A novel series of mechanical metamaterials with sign-changing coefficient of thermal expansion and their parameter analysis

•A series of novel structures with sign-changing properties of the coefficient of thermal expansion under heating and cooling are designed.•The analytical formula of their coefficients of thermal expansions are derived and verified by finite element method and parameter analysis are carried out.•The 2D structure is extended to three-dimensional form. Mechanical metamaterials show great application prospects in many fields such as aerospace, biomedical engineering, energy and transportation. The development of mechanical metamaterials with multiple peculiar properties is an important prerequisite for the development of intelligent sensors with excellent performance and the realization of multifunctional integration of structures. In this paper, a series of novel mechanical metamaterials are designed by adding rhomboid negative thermal expansion units into re-entrant hexagonal honeycombs, which have different signs of the coefficient of thermal expansion when the temperature rises or falls, and the analytical formula of their equivalent thermal expansion coefficient are derived. Parameter analysis and numerical simulations show that the metamaterial can realize the sign-changing properties of thermal expansion coefficient without entering the range of large geometric deformation under specific constituting materials and geometric parameters. In addition, this design idea is extended to three-dimensional form.