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Discrete and Continuous Growth of Deformable Cylinder

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Transactions on Engineering Technologies

Abstract

The finite deformations of the growing cylinder of incompressible elastic material are under consideration. We assume that the deformations are axisymmetric and do not change along the axis of cylinder. The discrete and continuous types of growing are studied. The analytical solutions of the corresponding boundary-value problems are derived. The results of numerical simulation of both discrete and continuous growth are given.

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References

  1. Gibson, I., Rosen, D.W., Stucker, B.: Additive Manufacturing Technologies. Rapid Prototyping to Direct Digital Manufacturing. Springer, New York (2009)

    Google Scholar 

  2. Choy, K.L.: Chemical vapour deposition of coatings. Prog. Mater. Sci. 48, 57–170 (2003)

    Article  Google Scholar 

  3. Nastasi, M., Mayer, J.W.: Ion Implantation and Synthesis of Materials. Springer, Berlin/Heidelberg/New York (2006)

    Book  Google Scholar 

  4. Aruytunyan, N.K., Drozdov, A.D., Naumov, V.E.: Mechanics of Growing Viscoelastoplastic Solids. Nauka, Moscow [in Russian] (1987)

    Google Scholar 

  5. Lychev, S.A., Manzhirov, A.V.: The mathematical theory of growing bodies. Finite deformations. J. Appl. Math. Mech. 77(4), 421–432 (2013)

    Article  MathSciNet  Google Scholar 

  6. Lychev, S.A., Manzhirov, A.V.: Reference configurations of growing bodies. Mech. Solids. 48(5), 553–560 (2013)

    Article  Google Scholar 

  7. Lychev, S.A.: Universal deformations of growing solids. Mech. Solids. 46(6), 863–876 (2011)

    Article  Google Scholar 

  8. Lychev, S.A., Manzhirov A.V.: Discrete and Continuous Growth of Hollow Cylinder. Finite Deformations. Lecture Notes in Engineering and Computer Science: Proceedings of The Congress on Engineering 2014 (WCE 2014), London, 2–4 July 2014, pp. 1327–1332 (2014)

    Google Scholar 

  9. Klarbring, A., Olsson, T., Stalhand, J.: Theory of residual stresses with application to an arterial geometry. Arch. Mech. 59, 341–364 (2001)

    MathSciNet  Google Scholar 

  10. Epstein, M., Maugin, G.A.: Thermomechanics of volumetric growth in uniform bodies. Int. J. Plast. 16(7), 951–978 (2000)

    Article  MATH  Google Scholar 

  11. Yavari, A.: A geometric theory of growth mechanics. J. Nonlinear Sci. 20(6), 781–830 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  12. Manzhirov, A.V., Lychev, S.A.: The mathematical theory of growing solids: finite deformations. Dokl. Phys. 57(4), 160–163 (2012)

    Article  MathSciNet  Google Scholar 

  13. Noll, W.: Materially uniform simple bodies with inhomogeneities. Arch. Ration. Mech. Anal. 27(1), 1–32 (1967)

    Article  MathSciNet  Google Scholar 

  14. Wang, C.C.: On the geometric structure of simple bodies, or mathematical foundations for the theory of continuous distributions of dislocations. Arch. Ration. Mech. Anal. 27(1), 33–94 (1967)

    Article  MATH  Google Scholar 

  15. Epstein, M.: The Geometrical Language of Continuum Mechanics. Cambridge University Press, New York (2010)

    Book  MATH  Google Scholar 

  16. Maugin, G.A.: Material Inhomogeneities in Elasticity. Chapman and Hall, London (1993)

    Book  MATH  Google Scholar 

  17. Marsden, J.E., Hughes, T.J.R.: Mathematical Foundations of Elasticity. Dover, New York (1994)

    Google Scholar 

  18. Choquet-Bruhat, Y., Dewitt-Morette, C., Dillard-Bleick, M.: Analysis, Manifolds and Physics. Part 1. Basics. North-Holland, Amsterdam (1982)

    Google Scholar 

  19. Truesdell, C.: A First Course in Rational Continuum Mechanics: General Concepts. Academic, Boston (1991)

    MATH  Google Scholar 

  20. Manzhirov, A.V., Lychev, S.A.: Residual stresses in growing bodies. In: Topical Problems in Solid and Fluid Mechanics, pp. 66–79. Elite Publishing House, Delhi (2011)

    Google Scholar 

  21. Gurtin, M.E., Murdoch, A.I.: A continuum theory of elastic material surfaces. Arch. Ration. Mech. Anal. 27, 291–323 (1975)

    MathSciNet  Google Scholar 

  22. Lurie, A.I.: Nonlinear theory of elasticity. North-Holland, Amsterdam (1990)

    MATH  Google Scholar 

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Acknowledgements

This work was supported by the Russian Science Foundation under Grant 14-19-01280.

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Authors and Affiliations

  1. Institute for Problems in Mechanics, pr-t Vernadskogo 101, str. 1, Moscow, 119526, Russia

    Sergei A. Lychev, Alexander V. Manzhirov & Pavel S. Bychkov

  2. Bauman Moscow State Technical University, ul. Baumanskaya 2-ya, 5/1, Moscow, 105005, Russia

    Alexander V. Manzhirov

Authors
  1. Sergei A. Lychev
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  2. Alexander V. Manzhirov
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  3. Pavel S. Bychkov
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Corresponding author

Correspondence to Sergei A. Lychev .

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Editors and Affiliations

  1. Multimedia Engineering College of Engioneering, Mokpo National University, Chonnam, Korea, Republic of (South Korea)

    Gi-Chul Yang

  2. IAENG Secretariat, International Association of Engineers, Hong Kong, Hong Kong SAR

    Sio-Iong Ao

  3. Dept of Applied Mathematics & Computing School of Engineering, Cranfield University, Cranfield, Bedfordshire, United Kingdom

    Len Gelman

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Lychev, S.A., Manzhirov, A.V., Bychkov, P.S. (2015). Discrete and Continuous Growth of Deformable Cylinder. In: Yang, GC., Ao, SI., Gelman, L. (eds) Transactions on Engineering Technologies. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9804-4_17

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  • DOI: https://doi.org/10.1007/978-94-017-9804-4_17

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-017-9803-7

  • Online ISBN: 978-94-017-9804-4

  • eBook Packages: EngineeringEngineering (R0)

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