Mechanical metamaterials are elastic systems designed to have unconventional or novel mechanical properties. A common goal is to achieve prescribed shapes along with adaptive and programmable responses. Kirigami, the paper art form, provides a scalable technique to pattern material geometry and mechanics locally by appropriate arrays of holes and slits.
We developed a theoretical framework to address kirigami mechanics, using the notion of image elastic charges, in analogy with electrostatics. This naturally captures the geometric incompatibility induced by the presence of a hole in an elastic medium and intuitively explains experimental and numerical results. In addition, image elastic charges also provide design principles to engineer specific kirigami patterns to locally relax stresses in an elastic material. Extensions to nonlinear and thermal effects are currently underway.