Curved creases redistribute global bending stiffness in corrugations: theory and experimentation

Abstract

Corrugations offer a convenient way to make thin, lightweight sheets into stiff structures. However, traditional, v-shaped corrugations made from straight creases result in highly anisotropic stiffness which leads to undesirable flexibility in some directions of loading. In this paper, we explore the bending stiffness of curved-crease corrugations with a planar midsurface—developable corrugations made by folding thin sheets about curves and without linerboard covers on the top or bottom. The curved-crease corrugations break symmetry in the pattern and can redistribute stiffness to resist bending deformations in multiple directions. To study these systems, we formulate a framework for predicting the bending stiffness of any planar-midsurface corrugation from its multiple geometric features at different scales. We use the framework to create two predictive methods that provide valuable insight into the global stiffness of corrugations without a detailed analysis. Results from these methods match well with experimental, three-point bending tests of five corrugation geometries made from polyester film. We found that corrugations with elliptical or parabolic curved-creases that intersect with one edge of the pattern are best at redistributing stiffness in multiple directions. While a straight-crease pattern has a stiffness of about 4 N/mm in one direction and about 0 N/mm in the other, a parabolic crease pattern has a stiffness of about 2.5 N/mm in both directions. These curved-crease corrugations can enable the self-assembly and fabrication of practical, stiff structures from simple, developable sheets.