Multi-Scale Design of Meta-Materials With Offset Periodicity

Meta-materials are a class of artificial materials with a wide range of bulk properties that are different from the base material they are made of. The term meta-material in the context of this research refers to a continuous, heterogeneous structure with prescribed elastic properties. Such meta-materials are designed using Topology Optimization (TO). Tools like SIMP interpolation, mesh filtering and continuation methods are used to address the numerical issues with Topology Optimization. In a previous research [1], by offsetting meta-material layers by a half-width of the Unit Cell, an auxetic honeycomb-like geometry was obtained. This was the first time such a shape was observed as the result of Topology Optimization targeting the effective shear modulus using square Unit Cells. This was obtained while designing the shear beam of a non-pneumatic wheel. This research studies the design of meta-materials using offsets other than zero or half-widths. The same problem [1] was solved for different values of offset, and the obtained geometries and volume fractions are studied. It is concluded that it may be beneficial for designers to consider offsetting meta-material layers with offsets other than half-width, to design novel, potentially better performing structures.