# 3D and 4D Printing of Multistable Structures
## 2 3D Printing of Mechanical Multistable Structures
### Mechanical Metamaterial  
A bistable element can be used as a unit structure to construct multistable mechanical metamaterials. Properly designed mechanical metamaterials can show unusual mechanical properties such as negative Poisson's ratio, negative stiffness, energy trapping, etc. [54; 55; 56; 57; 58; 59; 60]. For example, constrained tilted elastic beams can be used to construct multistable mechanical metamaterials (Figure 7a-f). While an axially compressed elastic beam only has a single stable state (Figure 7a), a constrained tilted beam with fixed and roller boundary conditions can hold another deformed stable state (Figure 7b). The force-displacement curve in Figure 7b shows that it can be used as a bistable element. The difference between E\({}_{\text{in}}\) and E\({}_{\text{out}}\) in the force-displacement curve is the amount of trapped energy in this bistable element (Figure 7b). Figure 7: **(a)** An axially compressed elastic beam does not show bistability. It fully recovers to its initial state when unloaded; **(b)** An constrained tilted elastic beam can show bistability and energy trapping (E\({}_{\text{in}}-\text{E}_{\text{out}}>0\)). The deformed tilted elastic beam can recover to its initial state when enough energy is applied; **(c)** Compression test of 3D-printed multistable mechanical metamaterials. The sequentially deformed structure maintains a deformed state even after unloading; **(d)** Measured force and displacement graph. The overall deformation tendency is independent of loading conditions; **(e)** Demonstration of multistable mechanical metamaterials as an energy absorber. A raw egg mounted on the multistable mechanical metamaterial survived when dropped from a height of 12.5 cm; **(f)** Measured acceleration-time curve of three different cases. The control sample was taped so that all beams were intentionally collapsed before the drop test. The snap-through sample shows snap-through behavior but not energy trapping. Multistable mechanical metamaterials show a significant decrease in acceleration (Adapted from [57]. Copyright (2015) John Wiley & Sons); **(g)** Examples of 3D multistable mechanical metamaterials (Adapted from [60]. Copyright (2016) John Wiley & Sons). Tilted beam bistable structures can be 3D-printed and have been used for multistable mechanical metamaterials. [PERSON] et al. fabricated multistable energy trapping structures via direct ink writing [57]. They printed a 4 \(\times\) 4 bistable structure using polydimethylsiloxane (PDMS), as shown in Figure 7c. When the fabricated multistable structure is uniaxially compressed, it undergoes snap-through four times because of four bistable layers along the compression direction. Figure 7d shows the measured force-displacement curve; four peaks correspond to the beginning of the snap-through. All peaks have the same magnitude because the structure consists of identical bistable layers. They also demonstrated that multistable metamaterials can be used as an energy absorber. As a proof-of-concept, they conducted a free-fall measurement of eggs. It is also compared to a control sample (taped) that does not show multistable behavior. An egg mounted on the multistable structure was unharmed and survived when it was dropped from the height (h) of 12.5 cm (Figure 7e). However, an egg on the control sample was broken because the control sample does not have the energy-absorbing capability. Figure 7f compares the acceleration-time graph for three cases: control sample, snap-through-only sample, and multistable sample. The control sample does not have an energy absorbing function and thus shows a high acceleration peak in a shortest time (blue curve). The snap-through-only sample shows a snap-through but without energy trapping. It still shows a reduced peak acceleration (green curve) compared to the control sample, due to the energy absorbing from the viscoelasticity of the material (not from the elastic energy trapping).