A multi-branch thermoviscoelastic model based on fractional derivatives for free recovery behaviors of shape memory polymers

A multi-branch thermoviscoelastic model based on fractional derivatives is proposed for the prediction of temperature-dependent free recovery behaviors of amorphous shape memory polymers (SMPs). The model is similar to the generalized fractional Maxwell model, which gives an approximation of the temperature-dependent storage modulus, loss modulus and loss factor by introducing the shift factor, usually derived from time-temperature superposition of isothermal data obtained at different temperatures. The simulation results show a satisfactory agreement with the experimental free recovery curves from shape memory tests. Moreover, this method is also proved valid for the triple-shape memory effect and multi-shape memory effect of shape memory polymers. In addition, it is an effective approach for the prediction of free recovery behaviors of the SMP-based syntactic foam consisting of hollow glass microspheres dispersed in a shape memory polymer matrix. The application of the fractional derivatives to the thermoviscoelastic constitutive model can effectively reduce the number of the required parameters while give an accurate prediction of viscoelastic behaviors and free recovery behaviors of SMPs.