Nonlinear mechanics of thin frames
arXiv:1801.08263 · doi:10.1103/PhysRevE.99.013002
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.
arXiv comment13 pages, 13 figures
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- On local kirigami mechanics II: Stretchable creased solutions
- Continuity and discontinuity of kirigami's high-extensibility transition: a statistical-physics viewpoint
- Geometric Theory of Mechanical Screening in two-dimensional solids
- 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