Shape Memory Polymers: Energy Method Superposition Constitutive Modeling

Abstract

Shape memory polymers (SMPs) have the capacity to stored strain energy under appropriate stimulus and pre-deformation conditions. Temperature is a good stimulus and predominantly used to activate the shape memory effects of SMPs. Complex engineering application use of SMPs are being developed or proposed and it becomes imperative to develop a simple but yet practical constitutive model that will capture the deformation and recovery of SMPs appropriately under different constraints and loading conditions. In this study, a thermo-mechanical constitutive model is developed for SMPs. A four step shape memorization and recovery is considered and a thermo-mechanical energy balance (first principles of thermodynamics) is done on the individual steps. For this study, the four steps considered are a) Pre-loading of the SMP at high temperature b) Constant strain at negative rate of change of temperature c) constraint release and shape fixity at low temperate and d) unconstrained free strain recovery. A free energy function is developed for the individual steps and superposition principle is used to define the storage free energy in the third step. Applying the second law of thermodynamics in Clausius-Duhem form, the stress-strain relation was developed. Also, in order to account for the polymer’s molecular architecture and morphology resulting in shape memory effect, a binding factor was approximately defined. The binding factor is primarily a function of temperature and secondarily a function of the viscosity of the material at high and low temperatures. The storage strain was assumed to be an internal variable that is generated from the mechanical loading of the SMP. The general model is reduced down to a specific viscoelastic model based on the assumption of the free energy function. The developed model is validated by comparing the predictions to experimental results in literature.