# 3D and 4D Printing of Multistable Structures
## 1 Introduction  
Three-dimensional (3D) printing, also called additive manufacturing, is a new paradigm in customized manufacturing. Compared to traditional subtractive manufacturing methods, 3D printing allows a bottom-up fabrication of complex 3D objects that are hard to create with conventional fabrication methods [1]. By using appropriate 3D printing techniques, various materials, such as metal powders, polymers, ceramics, and composites, can be printed in high resolution. It also reduces material waste during production. Therefore, 3D printing provides a cost-effective solution for prototyping, optimization, and customization. Because of these advantages, an increasing number of industries and sectors are adopting 3D printing [2; 3; 4; 5]. Figure 2 schematically explains various 3D printing processes. Stereolithography (SLA) uses photopolymerization to solidify photocurable liquids and create 3D structures. Photopolymers are cured by laser light, and the exposed portion of the polymers hardens. After each laser pass, the build plate moves down slightly until the 3D structure is completed. This idea was first introduced in 1984 [6] and, since then, many other 3D printing techniques have been invented. Digital light processing (DLP) is similar to SLA, but it can expose an entire layer at once using a projector, thus enabling large printing volumes at high speed. Polylet 3D printing uses liquid photopolymers that are dropped from a nozzle and cured layer-by-layer with ultraviolet (UV) light. Multi-material 3D printing can be readily realized in this method (but usually at a high cost). Direct laser writing (DLW) uses ultrafast laser pulses to induce nonlinear multi-photon absorption in a small laser spot and increase the resolution down to the sub-micrometer scale. Fused deposition modeling (FDM) is based on material extrusion, where thermoplastic materials are melted and extruded through a nozzle. After extrusion, thermoplastic materials are solidified again and piled up to form successive object layers. It is widely used in either low-cost 3D printers or professional 3D printers, but it often results in low surface quality. In direct ink writing (DIW), inks flow through a syringe nozzle because of their low viscosity with applied shear stress. After printing, the structure maintains its 3D shape owing to the high viscosity of inks in the absence of shear stress. Metal powders and ceramic powders can be 3D-printed via selective laser sintering (SLS). The powder is sintered by a high-power laser and piled up layer-by-layer to form metal or ceramic 3D structures. A few examples of 3D-printed components are shown in Figure 1: 3D-printed jet engine parts [7] (Figure 1a,b) and customized micro-lens (Figure 1c-e) [8; 9; 10; 11; 12; 13]. Four-dimensional (4D) printing adds active, responsive functions to 3D-printed structures. The 4D printing concept was first introduced by [PERSON] et al. in 2013 [14; 15]. They demonstrated a 3D-printed rod structure that automatically transformed into a predesigned 3D geometry when immersed in water. Four-dimensional printing is often realized by printing smart materials, such as liquid crystal elastomers (LCE) [16; 17; 18], hydrogels [19; 20; 21], and shape memory polymers (SMP) [22; 23; 24]. Such structures can respond to environmental stimuli. In this sense, 4D-printed structures are also called programmable matter, where a response can be programmed into materials via structural and compositional design. In 4D printing, 3D-printed structures can be transformed in shape in response to external stimuli, such as heat [25], water [26], light [27; 28], and pH [29]. Figure 3 shows several examples for 4D printing of smart materials. Figure 3a shows a 4D-printed hemispherical shell, made of LCE [30]. Owing to the reversible arrangement of liquid crystal molecules at different temperatures, shape morphing occurs in a pre-determined way. Figure 3b shows a gripper made of hydrogels [31]. Due to different swelling ratios between upper and lower layers, it can be bent when immersed in water.