A simplified constitutive model for predicting shape memory polymers deformation behavior

Shape memory polymers (SMPs) can keep a temporary shape after pre-deformation at a higher temperature and subsequent cooling. When they are reheated, their original shapes can be recovered. Such special characteristics of SMPs make them widely used in aerospace structures, biomedical devices, functional textiles and other devices. Increasing usefulness of SMPs motivates us to further understand their thermomechanical properties and deformation behavior, of which the development of appropriate constitutive models for SMPs is imperative. There is much work in literatures that address constitutive models of the thermo-mechanical coupling in SMPs. However, due to their complex forms, it is difficult to apply these constitutive models in the real world. In this paper, a three-element model with simple form is proposed to investigate the thermo-mechanical small strain (within 10%) behavior of polyurethane under uniaxial tension. Two different cases of heated recovery are considered: (1) unconstrained free strain recovery and (2) stress recovery under full constraint at a strain level fixed during low temperature unloading. To validate the model, simulated and predicted results are compared with Tobushi's experimental results and good agreement can be observed.