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Modeling the mechanical behavior of crystallizable shape memory polymers: incorporating temperature-dependent viscoelasticity

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Abstract

Shape memory polymers (SMPs) are soft active materials that have an ability to retain a temporary shape, and revert back to their original shape when triggered by a suitable stimulus, typically an increase in temperature. These materials are finding wide use in a variety of fields such as biomedical and aerospace engineering; hence it is important to model their mechanical behavior. Crystallizable shape memory polymers (CSMPs) is an important subclass of SMPs, and their temporary shape is fixed by a crystalline phase, while return to the original shape is due to the melting of this crystalline phase. In our earlier work, we have studied the mechanical behavior of CSMPs within a mechanical setting by considering the original amorphous network above the recovery temperature as a hyperelastic material. In this article, we extend our earlier work to incorporate the temperature-dependent viscoelasticity into the developed constitutive model to study the mechanical behavior of CSMPs. The viscoelastic behavior of the polymers at high temperature is simulated through a rate type model. Furthermore, the model of the semi-crystalline polymer after the onset of crystallization is developed based on the mixture theory and the theory of “multiple natural configurations”. In addition, we have applied the model to a specific boundary value problem, namely uniaxial extension. The shape memory cycles of the CSMPs under different stretch rates have been studied. The results are consistent with what has been observed in experiments.

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References

  1. Lendlein, A., Kelch, S.: Shape-memory polymers. Angew. Chem. Int. Ed. 41(12), 2035–2057 (2002)

    Google Scholar 

  2. Tobushi, H., Hara, H., Yamada, E., Hayashi, S.: Thermomechanical properties in a thin film of shape memory polymer of polyurethane series. Smart Mater. Struct. 5(4), 483–491 (1996)

    Article  Google Scholar 

  3. Lendlein, A., Jiang, H., Jünger, O., Langer, R.: Light-induced shape-memory polymers. Nature 434(7035), 879–882 (2005)

    Article  Google Scholar 

  4. Jiang, H., Kelch, S., Lendlein, A.: Polymers move in response to light. Adv. Mater. 18(11), 1471–1475 (2006)

    Article  Google Scholar 

  5. Lu, H.B., Huang, W.M., Yao, Y.T.: Review of chemo-responsive shape change/memory polymers. Pigm. Resin Technol. 42(4), 237–246 (2013). doi:10.1108/PRT-11-2012-0079

    Article  Google Scholar 

  6. Liu, C., Qin, H., Mather, P.T.: Review of progress in shape-memory polymers. J. Mater. Chem. 17(16), 1543–1558 (2007)

    Article  Google Scholar 

  7. Xue, L., Dai, S., Li, Z.: Biodegradable shape-memory block co-polymers for fast self-expandable stents. Biomaterials 31(32), 8132–8140 (2010). doi:10.1016/j.biomaterials.2010.07.043

    Article  Google Scholar 

  8. Eisenhaure, J.D., Rhee, S.I., Al-Okaily, A.M., Carlson, A., Ferreira, P.M., Kim, S.: The use of shape memory polymers for MEMS assembly. J. Microelectromech. Syst. 25(1), 69–77 (2016). doi:10.1109/JMEMS.2015.2482361

    Article  Google Scholar 

  9. Yakacki, C.M., Shandas, R., Lanning, C., Rech, B., Eckstein, A., Gall, K.: Unconstrained recovery characterization of shape-memory polymer networks for cardiovascular applications. Biomaterials 28(14), 2255–2263 (2007). doi:10.1016/j.biomaterials.2007.01.030

    Article  Google Scholar 

  10. Ge, Q., Dunn, C.K., Qi, H.J., Dunn, M.L.: Active origami by 4D printing. Smart Mater. Struct. 23(9), 094007 (2014). doi:10.1088/0964-1726/23/9/094007

    Article  Google Scholar 

  11. Reyntjens, W.G., Du Prez, F.E., Goethals, E.J.: Polymer networks containing crystallizable poly(octadecyl vinyl ether) segments for shape-memory materials. Macromol. Rapid Commun. 20(5), 251–255 (1999)

