Comprehensive study on shape shifting behaviors in FDM-based 4D printing of bilayer structures

4D printing of flat self-bending structures, aka “hinges”, has raised a new standard in many fields. By using these hinges in certain parts of a 3D-printed flat structure, a complex 3D shape with potential multifunctional application can be achieved from that flat structure. However, controlling and predicting the shape-shifting behavior of these hinges need an understanding of the shape memory effect in the process of anisotropic 3D printing. This paper proposes a reasonable semi-empirical model to predict the final shape-shifting behavior and magnitude of the hinges by having Fused Deposition Modeling (FDM) process parameters including printing speed, lamina thickness, nozzle temperature as well as printing pattern. In order to develop the model, first, a constitutive model with these four process parameters was extracted for strain of an SMP homogeneous single layer structure using a fractional Zener model accompanied with Multiple Linear Regression (MLR) technique; then, a relation for shape-shifting behavior of bilayer 4D-printed structures was developed using Timoshenko’s constitutive equations for beam torsion and curvature. Model predictions were compared to the experimental data, and results predicted both shape-shifting behavior and magnitude of the hinges with good agreement. Finally, a flowchart was suggested to design and achieve the desired shape-shifting behavior.