Modeling the thermodynamic behaviors of 4D-printed thermoplastic shape memory polymers in cold, warm, and hot programming

Abstract Shape memory polymers (SMPs) are smart materials with the ability to remember their original shapes and respond to external stimuli. 4D printing endows SMPs with unique thermomechanical behaviors distinct from traditionally fabricated SMPs, particularly in stress recovery responses. This paper, for the first time, investigates the thermodynamic characteristics of 4D-printed SMPs under cold, warm and hot programming. A new finite deformation constitutive model is developed to predict the thermodynamic response of 4D-printed SMPs. Integrated with the free volume theory, the Eyring equation, and the fictive temperature, a new physics-based phase evolution function is proposed and incorporated into the model. Experimental and simulation results reveal a non-monotonic stress recovery trend in that cold programming shows partial elastic energy dissipation due to stress concentration at defects, warm programming achieves an optimal balance between energy storage and viscous relaxation, while hot programming suffers from entropy-dominated energy loss. The proposed model effectively predicts the thermodynamic behavior of 4D-printed SMPs in cold, warm, and hot programming and successfully reproduces the thermomechanical phenomena different from traditionally fabricated SMPs.