# 3D and 4D Printing of Multistable Structures
## 3 4D Printing of Multistable Structures
### Solvent-Responsive Structures  
[PERSON] et al. demonstrated logic operation using stimuli-responsive bistable structures [63]. The bistable structures were fabricated via the direct ink writing (DIW) of glass fiber (GF) embedded polydimethysiloxane (PDMS). The GF in a PDMS network can be aligned along the extrusion direction. PDMS can absorb non-polar solvents such as toluene. Aligned GFs prevent PDMS from swelling along the aligned direction, so that anisotropic swelling can be achieved. The schematic of the bistable element is shown in Figure 10a. The bistable structure consists of two beams with fixed and roller boundary  
Figure 9: (**a**) Schematic of a rotational bistable structure that can be activated by heat: similar to Figure 6c but two fixed-pinned beams were replaced by fixed-fixed rubbery beams; (**b**) Operating procedure of the fabricated thermal actuator. It is possible to program the structure at room temperature. The rotated structure (stable state B) at room temperature returns to its original stable state A at 75 \({}^{\circ}\)C; (**c**) Images of the thermal actuator in 75 \({}^{\circ}\)C water. It returns to the initial stable state in 0.8 s; (**d**) Activation time of the thermal actuator for different rubbery beam thicknesses; (**e**) Comparison of the shape memory force and barrier force. Thermal actuation occurs when the shape memory force is larger than the barrier force (Adapted from [62]. Copyright (2019) John Wiley & Sons). conditions (same as Figure 7c). In this configuration, the structure can have monostability or bistability upon geometrical parameters. They kept the tilted angle as 45\({}^{\circ}\), while they changed the slenderness ratio (w/L). There exists a certain slenderness ratio that divides monostability and bistability, which is called a bifurcation point. Figure 10b shows the energy diagram of the monostable and bistable structures. The energy of the monostable structure monotonically increases, while the energy of the bistable structure has a local minimum that corresponds to a second stable state. Figure 10c shows the geometric phase diagram together with the image of printed structures. Due to the anisotropic swelling, the slenderness ratio of the PDMS-GF bistable structure can be increased when it is immersed in toluene. Therefore, bistability can turn into monostability (see the blue curve). At the transition point, the transition speed is found to be very fast (less than 0.01 s). They also fabricated a bistable structure using hydrogels embedded with nanofibrilated cellulose (NFC). The NFC filler prevents hydrogels from isotropic swelling in water. The researchers fabricated a proof-of-concept module for logic operation by selectively activating bistable elements in a polar or non-polar solvent (Figure 10d). Combining the PDMS-GF (activated by toluene) and hydrogel-NFC (activated by water) bistable elements together, they could demonstrate AND, OR, and NAND logic gates. The AND gate consists of a hydrogel valve and a PDMS-GF bistable unit (both water and toluene required). The OR gate consists of a combined hydrogel-NFC and PDMS-GF bistable unit (either water or toluene required). The NAND gate is constructed by connecting two input bistable units to one  
Figure 10: **(a)** Schematic and image of a bistable structure; **(b)** Energy-displacement curve of the bistable structure (I) and the monostable structure (III). The inset images are configuration of beams at each stable state; **(c)** The initially bistable structure (I) can transform into a monostable structure (III) due to anisotropic beam swelling. There is a transition at the bifurcation point (II). Representative images are also shown at the bottom for the bistable state (red), the bifurcation point when actuation occurs (green), and the monostable state (black); **(d)** Logic gates fabricated by combining glass fiber embedded polydimethylsiloxane (PDMS-GF) (activated by toluene) and hydrogel-nanofibrilated cellulose (NFC) (activated by water) bistable structures (Adapted from [63].