Negative thermal expansion mechanical metamaterial using the swastika shape

Abstract

Materials and structures operating under thermal fluctuation encounter thermal expansion and/or thermal stresses, which require components that allow expansion compensation in certain directions and zero expansion in other directions. A 2D mechanical metamaterial with negative thermal expansion and zero thermal expansion in the in-plane and out-of-plane directions, respectively, is established herein by inspiration from the swastika shape. The swastika units are rigid and are interconnected to each other by positioning the connecting materials, which possess high thermal expansion, at the inner surfaces of the swastika arms. In this way, thermal expansion of the connecting materials tends to draw the swastika units towards each other, thereby generating an overall thermal contraction. Theoretical results indicate that the negativity of the thermal expansion is enhanced by the size of the connecting materials, but suppressed by the size of the swastika units. The results also reveal that the connecting material thickness and the swastika arm length exert major roles while the connecting material length and the swastika arm width play minor roles in influencing the effective thermal expansion coefficient of the metamaterial. These observations offer solutions for quick coarse-tuning and slow fine-tuning of the metamaterial’s CTE. Although swastikas have cultural, religious, and even political connotations, the author would like to clarify that the swastika considered herein has been used purely for its geometric shape. The author does not intend to convey any cultural or ideological meaning by its use in this article.