Kirigami mechanics as stress relief by elastic charges

TL;DR

This paper introduces a geometric method using elastic charges to understand and predict stress relief mechanisms in perforated elastic sheets, validated through experiments and applicable to kirigami design.

Contribution

It develops a strain-dependent elastic charge approach to model buckling and stress relief in perforated sheets, offering a new design principle for stress management in elastic materials.

Findings

Strong softening of force response with curvature localization.

Wider frames buckle more easily than narrower ones for certain hole sizes.

Elastic image charges can guide kirigami design for stress relaxation.

Abstract

We develop a geometric approach to understand the mechanics of perforated thin elastic sheets, using the method of strain-dependent image elastic charges. This technique recognizes the buckling response of a hole under external load as a geometrically tuned mechanism of stress relief. We use a diagonally pulled square paper frame as a model system to quantitatively test and validate our approach. Specifically, we compare nonlinear force-extension curves and global displacement fields in theory and experiment. We find a strong softening of the force response accompanied by curvature localization at the inner corners of the buckled frame. Counterintuitively, though in complete agreement with our theory, for a range of intermediate hole sizes, wider frames are found to buckle more easily than narrower ones. Upon extending these ideas to many holes, we demonstrate that interacting elastic image charges can provide a useful kirigami design principle to selectively relax stresses in elastic materials.