Thermomechanical Constitutive Modeling of Shape Memory Behavior in Polymers based on Physics of Glass Transition and Entropy Elasticity

In this work we present the theory for a new three-dimensional finite strain constitutive model for shape memory behavior of polymers based on the physics of glass transition along with the entropy elasticity theory of rubber-like materials using statistical mechanics approach. A new expression for the evolution of frozen volume fraction is derived to characterize the rubbery-to-glassy phase transition. This expression provides a strong physical basis for the explanation of phase transition as opposed to the empirical expressions used in the literature. A new relation between the frozen volume fraction and configurational entropy of polymer network is also furnished which in turn leads to the derivation of a new equation for evolution of chain stretch for long molecular chains of the polymer network under consideration using the theory of finite strain entropy elasticity based on Langevin statistics. Generally ignored mechanical deformation dependence of specific heat of the material (in addition to the temperature dependence) is shown to play a crucial role in explaining the constitutive behavior as well as the link between the microstructural changes and macroscopic behavior. The capabilities of the model are demonstrated with uniaxial tension and compression loading conditions and the results are compared with results from the literature. The model is implemented within a finite element method framework for the commercial FEA software ABAQUS using user subroutine UMAT which enables the study of complex and 3-dimensional thermo-mechanical problems. A few examples of complex 3-dimensional problems such as torsional loading, polymer stent deformation, buckling of thin films on shape memory polymer substrates, etc. are discussed and their FEA solutions are presented. Finally, experimental validation/calibration of the model is presented which shows that the model captures the shape memory behavior shown by polymers appropriately.