Topological damping materials and methods thereof

A metamaterial comprising a plurality of unit cells, wherein each unit cell comprises:

• a plurality of cell walls defining an inner volume, wherein the plurality of cell walls comprises:
• a first horizontal wall extending along a first direction,
• a second horizontal wall disposed above the first horizontal wall and extending along a second direction that is parallel to the first direction,
• a first wall section,
• a second wall section,
• a third wall section, and
• a fourth wall section, wherein each of the first, second, third, and fourth wall sections are disposed between the first and second horizontal walls, wherein each of the first, second, third, and fourth wall sections comprises a first sloped wall, a second sloped wall, and an adjoining section disposed between the first and second sloped walls, and wherein the adjoining section is configured to allow the first and second sloped walls to be displaced along the normal direction and to be extended along a perpendicular direction;
• a first member disposed within the inner volume and comprising a first planar surface, wherein the first member extends from an inner surface of the first horizontal wall;
• a second member disposed within the inner volume and comprising a second planar surface, wherein the second member extends from an inner surface of the second horizontal wall, and wherein the second member comprises a plurality of stem sections, and wherein each stem section comprises a planar surface configured to interaction with a portion of the first planar surface of the first member;
• and
• an interacting joint comprising an interacting movement between the first and second planar surfaces upon displacement of one or more of the plurality of cell walls along the normal direction, wherein the interacting movement provides energy dissipation.