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.

Stretchable fibers dissipate energy via the sequential fracturing of a metallic core held together by an elastomeric shell.

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.

The ability to change shape and control curvature in 3D structures starting from planar sheets can aid in assembly and add functionality to an object. Herein, we convert planar sheets of shape memory polymers (SMPs) into 3D objects with controllable curvature by dictating where the sheets shrink. Ink patterned on the surface of the sheet absorbs infrared (IR) light, resulting in localized heating, and the material shrinks locally wherever the temperature exceeds the activation temperature, T. We introduce two different mechanisms for controlling curvature within SMP sheets. The 'direct' mechanism uses localized shrinkage to induce curvature only in regions patterned with ink. The 'indirect' mechanism uses localized shrinkage in regions patterned with ink to induce curvature in neighboring regions without ink through a balance of internal stresses. Finite element analysis predicts the final shape of the polymer sheets with excellent qualitative agreement with experimental studies. Results from this study show that curvature can be controlled by the distribution and darkness of the ink pattern on the polymer sheet. Additionally, we utilize the direct and indirect curvature mechanisms to demonstrate the formation and actuation of gripper devices, which represent the potential utility of this approach.