The meta-material design of the shear layer of a non-pneumatic wheel was completed using topology optimization. In order to reduce the hysteretic rolling loss, an elastic material is used and the shear layer microstructure is defined to achieve high compliance comparable to that offered by the elastomeric materials. To simulate the meta-material properties of the shear layer, the volume averaging analysis, instead of more popular homogenization methods, is used as the relative size of the shear layer places realistic manufacturing constraints on the size of unit cells used to generate the meta-material. In this design scenario the properties predicted by the homogenization methods are not accurate since the homogenization scaling assumptions are violated. A number of optimal designs are shown to have meta-material properties similar to those of the linear elastic properties of elastomers, making them good meta-material candidates for the shear layer of the non-pneumatic wheel.

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