# 3D and 4D Printing of Multistable Structures
## 1 Introduction
Figure 3c shows a self-bending structure upon light illumination [32]. Figure 1: (**a**) Jet engine fabricated by 3D printing application; (**b**) 3D-printed jet engine parts. From left figure, there are fuel nozzle, high-pressure turbine nozzle, high-pressure turbine blade (Adapted from [7]. Copyright (2017) Elsevier); (**c**) Tilted view of SEM image of the 3D-printed optical lens using micro-stereolithography. Scale bar: 500 μm; (**d**) Top view of SEM image of the 3D-printed optical lens using micro-stereolithography. Scale bar: 500 μm; (**e**) Measured surface profile of the 3D-printed optical lens (Adapted from [13]. Copyright (2020) John Wiley & Sons). A bilayer structure was fabricated using multi-color SMP printing, where blue and yellow SMP fibers were printed in a transparent elastomer matrix. Blue or red light can selectively heat yellow or blue SMP fibers, and thus the 3D-printed multicolor composite can be deformed into different shapes depending on light color. Four-dimensional printing could be useful for a wide range of potential applications, in actuators, switches, sensors, and deployable structures [33; 34; 35]. Usually, 3D-printed components are static structures with fixed shapes and functions. One possible route to realize highly reconfigurable structures is to use mechanical multistability. It allows multiple stable configurations, and reversible switching between them is possible under proper mechanical  
Figure 3: (**a**) Three-dimensional printed hemispherical structure using liquid crystal elastomers (LCE). Due to the anisotropic arrangement of the LC molecules, the structure expands in the z-direction at 200 \({}^{\circ}\)C (Adapted from [30]. Copyright (2017) ACS Publications); (**b**) Transformation of initially flat flower structure made by hydrogel bilayer blooming in the water. It takes 40 min to fully bloom (Adapted from [31]. Copyright (2019) John Wiley & Sons); (**c**) Transformation of initially flat stretched structure that bends on blue LED illumination and recover to the initial state on red LED illumination (Adapted from [32]. Copyright (2020) Nature Publishing Group). Figure 2: Schematic of various 3D printing processes: stereolithography (SLA)/digital light projector (DLP), Polylet (or Material jetting), direct laser writing (DLW), fused deposition modeling (FDM), direct ink writing (DIW), selective laser sintering (SLS) (Adapted from [8]. Copyright (2020) De Gruyter). actions. Precisely controlled reconfiguration via multistability can bring many new breakthroughs to 3D printing. In fact, multistability exists even in nature. The Venus flytrap is one example (Figure 4a). The initially opened Venus flytrap leaf can abruptly snatch a worm by flipping the curvature of its inner structure. This abrupt motion, also called snap-through, originates from elastic bistability in the leaf [36]. Figure 4b shows the elastic potential energy diagram of such a bistable structure. It has two stable configurations that are separated by an energy barrier. The slope in the energy diagram indicates the force applied at a given displacement. Enough force should be applied to overcome this barrier and transform into the other stable state. Once passing the hill of the barrier, the bistable structure is deformed into another configuration automatically. In this way, bistable structures can induce a rapid, large-magnitude movement and thus can be used to simplify actuation and motion control. They can also be used as mechanical switches, because they do not require energy to maintain a stable state. Bistability can be realized, for example, in strained bilayers and origami-based structures (Figure 4c) [37; 38]. More complicated multistable structures can also be realized by combining basic units together (Figure 4d) [39]. These multistable structures can be engineered with many different design parameters. More advanced functionalities and enhanced controllability can also be obtained in 4D printing by adopting active materials in multistable structures.