Modeling the thermoviscoelasticity of transversely isotropic shape memory polymer composites

Shape memory polymer composites (SMPCs) are emerging smart materials of great application potential due to high deformability and good shape memory properties, with improved mechanical properties compared to pure polymers. In the paper, a micromechanical model is developed to predict the thermoviscoelastic and shape memory properties of such composite systems. First of all, we extend the Mori–Tanaka method into Carson domain based on the Correspondence Principle in viscoelasticity. Thus, the relaxation moduli of SMPCs at different temperatures can be obtained by the thermoviscoelastic properties of the matrix and the reinforcement in the transformed Carson domain. Next the inversion of the relaxation moduli from the Carson domain to the time (physical) domain is accomplished numerically by a multi-precision algorithm. Then, the three-element fractional Zener model is employed to describe the temperature-dependent relaxation modulus and the constitutive relations of SMPCs, and the analytical solutions to the partially constrained shape recovery behaviors are obtained, as well as the stress–strain relations of the material at different temperatures. The overall micromechanical model is then implemented into Mathematica, and the simulation results are compared to and agree well with the experimental results of two different kinds of SMPCs. The paper provides an efficient method on predicting the complex behaviors of transversely isotropic SMPCs. (paper)