Nonlinear mechanics of thin frames

TL;DR

This paper investigates the nonlinear elastic behavior of thin frames with perforations, revealing how kirigami-inspired hole patterns influence mechanical properties and buckling, using elastic charge theory for analysis.

Contribution

It introduces the elastic charges technique to analyze the mechanics of perforated thin sheets, focusing on frames with sharp corners, advancing understanding of kirigami structures.

Findings

Holes generate elastic defects acting as sources of incompatibility.

Force-extension behavior of frames characterized by elastic charges.

Buckling transitions influenced by defect interactions.

Abstract

The dramatic effect kirigami, such as hole cutting, has on the elastic properties of thin sheets invites a study of the mechanics of thin elastic frames under an external load. Such frames can be thought of as modular elements needed to build any kirigami pattern. Here we develop the technique of elastic charges to address a variety of elastic problems involving thin sheets with perforations, focusing on frames with sharp corners. We find that holes generate elastic defects (partial disclinations) which act as sources of geometric incompatibility. Numerical and analytic studies are made of three different aspects of loaded frames - the deformed configuration itself, the effective mechanical properties in the form of force-extension curves and the buckling transition triggered by defects. This allows us to understand generic kirigami mechanics in terms of a set of force-dependent elastic charges with long-range interactions.