Described is a deformable, variable-stiffness cellular structure. The cellular structure a group of unit cells with each unit cell having a cellular geometry. The group of unit cells are formed of a variable-stiffness composite material (VSM). The VSM has a first stiffness state and a second stiffness state. Additionally, the cellular structure has a first shape and a second shape, with a gradation of shapes between the first shape and second shape. The transition from the first shape to the second shape occurs through using an actuation signal to actuate the VSM to change the stiffness of the cellular structure, thereby allowing the cellular structure to be deformed from the first shape to the second shape, and any shape therebetween. The cellular structure can be locked in the second shape through actuating the VSM from the second stiffness state to the first stiffness state.