Kirigami mechanics as stress relief by elastic charges

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.

arXiv comment6 pages, 4 figures; SI: 2 pages, 1 figure

References in corpus (10)

• Programmable Mechanical Metamaterials
• Buckling-Induced Kirigami
• Initial rigid response and softening transition of highly stretchable kirigami sheet materials
• Kirigami Actuators
• Conical defects in growing sheets
• Highly Stretchable MoS${}_2$ Kirigami
• Metric Description of Defects in Amorphous Materials
• Elastic interactions between 2D geometric defects
• Elastic Instability Triggered Pattern Formation
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Cited by in corpus (10)

• Forward and Inverse Design of Kirigami via Supervised Autoencoder
• Geometric charges and nonlinear elasticity of soft metamaterials
• Nonlinear mechanics of thin frames
• Thermal buckling and symmetry breaking in thin ribbons under compression
• On Local Kirigami Mechanics I: Isometric Conical Solutions
• Cutting holes in bistable folds
• On local kirigami mechanics II: Stretchable creased solutions
• Continuity and discontinuity of kirigami's high-extensibility transition: a statistical-physics viewpoint
• Bistability and equilibria of creased annular sheets and strips
• Elastic multipole method for describing linear deformation of infinite 2D solid structures with circular holes and inclusions