Design and study on the tailorable directional thermal expansion of dual-material planar metamaterial

Abstract

Current studies on tailoring the coefficient of thermal expansion of metamaterials focused on either complex bending-dominated lattice or the stretching-dominated lattice which transforms the spaces of triangle and tetrahedron. This paper proposes a kind of dual-material rectangular cell of tailorable thermal expansion, which reduces the complexities of design, calculation, and manufacture of lattice materials. The theoretical derivation using the matrix displacement method is adopted to study the thermal expansion properties of rectangular cell in the direction of height, the analytical expressions of coefficient of thermal expansion and optimization model are used to design the sizes of rectangular cell, and experimental verification is carried out. It is found that the middle cell of lattice had the same thermal expansion law as that of the unit cell. The rectangular cells of negative coefficient of thermal expansion −7 ppm/℃, zero coefficient of thermal expansion, and large positive coefficient of thermal expansion 36.2 ppm/℃ in the direction of height were realized, respectively. The consistency of theory, simulation, and experiment verifies that rectangular lattice material made of two kinds of common materials with a different coefficient of thermal expansions can achieve the design of coefficient of thermal expansion in the direction of height by choosing different material distribution and geometric parameters.