Shape Memory Polymers: Viscoelastic Thermomechanical Constitutive Modeling

Shape memory polymers (SMPs) are known to change their elastic stiffness as they respond to change in induced stimulus such as temperature. Under appropriate loading and pre-deformation, a shape memory effect can be captured as the stimulus change. From the nature of polymers, the pre-deformation can tend to be large and can in turn be memorized by SMPs. Due to this characteristic of SMPs, it makes a great candidate for morphing structures. To analyze complex structures a simple but yet practical constitutive model needs to be developed for commercial engineering application. In this paper, a thermomechanical constitutive model is proposed making use of the standard linear viscoelastic model. The total strain during the shape memorization process is defined by mechanical, thermal and storage strains. The rheological model defined is an elastic element in parallel with a Maxwell element, which in turn are both in series with storage and thermal element. Inclusion of a storage strain within the model reveals the internal strain storage mechanism as the temperature of the material drops. Similar work done in the past requires material parameters that can be arduous to determine in the laboratory. This model proposes a simplified approximate material parameter called a binding factor which accounts for the polymer’s molecular architecture and morphology as the temperature changes. Finally, the model is applied to a four step shape memorization and stress-free recovery process. For this study, the four steps considered are a) Pre-loading of the material at high temperature b) Constant strain fixity c) unconstrained relaxation at low temperature d) unconstrained free strain recovery. The developed model is validated by comparing the predictions to experimental results in literature.