A "mechanism-gradient" elasitic theory for planar kirigam

Recent reserach has shown that the soft modes of deformation in mechanism-based metamaterials, like origami and kirigami, are governed by an effective field theory (a PDE) linking the kinematics of their unit cell to the cell-averaged bulk deformation. Higher-order sources of elasticity dictate which solution to the effective theory will emerge under loads. Here we describe a "mechanism-gradient" theory that captures one-source of elasticity in planar kirigami (a model system for mechanism-based metamaterials). The theory is systematically derived from a general 2D hyperelasticity. A key ingredient to the derivation is the classical Flamant solution to isotropic linear elasticity, as it accounts for the "streching-like" distortion of the panels and hinges of soft modes in these system.