Topology optimization of extreme mechanical metamaterials considering the anisotropy of additive manufactured parts

Additive manufacturing (AM) has the advantage of fabricating complex geometries designed by topology optimization. However, the layer-by-layer stacking of AM causes the anisotropic property of the manufactured parts, which is rarely considered in the topology optimization of metamaterials. Hence, this paper presents a new method for the topology optimization of metamaterials with anisotropic properties. First, the elastic moduli in different directions of anisotropic materials are introduced into the solid isotropic material with penalization interpolation function. Then, the effective elastic properties of anisotropic metamaterials are evaluated using the energy-based homogenization method, and the formulation of the topology optimization of anisotropic metamaterials is constructed, and it is iteratively solved by the method of moving asymptotes algorithm. Finally, several two-dimensional and three-dimensional numerical examples and a set of mechanical experiment are conducted to demonstrate the effectiveness of the proposed method.