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Application of Fractional Calculus Methods to Viscoelastic Response of Amorphous Shape Memory Polymers

Published online by Cambridge University Press:  11 August 2015

C-Q. Fang ,
H.-Y. Sun  and
J.-P. Gu
C-Q. Fang
Affiliation:
State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, China
H.-Y. Sun*
Affiliation:
State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, China
J.-P. Gu
Affiliation:
State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, China Department of Materials Engineering, Nanjing Institute of Technology, Nanjing, China
*
* Corresponding author (hysun@nuaa.edu.cn)
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Abstract

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.

Keywords

Shape memory polymersFractional calculusViscoelasticityShape recovery
Type
Research Article
Information
Journal of Mechanics , Volume 31 , Issue 4 , August 2015 , pp. 427 - 432
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2015 

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References

1.Behl, M. and Lendlein, A., “Shape-Memory Polymers,” Materials Today, 10, pp. 20–28 (2007).Google Scholar
2.Lendlein, A. and Kelch, S., “Shape-Memory Polymers,” Angewandte Chemie International Edition, 41, pp. 2034–2057 (2002).Google Scholar
3.Ratna, D. and Karger-Kocsis, J., “Recent Advances in Shape Memory Polymers and Composites: A Review,” Journal of Materials Science, 43, pp. 254–269 (2008).Google Scholar
4.Leng, J. S., Lan, x., Liu, Y. J. and Du, S. Y., “Shape-Memory Polymers and Their Composites: Stimulus Methods and Applications,” Progress in Materials Science, 56, pp. 1077–1135 (2011).Google Scholar
5.Ivens, J., Urbanus, M. and De, Smet. C., “Shape Recovery in a Thermoset Shape Memory Polymer and Its Fabric-Reinforced Composites,” Express Polymer Letters, 5, pp. 254–261 (2011).Google Scholar
6.Nguyen, T. D., “Modeling Shape-Memory Behavior of Polymers,” Polymer Reviews, 53, pp. 130–152 (2013).Google Scholar
7.Liu, Y. J., Du, H. Y., Liu, L. W. and Leng, J. S., “Shape Memory Polymer Composites and their Applications in Aerospace: A Review,” Smart Materials and Structures, 23 p. 023001 (2014).Google Scholar
8.Tobushi, H., Hashimoto, T., Hayashi, S. and Yamada, E. J., “Thermomechanical Constitutive Modeling in Shape Memory Polymer of Polyurethane Series,” Journal of Intelligent Material Systems and Struc-tures, 8, pp. 711–718 (1997).CrossRefGoogle Scholar
9. Tobushi, H., Okumura, K., Hayashi, S. and Ito, N., “Thermomechanical Constitutive Model of Shape Memory Polymer,” Mechanics of Materials, 33, pp. 545–554 (2001).Google Scholar
10.Morshedian, J., Khonakdar, H. A. and Rasouli, S., “Modeling of Shape Memory Induction and Recovery in Heat-Shrinkable Polymers,” Macromolecular Theory and Simulations, 14, pp. 428–434 (2005).Google Scholar
11.Nguyen, T. D., Qi, H. J., Castro, F. and Long, K. N., “A Thermoviscoelastic Model for Amorphous Shape Memory Polymers: Incorporating Structural and Stress Relaxation,” Journal of the Mechanics and Physics of Solids, 56, pp. 2792–2814 (2008).Google Scholar
12.Diani, J., Liu, Y. and Gall, K., “Finite Strain 3D Thermoviscoelastic Constitutive Model for Shape Memory Polymers,” Polymer Engineering and Science, 46, pp. 486–492 (2006).Google Scholar
13.Khonakdar, H. A., Jafari, S. H., Rasouli, S., Morshedian, J. and Abedini, H., “Investigation and Modeling of Temperature Dependence Recovery Behavior of Shape-Memory Crosslinked Polyethylene,” Macromolecular Theory and Simulations, 16, pp. 43–52 (2007).Google Scholar
14.Qi, H. J., Nguyen, T. D., Castro, F., Yakack, C. H. and Shandas, R. J., “Finite Deformation Thermo-Mechanical Behavior of Thermally Induced Shape Memory Polymers,” Journal of the Mechanics and Physics of Solids, 56, pp. 1730–1751 (2008).Google Scholar
15.Hong, S. J., Yu, W. R., Youk, J. H. and Cho, Y. R., “Polyurethane Smart Fiber with Shape Memory Function: Experimental Characterization and Constitutive Modeling,” Fibers and Polymers, 8, pp. 377–385 (2007).Google Scholar
