Program multi-directional thermal expansion in a series of bending dominated mechanical metamaterials

Abstract

Most metamaterials based on the bi-material curved beam (BC) were designed through hinge joints and presented only a unidirectional programmable coefficient of thermal expansion (CTE). Here, by contrast, a series of mechanical metamaterials based on the beam BC are originally devised with fixed joints. Moreover, by integrating the triangular, quadrilateral and hexagon configurations with rotational symmetry, these metamaterials could exclusively program the CTE in multiple directions. The explicit expressions of the relative densities are theoretically established. It is shown that increasing the parameter L1/h and reduction of the angle θ is beneficial to achieve light weight performance in these metamaterials. Besides, the closed-form expressions of the CTE are also theoretically derived and verified through numerical modeling. The analysis confirms that the CTE of the metamaterial in multiple directions can be well programmed to be either positive or negative values by rationally selecting the material combination and geometrical parameters. The CTEs vary linearly with the parameters L1 and θ, while show the parabolic variation with parameter m. In addition, the coupling relationships between the CTE and relative density are revealed and provide a guideline to achieve the large positive or large negative CTEs as well as light weight simultaneously. This work originally devises and analyzes a series of metamaterials of light weight and multi-directional customized CTE for engineering applications.