Isotropic Quasi-Fluid Metamaterials Designed by Topology Optimization

Bi-mode artificial metamaterials have anisotropic mechanical properties, with the ratio of bulk modulus and shear modulus approaching an infinite value in ideal conditions. The microstructures of such metamaterials are currently mostly determined by parameter synthesis on the basis of existing heuristic configuration designs, which may considerably restrict their topologies and shapes. New octagon and hexagonal honeycomb bi-mode metamaterials (2D) are designed through a more systematic approach based on the independent point-wise interpolation method of topology optimization. The objective function is defined as a weighted combination of the bulk and shear moduli. By tuning the values of different weighted coefficients, the transition mechanism can be acquired from the regular microstructure to the bi-mode metamaterial with needle-like or double-cone rods. It is also found that simply increasing the volume fraction in the single material design cannot further improve the target performance, but introducing a small amount of hard material into the design domain can noticeably enhance the bulk modulus. One representative optimized microstructure is fabricated by 3D printing with stainless steel and polymer materials. Uniaxial quasi-static compression tests and finite element simulations reveal the layer-wise deformation modes of the bi-mode quasi-fluid metamaterial and its capacity to absorb external energy.