Elastic continuum modeling of flexible planar kirigami metamaterials

Kirigami is increasingly being used in the design of complex devices across scales, from soft robots to aerospace structures. Kirigami metamaterials made by repeatedly cutting holes in elastic sheets exhibit exotic properties. In this talk, we will combine experiment and theory to establish a new paradigm for predicting the shape change of a kirigami metamaterial in response to loads. We first provide a coarse-graining rule linking the design of the kirigami cell to the macroscale deformations of metamaterials, which gives geometric compatibility as nonlinear partial differential equations. Next, we develop a continuum elastic model, which accounts for three sources of elasticity: a bulk term that introduces stress when the effective fields deviate from those of a local mechanism, a term that resists gradients in slit actuation, and a term that accounts for hinge bending. We also provide the corresponding finite element formulation and implement it using the commercial software Abaqus. Simulations of the model match experiments across designs and loading conditions. Our work provides a new perspective to model kirigami metamaterials with low computational cost.