Mechanistic prediction of folding angles in 4D printed shape memory polymers under varied loading conditions

Four-dimensional printing technology empowers 3D-printed structures to change shapes upon external stimulation. However, most studies did not consider recovery under loaded conditions. This paper introduces a mechanistic prediction model for forecasting recovery angles in 4D printing utilizing shape memory polymer under various loads. The model integrates Neo–Hookean model to describe the non-linear stress–strain relationship with experimentally determined force density data to characterize polymer restoration properties under various loads. Validation was demonstrated by the recovery experiment of a 3D-printed polylactic acid-thermoplastic polyurethane composite structure loaded by means of a cord and pulley mechanism. The predictive outcomes exhibited reasonable agreement with experimental results, demonstrating a trend of more accurate forecasts as the applied load increased. The model can accommodate various active materials provided that the pertaining force density data is accessible. The predictive model supports the design, optimization and material selection for 4D-printed structures to meet specific performance requirements.