Simple geometric model to describe self-folding of polymer sheets

Self-folding is the autonomous folding of two-dimensional shapes into three-dimensional forms in response to an external stimulus. This paper focuses on light-induced self-folding of prestrained polymer sheets patterned with black ink. The ink absorbs the light and the resulting heat induces the polymer beneath the ink to relax faster than the rest of the sheet. A simple geometric model captures both the folding angle and folding kinetics associated with this localized shrinkage. The model assumes that (1) the polymer in contact with the ink shrinks at a rate determined by the temporal temperature profile of the hinge surface; (2) the bottom of the sheet, which is cooler, does not shrink considerably; and (3) a linear gradient of strain relaxation exists across the film between these two extremes. Although there are more complex approaches for modeling folding, the appeal of this model is its simplicity and ease of use. Measurements of the macroscopic, thermally driven shrinkage behavior of the sheets help predict the kinetics of folding by determining how fast the top of the hinge shrinks as a function of temperature and time. These measurements also provide information about the temperature required to induce folding and offer indirect measurement of the glass transition temperature of the polymer that comprises the sheet.