Continuum Field Theory for the Deformations of Planar Kirigami
Abstract
Mechanical metamaterials exhibit exotic properties that emerge from the interactions of many nearly rigid building blocks. Determining these properties theoretically has remained an open challenge outside a few select examples. Here, for a large class of periodic and planar kirigami, we provide a coarsegraining rule linking the design of the panels and slits to the kirigami's macroscale deformations. The procedure gives a system of nonlinear partial differential equations expressing geometric compatibility of angle functions related to the motion of individual slits. Leveraging known solutions of the partial differential equations, we present an illuminating agreement between theory and experiment across kirigami designs. The results reveal a dichotomy of designs that deform with persistent versus decaying slit actuation, which we explain using the Poisson's ratio of the unit cell.
 Publication:

Physical Review Letters
 Pub Date:
 May 2022
 DOI:
 10.1103/PhysRevLett.128.208003
 arXiv:
 arXiv:2108.00336
 Bibcode:
 2022PhRvL.128t8003Z
 Keywords:

 Condensed Matter  Soft Condensed Matter;
 Mathematics  Analysis of PDEs
 EPrint:
 5 pages, 4 Figures and a supplement