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Modeling thermomechanical processes in shape memory polymers under finite deformations

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Abstract

A model taking into account finite deformations is constructed for the behavior of a shape memory polymer which undergoes a transition from the highly elastic to the vitreous state and back during deformation and temperature change. The obtained relations are tested on problems which have experimental support.

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References

  1. V. A. Likhachev, “Shape Memory Effect,” Soros. Obrazovat. Zh., No. 3, 107–114 (1997).

    Google Scholar 

  2. V. P. Matveenko, O. Yu. Smetannikov, N. A. Trufanov, and I. N. Shardakov, Thermomechanics of Polymer Materials in the Relaxation Transition (Fizmatlit, Moscow, 2009) [in Russian].

    Google Scholar 

  3. V. A. Beloshenko, V. N. Varyukhin, and Yu. V. Voznyak, “Shape Memory Effect in Polymers,” Usp. Khim. 74 (3), 285–306 (2005).

    Article  Google Scholar 

  4. Z. G. Wei, R. Sandström, and S. Miyazaki, “Shape Memory Materials and Hybrid Composites for Smart Systems, Part 1. Shape Memory Materials,” J. Mater. Sci. 33, 3743–3762 (1998).

    Article  ADS  Google Scholar 

  5. M. Behl and A. Lendlein, “Shape Memory Polymers. Review,” Materials Today 10 (4), 20–28 (2007).

    Article  Google Scholar 

  6. Y. Liu, H. Du, L. Liu, and J. Leng, “Shape Memory Polymers and Their Composites in Aerospace Applications: A Review,” Smart Materials Structures 23 (2), 23001–23022 (2014); DOI: 10.1088/0964-1726/23/2/023001.

    Article  Google Scholar 

  7. Yi-Chao Chen and D. C. Lagoudas, “A Constitutive Theory for Shape Memory Polymers. Part 1. Large Deformations,” J. Mech. Phys. Solids 56, 1752–1765 (2008).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  8. B. L. Volk, D. C. Lagoudas, and Yi-Chao Chen, “Analysis of the Finite Deformation Response of Shape Memory Polymers: II. 1D Calibration and Numerical Implementation of a Finite Deformation, Thermoelastic Model,” Smart Materials Structures 19 (7), 75006–75016 (2010); DOI: 10.1088/0964-1726/19/7/075006.

    Article  Google Scholar 

  9. K. A. Tikhomirova, N. A. Trufanov, and I. N. Shardakov, “Numerical and Experimental Study of the Thermomechanical Behavior of Vitrified Polymers in the Case of Large Deformations,” Vychisl. Mekh. Sploshn. Sred 6 (4), 475–482 (2013).

    Google Scholar 

  10. R. G. Kulikov and T. G. Kulikova, “Numerical Method of Solution of the Problem of Deformation of a Crystallizing Polymer Medium Taking into Account Large Deformations,” Vychisl. Mekh. Sploshn. Sred 7 (2), 172–180 (2014).

    Google Scholar 

  11. K. K. Westbrook, P. H. Kao, F. Castro, et al., “A 3D Finite Deformation Constitutive Model for Amorphous Shape Memory Polymers: A Multi-Branch Modeling Approach for Nonequilibrium Relaxation Processes,” Mech. Materials 43, 853–869 (2011).

    Article  Google Scholar 

  12. M. Baghani, R. Naghdabadi, and J. Arghavani, “A Large Deformation Framework for Shape Memory Polymers: Constitutive Modeling and Finite Element Implementation,” J. Intelligent Material Systems Structures 24 (1), 21–32 (2013).

    Article  Google Scholar 

  13. J. Liu, K. Gall, M. L. Dunn, et al., “Thermomechanics of Shape Memory Polymers: Uniaxial Experiments and Constitutive Modeling,” Int. J. Plasticity 22, 279–313 (2006).

    Article  MATH  Google Scholar 

  14. R. S. Novokshanov and A. A. Rogovoi, “On the Construction of Evolutionary Constitutive Relations for Finite Strains,” Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 4, 77–95 (2002).

    Google Scholar 

  15. R. S. Novokshanov and A. A. Rogovoi, “Evolutionary Constitutive Relations for Finite Viscoelastic Strains,” Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 4, 122–140 (2005).

    Google Scholar 

  16. A. A. Rogovoi, “Constitutive Relations for Finite Elastic–Inelastic Deformations,” Prikl. Mekh. Tekh. Fiz. 46 (5), 138–149 (2005) [J. Appl. Mech. Tech. Phys. 46 (5), 730–739 (2005)].

    MathSciNet  MATH  Google Scholar 

  17. A. A. Rogovoi, “Thermodynamics of Finite-Strain Elastic–Inelastic Scattering,” Prikl. Mekh. Tekh. Fiz. 48 (4), 144–153 (2007) [J. Appl. Mech. Tech. Phys. 48 (4), 591–598 (2007)].

    MathSciNet  Google Scholar 

  18. A. A. Rogovoi, “Kinematics of Finite-Strain Elastic–Inelastic Scattering,” Prikl. Mekh. Tekh. Fiz. 49 (1), 165–172 (2008) [J. Appl. Mech. Tech. Phys. 49 (1), 136–141 (2008)].

    MathSciNet  Google Scholar 

  19. A. A. Rogovoi, “Formalized Approach to Construction of the State Equations for Complex Media under Finite Deformations,” Continuum Mech. Thermodynamics 24, 81–114 (2012); DOI: 10.1007/s00161-011-0220-y.

    Article  ADS  MathSciNet  Google Scholar 

  20. B. L. Volk, D. C. Lagoudas, Yi-Chao Chen, and K. S. Whitley, “Analysis of the Finite Deformation Response of Shape Memory Polymers. 1. Thermomechanical Characterization,” Smart Materials Structures 19 (7), 75005–75014 (2010); DOI: 10.1088/0964-1726/19/7/075005.

    Article  Google Scholar 

  21. C. Truesdell, A First Course in Rational Continuum Mechanics (J. Hopkins Univ., Baltimore, Maryland, 1972).

    Google Scholar 

  22. A. A. Rogovoi and O. S. Stolbova, “Modeling Elastic–Inelastic Processes in Shape Memory Alloys at Finite Deformations,” Prikl. Mekh. Tekh. Fiz. 54 (2), 148–162 (2013) [J. Appl. Mech. Tech. Phys. 54 (2), 295–307 (2013)].

    MathSciNet  Google Scholar 

  23. A. I. Lur’e, Nonlinear Theory of Elasticity (Nauka, Moscow 1980; North-Holland, Amsterdam, 1990).

    MATH  Google Scholar 

  24. A. A. Rogovoi, “Differentiation of Scalar and Tensor Functions of Tensor Arguments,” Vestnik. Perm. Gos. Tekh. Univ., Din. Prochnost’ Mashin, No. 2, 83–90 (2001).

    Google Scholar 

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Correspondence to A. A. Rogovoi.

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Original Russian Text © A.A. Rogovoi, O.S. Stolbova.

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 56, No. 6, pp. 143–157, November–December, 2015.

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Rogovoi, A.A., Stolbova, O.S. Modeling thermomechanical processes in shape memory polymers under finite deformations. J Appl Mech Tech Phy 56, 1059–1070 (2015). https://doi.org/10.1134/S0021894415060164

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  • DOI: https://doi.org/10.1134/S0021894415060164

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