Mechanics of biomimetic 4D printed structures.

Recent progress in additive manufacturing and materials engineering has led to a surge of interest in shape-changing plate and shell-like structures. Such structures are typically printed in a planar configuration and, when exposed to an ambient stimulus such as heat or humidity, swell into a desired three-dimensional geometry. Viewed through the lens of differential geometry and elasticity, the application of the physical stimulus can be understood as a local change in the metric of a two dimensional surface embedded in three dimensions. To relieve the resulting elastic frustration, the structure will generally bend and buckle out-of-plane. Here, we propose a numerical approach to convert the discrete geometry of filament bilayers, associated with print paths of inks with given material properties, into continuous plates with inhomogeneous growth patterns and thicknesses. When subject to prescribed growth anisotropies, we can then follow the evolution of the shapes into their final form. We show that our results provide a good correspondence between experiments and simulations, and lead to a framework for the prediction and design of shape-changing structures.