Modelling of shape memory polymer sheets that self-fold in response to localized heating.

We report a nonlinear finite element analysis (FEA) of the thermo-mechanical shrinking and self-folding behavior of pre-strained polystyrene polymer sheets. Self-folding is useful for actuation, packaging, and remote deployment of flat surfaces that convert to 3D objects in response to a stimulus such as heat. The proposed FEA model accounts for the viscoelastic recovery of pre-strained polystyrene sheets in response to localized heating on the surface of the polymer. Herein, the heat results from the localized absorption of light by ink patterned on the surface of the sheet. This localized delivery of heat results in a temperature gradient through the thickness of the sheet, and thus a gradient of strain recovery, or shrinkage, develops causing the polymer sheet to fold. This process transforms a 2D pattern into a 3D shape through an origami-like behavior. The FEA predictions indicate that shrinking and folding are sensitive to the thermo-mechanical history of the polymer during pre-straining. The model also shows that shrinkage does not vary linearly through the thickness of the polymer during folding due to the accumulation of mass in the hinged region. Counterintuitively, the maximum shrinkage does not occur at the patterned surface. Rather, it occurs considerably below the top surface of the polymer. This investigation provides a fundamental understanding of shrinking, self-folding dynamics, and bending angles, and provides design guidelines for origami shapes and structures.