# 3D and 4D Printing of Multistable Structures
## 2 3D Printing of Mechanical Multistable Structures  
### Strained Layer  
One of the possible ways to realize mechanical multistability is the use of pre-strained layers [40; 41; 42; 43]. In 3D printing, a residual thermal stress often remains after printing and it can cause a distortion of printed structures. Therefore, it is usually considered as a harmful effect and should be minimized. However, this residual stress can also be utilized in a clever way to create multistable structures. For example, [PERSON] et al. fabricated bistable shell structures using selective laser sintering of metal powders [44]. A residual stress remains after the sintering process, and bistable shell structures can be formed (Figure 5a,b). The researchers printed cylindrical shells with varying curvatures. Figure 5a shows as-printed shapes, while Figure 5b shows another stable state. They also found that, when the pre-strain of the structure is too high, the structure becomes monostable (see the uppermost part in Figure 5a,b). They also confirmed this behavior with analytic modeling.  
[PERSON] et al. reported a pre-strained bilayer using fused deposition modeling (FDM) [45]. FDM 3D printing can create pre-strain along the printing direction and this can be used to encode proper strains in printed structures. Figure 5c shows a schematic of the printed structure and its behavior. They printed a thin plate using polylatic acid (PLA). The lower half of the plate was printed in the x direction, while the upper half of the plate was printed in the y direction. The printed structure remains flat after printing due to the high stiffness of PLA at room temperature. However, above the glass transition temperature (T\({}_{\text{g}}\)), the strain is released in the printed PLA plate. Then, a saddle-like bistable shape can be induced by the difference in the recovery direction between the upper and lower parts. This bistable shape can be flipped from upward to downward and vice versa. Above the T\({}_{\text{g}}\), the PLA plate can be deformed to arbitrary shapes too. When the structure is cooled down to room temperature, the temporary shape is fixed and does not show bistability. However, because of the shape memory  
Figure 5: (**a**) As-printed shape of cylindrical shells (Radii 5,6,7,8,9,10 mm after removal from the build plate); (**b**) Another stable state of 3D-printed cylindrical shells (Adapted from [44]. Copyright (2019) IOP Publishing); (**c**) Morphing behavior of a 3D-printed bilayer structure. It remains flat below T\({}_{\text{g}}\). The initially flat structure can be activated to a bistable structure above T\({}_{\text{g}}\). It can maintain an arbitrary shape due to the shape memory polymer characteristic; (**d**) Bistability can be expanded to multistability with proper design: multistable chair structure and bistable Venus flytrap; (**e**) Bilayer structure and gripper design utilizing iron/polylatic acid (PLA) filaments. The gripper is activated by a magnet (Adapted from [45]. Copyright (2020) Elsevier).  
properties of PLA [25; 46], when the structure is heated again above the \(\mathrm{T_{g}}\), it goes back to its permanent, bistable shape. In this way, temperature can be used as a switch for bistability. They expanded their idea to multistable structures (Figure 5d), and their 3D-printed bilayers were also applied to a gripper that operates under mechanical or magnetic actuation (Figure 5e).