  Manipulation of thin sheets by folding and cutting offers opportunity to
engineer structures with novel mechanical properties, and to prescribe complex
force-displacement relationships via material elasticity in combination with
the trajectory imposed by the fold topology. We study the mechanics of cellular
Kirigami that rotates upon compression, which we call Flexigami; the addition
of diagonal cuts to an equivalent closed cell permits its reversible collapse
without incurring significant tensile strains in its panels. Using
finite-element modeling and experiment we show how the mechanics of flexigami
is governed by the coupled rigidity of the panels and hinges and we design
flexigami to achieve reversible force response ranging from smooth
mono-stability to sharp bi-stability. We then demonstrate the use of flexigami
to construct laminates with multi-stable behavior, a rotary-linear boom
actuator, and self-deploying cells with activated hinges. Advanced digital
fabrication methods can enable the practical use of flexigami and other
metamaterials that share its underlying principles, for applications such as
morphing structures, soft robotics and medical devices.
