A novel fractional viscoelastic constitutive model for shape memory polymers

Abstract

Shape memory polymers (SMPs) are a class of smart materials which can recover from a deformed shape to their original shape by a certain external stimulus. To predict the deformation behaviors of SMPs, different constitutive models have been developed in the last few years. However, most of the constitutive models need many parameters to be determined by specific experiments and complex calibration processes. This drawback has limited their application in promoting the development of SMPs. Thus, it is imperative to develop a new constitutive model which is not only accurate, but also relatively simple. In our work, a novel fractional viscoelastic constitutive model coupling with time‐temperature superposition principle is first proposed for SMPs. Then, frequency sweep and temperature sweep experiments are conducted to determine the parameters of the model. Finally, the shape memory free recovery experiments are carried out to validate the predictive capability of the developed model. By comparing the predicted results with experimental data, we find that though our model has only eleven parameters in total, it could capture the thermomechanical behaviors of SMPs in very good agreement with experimental results. We hope the proposed new model provide researchers with guidelines in designing and optimizing of SMP applications. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018, 56, 1125–1134

Using fractional derivatives for improved viscoelastic modeling of textile composites. Part I: Fabric yarns

“…More recently, the fractional models have been used to predict the behavior of polymeric materials, such as thermally activated shape memory polymers (SMPs), 13,14 glass fibers coated with polytetrafluoroethylene (PTFE), 15 an epoxy resin, a thermoplastic, and a semi-crystalline biodegradable polymer, 16 polymer melts, 17 and magnetoactive elastomers (MAEs). 18 The viscoelastic response of thermally activated SMPs were investigated by Fang et al 13 They fitted experimental data available in the literature, to the derived constitutive models based on fractional calculus, and then compared them with traditional viscoelastic models.…”

“…18 In another application, using fractional differential models, the complex thermomechanical properties of the SMPs was analyzed by Pan and Liu. 14 A fractional viscoelastic constitutive model was first proposed for SMPs. Then, via frequency sweep, the tests showed the variation of some parameters such as storage and loss moduli with respect to frequency.…”

A comprehensive review on thermomechanical constitutive models for shape memory polymers

“…They believed that this method gives more accurate results, in addition to lower number of material parameters (Koeller, 1984; Li et al, 2017c; Müller et al, 2011; Pan and Liu, 2018; Xiao et al, 2016a). So far, about six models have been developed with this method (Fang et al, 2016, 2018; Li et al, 2017c; Pan and Liu, 2018; Zeng et al, 2018b, 2018c). In the same way, Fang et al (2016) predicted an acrylate-based SMP (tBA/PEGDMA) response in the strain recovery considering the viscoelastic fractional approach as well as a three-element linear fractional-order Zener model.…”

“…Then, Li et al (2017c), taking advantage of the same approach and a linear SLS model, studied the shape recovery behavior of SMP. In order to consider the recovery response, Pan and Liu (2018) employing the generalized Maxwell–Wiechert model with two non-equilibrium branches, modeled the SME in styrene-based thermoset polymer (the model was 1D and limited to small strains). Zeng et al (2018b), applying the same approach used generalized Maxwell–Wiechert model with four branches to more accurately describe the behavior of a Veriflex-epoxy as a thermoset SMP (experimental results of Yu et al, 2016) in shape recovery.…”

Theoretical and Numerical Analysis of Mechanical Behaviors of a Metamaterial-Based Shape Memory Polymer Stent

“…For the SMP stent material, a series of constitutive models are developed to describe the unique thermo-mechanical behavior [41,42]. Nevertheless, most constitutive models are confined with describing large deformation of SMPs or complex expressions [43][44][45][46]. In our work, a modified rheological model presented in our previous work [47] is adapted to analyze the thermo-mechanical behavior of SMP stent.…”