Systematic engineering of components that employ metamaterials has expanded the mechanical design field in recent years. Yet, topology optimization remains a burdensome tool to utilize within a systematic engineering paradigm. In this work, the design of a metamaterial shear beam for a nonpneumatic wheel using a systematic, two-level design approach is discussed. A top-level design process is used to determine the geometric and effective material properties of the shear beam, and linking functions are established and validated for the design of a shear layer mesoscale structure. At the metamaterial design level, innovative homogenization and topology optimization methods are employed to determine a set of locally optimal geometric designs for the shear layer. One geometry, the auxetic honeycomb, is shown to be an optimum to the minimum volume topology optimization problem for materials subjected to pure shear boundary conditions. As such, this geometry is identified as a candidate for the shear layer.

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