Design of low-porosity auxetic tessellations with reduced mechanical stress concentrations

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.