Topological design for isotropic metamaterials using anisotropic material microstructures

Isotropic porous materials retain the same physical properties in any direction, regardless of the measurement direction. Therefore, mechanical metamaterials with isotropic properties are widely welcomed in engineering. Most of the existing artificial isotropic structures are composed of isotropic solid materials, and the design approach is singular and limited. There are numerous anisotropic materials in nature. Can we expand our approach by using anisotropic porous materials to obtain isotropic microstructures? This study answers this question, which focuses on the topological design of microstructures with multiple mechanical properties using given anisotropic materials. The considered mechanical properties include the maximum bulk modulus, shear modulus, equivalent elastic modulus, and multi-objective design. Smooth evolutionary method is adopted to find the final micro-topologies, with both the isotropic and volume fraction constraints imposed simultaneously. The macroscopic equivalent properties of the matrix materials and the obtained isotropic materials are evaluated using the homogenization method. Finally, the feasibility and effectiveness of the proposed method are verified by four numerical examples. Many interesting isotropic metamaterials are obtained, and some of the final structures are manufactured through 3D printing. This method can provide ideas for the design of other intelligent material microstructures with isotropic properties.