# 3D and 4D Printing of Multistable Structures
## 3 4D Printing of Multistable Structures  
### Heat-Responsive Structures  
Four-dimensional printing can be implemented by printing smart materials. For example, SMPs can be employed as an active material in 4D printing. SMPs are smart materials that memorize a permanent shape. SMPs soften above the \(\mathrm{T_{g}}\) and allow reshaping. This temporary shape can be fixed by cooling back to room temperature (also called thermo-mechanical programming), where SMPs exhibit significant stiffness. An SMP can be deformed into multiple, arbitrary temporary shapes and return to a permanent shape again upon a proper external stimulus (heat or light). Because SMPs can be readily printed in conventional 3D printers, SMPs have been widely considered for 4D printing research. By adopting SMPs in multistable structures, more advanced functionalities and enhanced controllability can be realized. Multistability can also help in increasing the load bearing capacity and the magnitude of actuation force. For example, [PERSON] et al. devised a 3D-printed programmable actuator by combining a bistable structure with SMPs [35; 61]. Figure 8a shows a schematic of their bistable structure (von Mises truss). Trusses are made of rigid materials, while beams and joints are based on compliant mechanisms. It possesses two stable states (retracted and extended states) which can be combined together to form a 3D geometry (Figure 8b). This bistable structure can be actuated by SMP strips. These strips can be deformed to a contracted shape above \(\mathrm{T_{g}}\). When cooled back to room temperature, SMP strips maintain the deformed shape (programmed state) (Figure 8c). Due to the SMP recovery, the deformed SMP strips return to the original state again above the \(\mathrm{T_{g}}\) (activation). Figure 8d shows the bistable energy and force diagram. Once the SMP recovery force overcomes the energy barrier of the bistable structure, the unit actuator can snap-through to another stable state automatically. The recovery force can overcome the energy barrier by adjusting the thickness of SMP strips (Figure 8e). They also developed an autonomous actuator to realize soft, untethered robots for navigation and delivery [61]. Figure 8f shows a schematic of the proposed actuator. By attaching fins to the bistable structure, it can be actuated in water by a fin stroke. The large displacement of the bistable structure and the amplification of the actuation force helps the robot to swim in water. The programmed SMP actuator can return to its original state above \(\mathrm{T_{g}}\). When the SMP strip overcomes the energy barrier of the bistable structure, the robot can stroke its fins. Figure 8g shows images of the swimming robots. The robot can show sequential propulsion or directional motion by adjusting the thickness of SMP strips. [PERSON] et al. used a rotational bistable structure (Figure 6) to fabricate a smart thermal actuator [62]. Multistable structures can simplify actuation and motion control without complicated control systems. Figure 9a shows the design schematic of the structure. They employ two different digital SMPs (rigid and rubbery ones) to enable large-angle, thermal actuation in a controlled manner. The rigid beam has a fixed-pinned boundary, while the rubbery one has a fixed-fixed boundary. Two rigid beams define the overall bistability, while the rubbery beams act as a control knob. Those multistable structures do not require heating in the programming stage and this significantly simplifies the actuation procedure (Figure 9b,c). Figure 8: (**a**) Schematic of a 3D-printed von Mises bistable structure. The rigid bracket provides structural rigidity, while the flexible joints provide a rotational motion of the truss; (**b**) a 3D-printed bistable flat structure can be reconfigured to a 3D geometry via bistability (Adapted from [35].