In some embodiments, a variable stiffness structure is provided having constant stiffness material layers and variable modulus material layers arranged in alternating layers. The variable modulus material layers have a material with a changeable elastic modulus in response to an applied energy field so as to allow reversible coupling and decoupling of stress transfer between successive layers of the constant stiffness material layers to provide a change in a bending stiffness of the variable stiffness structure. The constant stiffness material layers may include segmented portions. The constant stiffness material layers may have segmented portions arranged such that successive layers of the plurality of constant stiffness material layers have overlapping segmented portions. The variable modulus material layers may have shaped structures, for example, corrugation, pillars, striations, tubular, or honeycomb configurations.