Morphable active corrugate structure and aeronautical wings are provided herein including one or more skins or envelopes, and a sheet having independently actuable hinge domains attached to the one or more skins or envelopes and independently actuable facet domains, each of the hinge domains and facet domains configured with through-thickness differential expansion coefficients, wherein differential strains in at least one of the hinge domains or the facet domains cause the sheet to expand or contract along a flexible axis of the sheet, wherein the sheet is attached to the upper and lower skins at respective upper and lower of the hinge domains.