Modeling Functionally Graded 4D Printed Shape Memory Polymers

A functionally graded material is characterized by spatially varying properties that depend on position within the structure. In addition to unit cell designs incorporating material gradients, shape memory materials can be exploited by locally programming their shape recovery behavior through controlled adjustment of the printing parameters in a fused filament fabrication (FFF) process. Predicting the resulting shape change and establishing a link between print parameters and the effective material properties has been addressed in the literature. However, the definition of suitable design parameters that can serve as targets for optimization has not yet been fully realized. Additional challenges arise when attempting to connect the G‑code to a predictive simulation capable of capturing the directional properties induced by the printing process. This work presents a methodology to experimentally characterize the recoverable strain of 4D‑printed structures without requiring a full thermal simulation of the printing process. The approach is based on beam theory and curvature measurements, using a strain ansatz to describe the pre‑activated state of the material. The measured curvature is interpreted as the outcome of a strain gradient introduced during printing. Furthermore, the simulation is coupled directly with the G‑code, enabling access to directional and process‑induced information. Using this framework, a 4D unit cell design can be developed and the shape change behavior can be subjected to homogenization, thereby extending a multiscale optimization framework to enable the design of functionally graded materials manufactured via 4D printing.