Bistable auxetics

A building block of an auxetic metamaterial, the building block comprising:

• a rotating element centrally disposed within the building block and having three or more vertex points, the rotating element being rotatable about a center of rotation;
• three or more translating elements disposed around the rotating element, having a shape different than that of the rotating element, and pivotally connected thereto by hinges, each one of the translating elements being pivotally connected to a respective one of the vertex points of the rotating element by a corresponding hinge to permit relative rotation between the translating elements and the rotating element, the three or more translating elements being non-plastically and reversibly displaceable relative to the rotating element from a collapsed position of the building block to an expanded position of the building block upon application of a first load and non-plastically and reversibly deformable from the expanded position to the collapsed position upon application of a second load, the three or more translating elements being substantially non-rotatable from the collapsed position to the expanded position;
• and
• wherein the building block is in a first stable state in the collapsed position and in a second stable state in the expanded position, wherein the rotating element maintains a first fixed orientation relative to the three or more translating elements in the first stable state and maintains a second fixed orientation relative to the three or more translating elements in the second stable state such that, in the first stable state, the building block maintains the collapsed position after removal of the second load applied thereon and, in the second stable state, the building block maintains the expanded position after removal of the first load applied thereon, wherein, between the expanded position and the collapsed position, the building block moves toward a closest one of the expanded position and the collapsed position after removal of either of the first load and the second load applied on the building block, wherein translation of the translating elements in respective opposed directions away from the center of rotation of the rotating element causes rotation of the rotating element such that the building block deforms from the first stable state to the second stable state, and translation of the translating elements in respective opposed directions toward the center of rotation of the rotating element causes rotation of the rotating element such that the building block deforms from the second stable state to the first stable state.

A unit cell of an auxetic meta material, the unit cell comprising:

• a plurality of building blocks, each building block comprising:
• a rotating element centrally disposed within the building block and having three or more vertex points, the rotating element being rotatable about a center of rotation;
• three or more of translating elements disposed around the rotating element, having a shape different than that of the rotating element, and pivotally connected thereto by hinges, each one of the translating elements being pivotally connected to one of the vertex points of the rotating element by a corresponding hinge to permit relative rotation between the translating elements and the rotating element, the three or more translating elements being non-plastically and reversibly displaceable relative to the rotating element from a collapsed position of the building block to an expanded position of the building block upon application of a first load and non-plastically and reversibly deformable from the expanded position to the collapsed position upon application of a second load, the three or more translating elements being substantially non-rotatable from the collapsed position to the expanded position;
• and
• wherein the building block is in a first stable state in the collapsed position and in a second stable state in the expanded position, wherein the rotating element maintains a first fixed orientation relative to the three or more translating elements in the first stable state and maintains a second fixed orientation relative to the three or more translating elements in the second stable state such that, in the first stable state, the building block maintains the collapsed position after removal of the second load applied thereon and, in the second stable state, the building block maintains the expanded position after removal of the first load applied thereon, wherein, between the expanded position and the collapsed position, the building block moves toward a closest one of the expanded position and the collapsed position after removal of either of the first load and the second load applied on the building block, wherein translation of the translating elements in respective opposed directions away from the center of rotation of the rotating element causes rotation of the rotating element such that the building block deforms from the first stable state to the second stable state, and translation of the translating elements in respective opposed directions toward the center of rotation of the rotating element causes rotation of the rotating element such that the building block deforms from the second stable state to the first stable state;
• wherein two adjacent building blocks are at least connected to each other by connecting a first translating element of a first building block to a second translating element of a second building block.