A physically-based thermo-viscoelastic constitutive model of phantom and entangled networks in amorphous shape memory polymers

Amorphous shape memory polymers (SMPs) are one of the most prominent smart and intelligent materials, whose constitutive models play important roles for their engineering designs and applications. Over the past decades, various thermo-viscoelastic constitutive models have been developed to simulate their shape memory behaviors, but these models are mostly phenomenological and often unable to explain the underlying mechanisms of their viscoelasticity and shape memory effects. Herein we propose a physically-based thermo-viscoelastic constitutive model to describe SMPs’ shape memory behaviors. We propose that the SMPs are composed of both hard and soft phase chains. The hard phase chains form a backbone network showing strong elastic responses, which can be modeled with a phantom network model. Whereas the soft phase chains form transient networks and entangled networks exhibiting viscoelastic behaviors, which can be explained using contour length relaxation and disentanglement relaxation phenomena. Time-temperature superposition principle is then incorporated to capture critical time-temperature dependence of the viscoelasticity and thermally induced shape memory effect. The proposed model has been implemented numerically and validated using shape memory experimental results at different recovery temperatures and heating rates, during the shape memory processes of amorphous SMPs. This work presents a good understanding of the viscoelasticity and shape memory effects of amorphous SMPs at the polymer chain level, and also provides an effective constitutive model for practical applications.