Elastocapillary kirigami

Kirigami--the ancient Japanese art of paper cutting--inspired a myriad of applications in different fields and across multiple scales. It has been found to be of special relevance to applications in reconfigurable structures (e.g., large deployable structures) and microstructures (e.g., stretchable graphene sheets). Indeed, careful tailoring of cut patterns in thin elastic sheets results in structures with interesting non-linear macroscopic responses emerging from local out-of-plane buckling [1,2]. The rise interest in kirigami, combined with the emergence of recent technological developments in manufacturing techniques of fluid-like soft materials, has ushered in a new generation of industrial applications and motivated this work on elastocapillary kirigami. Using the mean-field formulation, we study the interaction of a thin elastic sheet of kirigami with a fluid substrate [3]. Within this framework, we classify the critical behaviour of linear-cut kirigami over a fluid substrate with respect to symmetry considerations at the level of the unit cell. The analysis reveals that the anti-symmetric post-buckling configuration displays a discontinuous (first order) phase transition with respect to imposed normalised displacement; which suggests phase localisation as the individual cell gets trapped in a meta-stable state and the subsequent phase propagation through kirigami structures. In contrast to this, the symmetric post-buckling configuration deforms continuously via a second order phase transition; which suggests a continuous phase transition. The theoretical analysis is supported by a body of experiential work confirming the existence of buckling localisation and its subsequent propagation in linear-cut kirigami.