Routes to program thermal expansion in three-dimensional lattice metamaterials built from tetrahedral building blocks

Abstract

Thermal expansion can be problematic in manifold applications that require thermal stability, yet it can also be purposely exploited to meet specific directional requirements of thermal deformation. Opportunities to tailor thermal expansion in architected materials exist, but design options that are stiff and provide full directional authority on thermal expansion are currently limited by the structural characteristics of existing concepts. In this work, we report routes to systematically engineer thermally responsive lattice materials that are built from dual-material tetrahedral units that are stiff and strong. Drawing from concepts of vector analysis, crystallography, and tessellation, a scheme is presented for three-dimensional lattices to program desired magnitude and spatial directionality, such as unidirectional, transverse isotropic, or isotropic, of thermal expansion. Demonstrations on thermal expansion and mechanical properties include theoretical, computational, and experimental studies of nine representative concepts, from tetrahedral building blocks to compound unit cells that can tessellate structurally efficient lattices with tunable magnitude and prescribed directionality of thermal expansion.