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The star-shaped auxetic structures with sharp reentrant corners are highly stressed in practice. In this article, a novel planar auxetic material is designed by introducing periodic cookie-shaped pattern to decrease the risk of structure failure. Then both auxetic and band gap properties are comprehensively investigated numerically. The results reveal that the stress level significantly decreases by an order of magnitude. Moreover, the designed structure can yield a large complete band gap in a much lower frequency region and has a good self-collimation effect. Finally, the parameter analysis allows one to tailor an auxetic phononic metamaterial with optimal acoustic and mechanical properties.

A novel planar auxetic phononic crystal with periodic cookie-shaped cellular microstructures