A constitutive model for predicting the time-dependent behavior of multi-material 4D printed structures

The primary difference between 3-dimensional printing (3D) and 4-dimensional (4D) printing is the evolution of the 4D printed structures to exhibit shape-morphing characteristics with time. This fourth dimension “time” in 4D printing is the most important aspect in governing the behavior of printed structures. Currently, there is a lack of generic models to predict the time-dependent response of the 4D printed shape memory polymer structures. In this study, a constitutive forward model was developed by extending the classic Timoshenko bi-metal model and validated with results from experiments. Sample strips fabricated using the combination of RGD8525 digital material and Agilus30 elastomer displayed complete shape recovery in ~ 9 s. The curvature of the samples during shape recovery was determined by image processing of the recorded video at specific time intervals. When compared with the linear Timoshenko model, the developed model is in good correlation with the experimental results with an average error of 7.5%. The model enables the prediction of the shape morphing behavior of 4D printed multi-material structures over time prior to printing using two-time constants. The fundamental and generic model will serve as a starting point and general guideline for future developments in modeling the behavior of 4D printed structures.