Lattice-based metamaterials and methods of use

A method for constructing a lattice-based polar metamaterial for elastic cloaking, the method comprising:

• identifying a background medium comprising a plurality of mass nodes coupled by connecting springs and having a conventional tensor in a virtual space, the plurality of mass nodes coupled by connecting springs and forming a virtual lattice;
• fixing a physical domain lattice comprising a plurality of mass nodes coupled by connecting springs forming a physical lattice, wherein the physical lattice comprises a concave polygonal void defining a cloaking void;
• transforming the virtual space into the physical domain with the concave polygonal void defining a cloaking void, and defining the transformation based on the geometry of the physical domain to give a transformation gradient;
• based on the defined transformation, mapping the mass nodes of the virtual space to new locations in the transformed physical space;
• coupling the mass nodes of the physical lattice in the physical space by adjusting the lengths of the connecting springs and adjusting the sizes of the mass nodes while maintaining the spring constants of the connecting springs and maintaining the mass of each mass node.