  Kirigami metamaterials dramatically change their shape through a coordinated
motion of nearly rigid panels and flexible slits. Here, we study a model system
for mechanism-based planar kirigami featuring periodic patterns of
quadrilateral panels and rhombi slits, with the goal of predicting their
engineering scale response to a broad range of loads. We develop a generalized
continuum model based on the kirigami's effective (cell-averaged) nonlinear
deformation, along with its slit actuation and gradients thereof. The model
accounts for three sources of elasticity: a strong preference for the effective
fields to match those of a local mechanism, inter-panel stresses arising from
gradients in slit actuation, and distributed hinge bending. We provide a
finite-element formulation of this model and implement it using the commercial
software Abaqus. Simulations of the model agree quantitatively with experiments
across designs and loading conditions.
