Cellular solids with tunable positive or negative thermal expansion of unbounded magnitude

Material microstructures are presented with a coefficient of thermal expansion larger in magnitude than that of either constituent. Thermal expansion can be large positive, zero, or large negative. Three-dimensional lattices with void space exceed two-phase bounds but obey three-phase bounds; lattices and normal materials have a trend of expansion decreasing with modulus. Two-phase composites with a negative stiffness phase exceed bounds that assume positive strain energy density. The author determined Young’s modulus and its relation to thermal expansion. Behavior of these composites is compared with that of homogeneous solids in expansion-modulus maps.