New perspective on the creep characteristic of fiber–dependent shape memory polymers: variable–order fractional constitutive model

With the aim of describing and explaining the creep tensile property of shape memory polymers (SMPs) better, a variable--order fractional creep constitutive model with fewer parameters and good simulation performance was constructed on the basis of existing constitutive models. The consists of a Hookean spring connected in series with a Newtonian dashpot was employed to propose a new variable--order fractional Maxwell model for SMPs. Drawing support from the Laplace transform, we derive the analytical solution of this novel model. The verification of the obtained theoretical results with the creep test data for different fiber weight fractions and stress levels available from the literature reveals their satisfactory agreement. It can be concluded that the developed variable--order fractional constitutive model can better describe the complex viscoelastic relationship of shape memory polymers which is difficult to be described by the classical integer order derivative, and obtain a more accurate constitutive model of shape memory polymers with fewer parameters.