    Article  Google Scholar 

  12. Barot, G., Rao, I.J.: Constitutive modeling of the mechanics associated with crystallizable shape memory polymers. Z. Angew. Math. Phys. 57(4), 652–681 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  13. Barot, G., Rao, I.J., Rajagopal, K.R.: A thermodynamic framework for the modeling of crystallizable shape memory polymers. IJES 46(4), 325–351 (2008)

    MathSciNet  MATH  Google Scholar 

  14. Moon, S., Cui, F., Rao, I.J.: Constitutive modeling of the mechanics associated with triple shape memory polymers. IJES 96, 86–110 (2015). doi:10.1016/j.ijengsci.2015.06.003

    MathSciNet  Google Scholar 

  15. Moon, S., Rao, I.J., Chester, S.A.: Triple shape memory polymers: constitutive modeling and numerical simulation. J. Appl. Mech. Trans. ASME 83(7), 071008 (2016). doi:10.1115/1.4033380

    Article  Google Scholar 

  16. Michal, B.T., Jaye, C.A., Spencer, E.J., Rowan, S.J.: Inherently photohealable and thermal shape-memory polydisulfide networks. ACS Macro Lett. 2(8), 694–699 (2013). doi:10.1021/mz400318m

    Article  Google Scholar 

  17. Atkin, R.J., Craine, R.E.: Continuum theory of mixtures: basic theory and historical development. Q J Mech Appl Math. 29(2), 209–244 (1976)

  18. Rajagopal, K.R., Srinivasa, A.R.: Mechanics of the inelastic behavior of materials—part 1, theoretical underpinnings. Int. J. Plast 14(10–11), 945–967 (1998)

    Article  MATH  Google Scholar 

  19. Rajagopal, K.R., Wineman, A.S.: A constitutive equation for nonlinear solids which undergo deformation induced microstructural changes. Int. J. Plast 8(4), 385–395 (1992). doi:10.1016/0749-6419(92)90056-I

    Article  MATH  Google Scholar 

  20. Rajagopal, K.R., Srinivasa, A.R.: On the inelastic behavior of solids—part 1: twinning. Int. J. Plast 11(6), 653–678 (1995)

    Article  MATH  Google Scholar 

  21. Rajagopal, K.R., Wineman, A.S.: A note on viscoelastic materials that can age. Int. J. Non-Linear Mech. 39(10), 1547–1554 (2004)

    Article  MATH  Google Scholar 

  22. Cui, F., Moon, S., Rao, I.J.: Modeling the viscoelastic behavior of amorphous shape memory polymers at an elevated temperature. Fluids 1(2), 15 (2016)

    Article  Google Scholar 

  23. Rao, I.J., Rajagopal, K.R.: A thermodynamic framework for the study of crystallization in polymers. Z. Angew. Math. Phys. 53(3), 365–406 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  24. Sodhi, J.S., Rao, I.J.: Modeling the mechanics of light activated shape memory polymers. IJES 48(11), 1576–1589 (2010)

    Google Scholar 

  25. Rajagopal, K.R., Srinivasa, A.R.: A thermodynamic frame work for rate type fluid models. J. Non-Newton. Fluid Mech. 88(3), 207–227 (2000)

    Article  MATH  Google Scholar 

  26. Rao, I.J., Rajagopal, K.R.: Study of strain-induced crystallization of polymers. Int. J. Solids Struct. 38(6–7), 1149–1167 (2001). doi:10.1016/S0020-7683(00)00079-2

    Article  MATH  Google Scholar 

  27. Rao, I.J., Rajagopal, K.R.: Phenomenological modeling of polymer crystallization using the notion of multiple natural configurations. Interfaces Free Bound. 2(1), 73–94 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  28. Rao, I.J., Rajagopal, K.R.: On the modeling of quiescent crystallization of polymer melts. Polym. Eng. Sci. 44(1), 123–130 (2004)

    Article  Google Scholar 

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Correspondence to I. Joga Rao.

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Cui, F., Moon, S. & Joga Rao, I. Modeling the mechanical behavior of crystallizable shape memory polymers: incorporating temperature-dependent viscoelasticity. Int J Adv Eng Sci Appl Math 9, 21–29 (2017). https://doi.org/10.1007/s12572-016-0177-y

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