Two-dimensional tessellations of alternating high-aspect ratio voids, such as ellipses, are known to induce auxetic behavior in engineering materials. An undesirable side effect of using high-aspect ratio shapes is an increased stress concentration at the ends of the voids. A novel rational process for designing auxetic tessellations with reduced stress concentration using Gielis’ Superformula and Nelder–Mead optimization is presented in this work. Results lead to an end-shape with a peak stress nearly 40% less than that of a comparable baseline circular stop-hole end-shape at the same porosity.

中文翻译：

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减少机械应力集中的低孔隙率拉胀镶嵌的设计

已知交替的高纵横比空隙（例如椭圆）的二维镶嵌会引起工程材料的拉胀行为。使用高纵横比形状的不良副作用是空隙末端的应力集中增加。在这项工作中，提出了一种使用 Gielis 的超级公式和 Nelder-Mead 优化设计具有降低应力集中的拉胀曲面细分的新颖合理过程。结果导致具有峰值应力的端部形状比相同孔隙率下的可比基线圆形止动孔端部形状的峰值应力小近 40%。