A thermodynamic constitutive model based on uncoupled physical mechanisms for polymer-based shape memory composites and its application in 4D printing

Four-dimensional (4D) printing is a new interdisciplinary research field that integrates sophisticated manufacturing, smart materials and mechanics. Shape memory polymer (SMP) and their composites (SMPCs) have been widely used in the field of 4D printing due to their smart and rapid response. Thus, we develop a novel thermodynamic constitutive model for SMP and SMPC, and investigate its application in 4D printing. Structure relaxation and stress relaxation are considered to follow different physical mechanisms but are related by an internal thermodynamic state variable that can represent the non-equilibrium structure. Founded on the thermodynamic variable, a physics-based fictive temperature theory is constructed for structure relaxation, and also a new stress relaxation model is proposed to characterize the time-dependent behaviors related to mechanical changes. It is shown that the influences of temperatures, strain rates, pre-strains, reinforcing fillers, and recovery conditions on stress-strain and shape memory responses are well predicted by the thermodynamic constitutive model.