Revealing the self-similarity of creases in thin films

Creases form on thin sheets as a result of stress singularities that occur during the folding or crumpling. This changes the geometric appearance as well as the mechanical response leading to a class of tunable structures that can display deformation patterns that are not possible in a flat sheet. The Miura-Ori pattern is an example where the folded sheet has a negative Poisson’s ratio and can bend to a saddle shape (negative gaussian curvature). Folding patterns are being utilized over a large variety of applications spanning from medical devices such as heart stents to space applications where thin membranes are folded to maximize stowage and easy deployment. Capturing the effects of a crease is important to correctly model the response of such applications.

A single crease can be idealized as a torque spring and hence can be characterized with two parameters: the equilibrium fold angle and the torque spring stiffness. When combined with the panel bending rigidity, we can accurately capture the macroscopic behavior of the creased sheet. We evaluate the current methods of estimating the torque stiffness which measures the variation of fold angle as a function of the crease moment. We compare the stiffness values from three different boundary conditions and discuss the best practices to minimize potential errors. Next, we introduce an alternate method to measure the torque stiffness directly from the force – extension data utilizing the self-similarity of the elastica combined with a torque spring. This method does not need to measure the crease moment or the angle which can significantly simplify the experimental setup.

Although the torque spring idealization assumes the crease to be a singular point, curvature changes over a finite length scale, which is in the order of the sheet thickness. We model the crease formation as an elastica that accounts for material plasticity, which provides an insight on the distribution of plastic curvatures that can quantify the crease length scale to its material properties and folding parameters.