**2. Conceptual Design**

#### *2.1. Four-Dimensional Printing SMPs*

In this section, by understanding the shape-memory effect (SME) and FDM technology, the FG 4D printing concept for designing adaptive structures is introduced. Temperature-sensitive SMPs are a class of smart materials that can recover their original shape from a temporary programmed shape by heating. In the programming step, the material, initially in a strain/stress-free state at a temperature lower than the transition temperature (*T* < *Tg*), is firstly heated up to *Th* that is higher than transition temperature (*Tg* < *Th*). The material that is stable at the rubbery phase is then loaded and held fixed while being cooled down to *Tl*, which is less than the transition temperature (*Tl* < *Tg*). By removing the constraints, an inelastic strain, so-called prestrain, remains in the material and forms an irregular shape. The material is in a free-stress state at this stage. In the shape recovery process, the SMP is heated to recover its original shape, which is known as free strain recovery, and finally is cooled back to the low temperature.

FDM technology, as a filament-based material-extrusion 3D printing method, applies a similar thermomechanical process on the material during the fabrication. Therefore, it may have the potential to fabricate 4D SMP architectures along with the shape programming. Figure 1 depicts a schematic of FDM technology. At first, the material is heated inside the liquefier up to *T*ln, which is higher than the transition temperature (*Tg*), and then forced out of the nozzle and deposited onto the platform by the 4D printer head moving at speed *Sp*. In this step, the material is stretched similar to the heating–loading process of the SMP programming step that induces the prestrain. Therefore, the printing speed may affect the prestrain value. It would be sensible that greater speed produces more significant mechanical loading, hence inducing greater prestrain. After deposition, the printed layer cools and solidifies in the same manner as the cooling step in the programming process. After 4D printing the layer, the platform moves downward, and the 4D printer head proceeds to deposit the following layer. The programming procedure is finalized by mechanical unloading through removing the printed object from the build tray.

The thermal/surface boundary condition between the 4D-printed layers may affect the through-the-thickness prestrain regime. For instance, while the first printing layer is deposited on the stiff and rough build tray, other layers above it are laid on the previously printed polymeric layers. Therefore, material and surface conditions may affect bonding and stretching conditions, reducing the first layer prestrain. The first layer is expected to show the lowest prestrain value. By printing the second layer, the first layer is partially reheated, and this extra heat may reduce the prestrain value. In other words, the first layer and layers above it, except the end layer, are always reheated, and their prestrain value is decreased. Since the last layer never gets any extra heat, it is expected to have the maximum prestrain. It may be concluded that the prestrain regime may have an increasing trend through the thickness upward from the lower to the upper layer. This additive manufacturing process

can be called FG 4D printing as the material is programmed during the fabrication in the same manner as an FG material.

**Figure 1.** A schematic of the fused deposition modeling (FDM) method.
