A series of metamaterials exhibiting negative thermal expansion inspired by leaflet pattern in compound leaf

Abstract

The integrity of multifunctional materials will be the focal point and emphasis in material development when facing increasingly complex environments and stricter requirements. The present work initiates an inspired design and conducts a comprehensive analysis of thermo-stretching-dominated metamaterials with negative thermal expansion (NTE) to provide diverse options for multifunctional requirements. Inspired by leaflet patterns in compound leaf, nine NTE metamaterials, including five novel structures, are proposed by varying the number (2, 3, and 4) of struts with high coefficients of thermal expansion (CTE) based on the fork-shaped structures. Additionally, novel complete structures and hybrid versions of these metamaterials are proposed to enhance structural stiffness while preserving NTE properties through the construction of stable triangle microstructures. Theoretical analysis is employed to establish analytical models of CTE for these metamaterials, while the stiffness matrix method is used for efficient calculation of their effective stiffness, Poisson’s ratio, and strength, which is validated by numerical simulations. The angle θ emerges as a particularly significant parameter influencing these effective thermoelastic properties. Compared with other metamaterials, the present metamaterials exhibit slightly higher effective stiffness while maintaining NTE concurrently and can also achieve the maximal NTE characteristic. Comparisons between these metamaterials demonstrate their feasibility for multifunctional applications across diverse scenarios according to specific property requirements. The proposal of these novel metamaterials can provide more options to cater to diverse engineering requirements such as aerospace satellite structures, high-precision space telescope mirrors, constructional engineering, etc.