16.Heuchel, M., Cui, J., Kratz, K., Kosmella, H. and Lendlein, A., “Relaxation Based Modeling of Tunable Shape Recovery Kinetics Observed under Isothermal Conditions for Amorphous Shape-Memory Polymers,” Polymer, 51, pp. 6212–6218 (2010).CrossRefGoogle Scholar
17.Zhang, Q. and Yang, Q. S., “Recent Advance on Constitutive Models of Thermal-Sensitive Shape Memory Polymers,” Journal of Applied Polymer Science, 123, pp. 1502–1508 (2012).Google Scholar
18.Ge, Q., Yu, K., Ding, Y. F. and Qi, H. J., “Prediction of Temperature-Dependent Free Recovery Behaviors of Amorphous Shape Memory Polymers,” Soft Matter, 8, p. 11098 (2012).Google Scholar
19.Xiao, R., Choi, J., Lakhera, N., Yakacki, C. M., Frick, C. P. and Nguyen, T. D., “Modeling the Glass Transition of Amorphous Networks for Shape-Memory Behavior,” Journal of the Mechanics and Physics of Solids, 61, pp. 1612–1635 (2013).Google Scholar
20.Yu, K., Ge, Q. and Qi, H. J., “Reduced Time as a Unified Parameter Determining Fixity and Free Recovery of Shape Memory Polymers,” Nature Communications, 5 p. 3066 (2014)Google Scholar
21.Chen, J. G., Liu, L. W., Liu, Y. J. and Leng, J. S., “Thermoviscoelastic Shape Memory Behavior for Epoxy-Shape Memory Polymer,” Smart Materials and Structures, 23, p. 055025 (2014).Google Scholar
22.Nutting, P. G., “A New Generalized Law of Deformation,” Journal of the Franklin Institute, 191, pp. 679–685 (1921).Google Scholar
23.Gemant, A., “A Method of Analyzing Experimental Results Obtained from Elasto-Viscous Bodies,” Journal of Applied Physics, 7, pp. 311–317 (1936).Google Scholar
24.Bagley, R. L. and Torvik, P. J., “Fractional Calcu-lus-a Different Approach to the Analysis of Viscoelastically Damped Structures,” AIAA Journal, 21, pp. 741–748 (1983).Google Scholar
25.Rogers, L., “Operators and Fractional Derivatives for Viscoelastic Constitutive Equations,” Journal of Rheology, 27, pp. 351–372 (1983).Google Scholar
26.Bagley, R. L. and Torvik, P. J., “On the Fractional Calculus Model of Viscoelastic Behavior,” Journal of Rheology, 30, pp. 133–155 (1986).Google Scholar
27.Pritz, T., “Analysis of Four-Parameter Fractional Derivative Model of Real Solid Materials,” Journal of Sound and Vibration, 195, pp. 103–115 (1996).CrossRefGoogle Scholar
28.Shimizu, N. and Zhang, W., “Fractional Calculus Approach to Dynamic Problems of Viscoelastic Materials,” JSME International Journal, Series C, Mechanical Systems, Machine Elements and Manufacturing, 42, pp. 825–837 (1999).Google Scholar
29.Koeller, R. C., “Applications of Fractional Calculus to the Theory of Viscoelasticity,” Journal of Applied Mechanics, 51, pp. 299–307 (1984).Google Scholar
30.Welch, S. W. J., Rorrer, R. A. L. and Duren, J. R. G., “Application of Time-Based Fractional Calculus Methods to Viscoelastic Creep and Stress Relaxation of Materials,” Mechanics of Time-Dependent Materials, 3, pp. 279–303 (1999).Google Scholar
31.Pritz, T., “Five-Parameter Fractional Derivative Model for Polymeric Damping Materials,” Journal of Sound and Vibration, 265, pp. 935–952 (2003).Google Scholar
32.Caputo, M. and Mainardi, F., “A New Dissipation Model Based on Memory Mechanism,” Pure and Applied Geophysics, 91, pp. 134–147 (1971).Google Scholar
33.Xiao, S. W., Zhou, X., Hu, X. L. and Luo, W. B., “Linear Rheological Solid Model with Fractional Derivative and its Application,” Engneering Mechanics, 29, pp. 354–358 (2012).Google Scholar
34.Diani, J., Gilormini, P., Frédy, C. and Rousseau, I., “Predicting Thermal Shape Memory of Crosslinked Polymer Networks from Linear Viscoelasticity,” International Journal of Solids and Structures, 49, pp. 793–799 (2012).Google Scholar
35. 7D-Soft High Technology Inc., 7D-Soft High Technology Inc. 1st Opt Manual, Release 1.5, http:/www.7d-soft.com.Google Scholar
36.Fenander, A., “Modal Synthesis when Modeling Damping by Use of Fractional Derivatives,” AIAA Journal, 34, pp. 1051–1058 (1996).Google Scholar
37.Bagley, R. L. and Torvik, P. J., “A Theoretical Basis for the Application of Fractional Calculus to Viscoelasticity,” Journal of Rheology, 27, pp. 201–210 (1983).Google Scholar
38.Gloeckle, W. G. and Nonnenmacher, T. F., “Fractional Integral Operators and Fox Functions in the Theory of Viscoelasticity,” Macromolecules, 24, pp. 6426–6434 (1991).CrossRefGoogle Scholar