Constitutive models based on fractional calculus are utilized to investigate the viscoelastic response of thermally activated shape memory polymers (SMPs). Fractional calculus-based viscoelastic equations are fitted to experimental data existing in literature compared with traditional viscoelastic models. In addition, a fractional rheology model is applied to simulate the isothermal recovery of an amorphous SMP. The fit results show a significant improvement in the description of the strain recovery response of SMP by the fractional calculus method.

The nano-carbon powders are often used as fillers to endow the shape memory polymers (SMPs) with electroconductivity. It has been found that the shape memory effects (SMEs) of SMPs filled with nano-carbon powder can be triggered both by temperature and by water. To reveal the driving mechanism of SMEs, a constitutive model for describing the thermally activated and moisture activated SMEs of these shape memory polymer composite (SMPCs) is developed here. Because both of the SMEs share the same driving mechanism, the variable moisture is incorporated into the framework of a thermo-mechanical modeling approach to disclose the effect of moisture on the thermoviscoelastic properties. The SMPCs are regarded as isotropic materials and the effect of carbon powder on the mechanical properties of the matrix is also considered in the paper. Because the complete recovery may not be reached even they are exposed to the stimulus environment long enough, the blocking mechanism is also considered here. This is the mainly new contribution compared to the early work. Using the method of parameter determination presented here, the effectiveness of the proposed hygro-thermo-mechanical constitutive model is confirmed by comparing the model results with the test data of uniaxial deformation from the literature. GRAPHICAL ABSTRACT

In order to predict thermo-mechanical properties of woven fabric reinforced shape memory polymer composites (WFRSMPCs), the multi-scale theory is employed to establish the microscopic model for fiber bundles and the mesoscopic model for WFRSMPCs respectively. Firstly, the viscoelastic properties of WFRSMPCs with different process parameters are studied numerically in the paper. Then the free recovery and the constrained recovery of WFRSMPCs are studied respectively and the effects of heating rates and process parameters on shape memory properties of WFRSMPCs are investigated. The research in the paper could provide a basis for design and application of WFRSMPCs in engineering.

Polymers of two-way shape memory effects (SMEs) are of great application potential ranging from intelligent actuators to artificial muscles due to their reversible shape response on the basis of an on-off stimulus such as a cooling-heating cycle, which motivates the development of theoretical tools to support their design. In the paper, a three-dimensional phase transition finite deformation constitutive model is proposed to phenomenologically describe the underlying mechanisms of the one-way and two-way SMEs in thermal-responsive semi-crystalline polymers. A unified transition equation is proposed to depict the volume changes of crystalline phase during both crystallization and melting transitions. The crystallization-induced elongation and melting-induced contraction behaviours in two-way SMEs are assumed to be realized by an elongation-contraction element and its temperature-dependent strain evolution rules. The overall constitutive model is then implemented into Mathematica, and the model predictions are compared to and agree well with the experimental results. The paper provides an efficient method on modeling the thermal-induced two-way SMEs under stress conditions in semi-crystalline polymers and detailed discussion about the influence of several parameters such as the crosslinking density, the applied external load and the cooling/heating rate.

A three-branch viscoelastic model based on fractional derivatives is proposed for the viscoelastic behaviours of solid propellants. The simulation results show a satisfactory agreement with the stress relaxation modulus and complex modulus of solid propellants. As a comparison, the static modulus is also characterized by traditional viscoelastic model with integer-order derivatives. Results show that the application of the fractional derivatives to the viscoelastic constitutive model can effectively reduce the number of the required parameters while giving an accurate prediction of viscoelastic behaviours of solid propellants. Moreover, a simple and effective direct search method based on simulated annealing and Powell's mothed is proposed for the data fitting. This article is part of the theme issue ‘Advanced materials modelling via fractional calculus: challenges and perspectives'.