Skip to main content
SpringerLink
Log in

Boundary layers in finite thermoelasticity

  • Published:
Journal of Elasticity Aims and scope Submit manuscript

Abstract

In this paper, we study inhomogeneous deformations within the context of finite thermoelasticity with a view towards highlighting the developments of “boundary layer” like structures. We find that such structures manifest themselves by virtue of the material's ability to shear soften or shear stiffen. When the material moduli depend both on the temperature and the stretch, their effects can either reinforce or mitigate one another, thereby leading to the accentuation or annihilation of the boundary layer structure.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. C., Truesdell and W., Noll, The non-linear field theories of mechanics. In: Flugge (ed.), Handbuch der Physik, III/3, Berlin-Heidelberg-New York: Springer (1965).

    Google Scholar 

  2. P., Chadwick and L.T.C., Seet, Trends in elasticity and thermoelasticity. In: R.E., Czarnota-Bojarski, M., Sokolowski and H., Zorski (eds). Groningen: Wolters-Noordhoff (1971) pp. 29–57.

    Google Scholar 

  3. P.J., Flory, Principles of Polymer Chemistry. Ithaca, New York: Cornell University Press (1953).

    Google Scholar 

  4. L.R.G., Treloar, The Physics of Rubber Elasticity, 3rd edn. Oxford: Clarendon Press (1975).

    Google Scholar 

  5. G., Allen, G., Bianchi and C., Price, Trans. Faraday Society 59 (1963) 2493–2502.

    Google Scholar 

  6. J.F., Besseling and H.H., Voetman, Thermo-elastic effects in rubber. Archiwuum Mechaniki Stosowanej 20 (1968) 189–202.

    Google Scholar 

  7. P., Chadwick, Thermo-mechanics of rubber-like materials. Phil. Trans. Royal Society 276 (1974) 371–402.

    Google Scholar 

  8. P.J., Blatz, Application of large deformation theory to thermomechanical behavior of rubber-like polymers—porous, unfilled and filled. In: F.R., Eirich (ed.), Rheology, New York and London: Academic Press (1969) pp. 1–55.

    Google Scholar 

  9. O.W., Dillon, A non-linear thermoelasticity theory. Journal of Mechanics & Physics of Solids 10 (1962) 123–131.

    Google Scholar 

  10. G., Herrman, On second-order thermoelastic effects. Journal of Applied Mathematics and Physics (ZAMP) 15 (1964) 235–262.

    Google Scholar 

  11. S.E., Martin and D.E., Carlson, The behavior of elastic heat conductors with second-order response functions. Journal of Applied Mathematics and Physics (ZAMP) 28 (1977) 311–328.

    Google Scholar 

  12. J.L., Ericksen, Deformations possible in every compressible isotropic perfectly elastic material. J. Math. Phys. 34 (1955) 126–128.

    Google Scholar 

  13. J.L., Ericksen, Deformations possible in every isotropic incompressible perfectly elastic body. Journal of Applied Mathematics and Physics (ZAMP) 5 (1954) 466–486.

    Google Scholar 

  14. M. M., Carroll, Controllable deformations of incompressible simple materials, Intl. J. Engineering Science 5(1967) 515–525.

    Google Scholar 

  15. A.S. Wineman, Universal deformations of incompressible simple materials. Ann Arbor: University of Michigan Technical Report (1967).

  16. R.L., Fosdick, Dynamically possible motions of incompressible, isotropic, simple materials. Archive for Rational Mechanics and Analysis 29 (1968) 272–288.

    Google Scholar 

  17. H.J., Petroski and D.E., Carlson, Controllable states of elastic heat conductors. Archive for Rational Mechanics and Analysis 31 (1968) 127–150.

    Google Scholar 

  18. H.J., Petroski and D.E., Carlson, Some exact solutions to the equations of non-linear thermoelasticity. Journal of Applied Mechanics 37 (1970) 1151–1154.

    Google Scholar 

  19. S.S. Antman, A family of semi-inverse problems in non-linear elasticity. In: De La Penha and Madeiros (1978) pp. 1–24.

  20. S.S., Antman and Guo, Large shearing oscillations of incompressible non-linear elastic bodies. Journal of Elasticity 14 (1984) 249–262.

    Google Scholar 

  21. P., Boulanger and M., Hayes. Finite amplitude waves in some non-linear elastic media. Proc. R. Irish Academy 89A (1989) 135–146.

    Google Scholar 

  22. M.M., Carroll, Finite amplitude standing waves in compressible elastic solids. Journal of Elasticity 8 (1978) 323–328.

    Google Scholar 

  23. M.M., Carroll, Finite strain solutions in compressible isotropic elasticity. Journal of Elasticity 20 (1988) 65–92.

    Google Scholar 

  24. M.M., Carroll, Some results on finite amplitude elastic waves. Acta Mechanica 3 (1967) 167–181.

    Google Scholar 

  25. M.M. Carroll and C.O. Horgan, Quart. Applied Mathematics, in press.

  26. R.W., Ogden, Plane deformations of incompressible isotropic elastic solids: an integral equation formulation. Mech. Res. Commun. 4 (1977) 347–352.

    Google Scholar 

  27. D.A., Isherwood and R.W., Ogden, Towards the solution of finite plane-strain problems for compressible elastic solids. Int. J. Solids Structures 13 (1977) 105–123.

    Google Scholar 

  28. E., Varley and E., Cumberbatch, The finite deformation of an elastic material surrounding an elliptic hole. In: R.S., Rivlin (ed.), Finite Elasticity. New York: (ASME) (1977) pp. 51–64.

    Google Scholar 

  29. D.M., Haughton, Boundary layer solutions for incompressible elastic cylinders. International J. Engineering Science 30 (1992) 1027–1040.

    Google Scholar 

  30. P., Currie and M.A., Hayes, On non-universal finite elastic deformations. In: D.E., Carlson and R.T., Shields (eds), The Hague: Martinus Nijhoff Publishers (1981) pp. 143–150.

    Google Scholar 

  31. M.A., Hayes and K.R., Rajagopal, Inhomogeneous finite amplitude motion in a neo-Hookean solid. Proc. R. Irish. Academy 92A (1992) 137–147.

    Google Scholar 

  32. D., Fu, K.R., Rajagopal and A.Z., Szeri, Non-homogeneous deformations in a wedge of Mooney-Rivlin material. Int. J. Non-Linear Mech. 25 (1990) 375–387.

    Google Scholar 

  33. K.R., Rajagopal and M.M., Carroll, Inhomogeneous deformations of non-linearly elastic wedges. Int. J. Solids Structures 28 (1992) 735–744.

    Google Scholar 

  34. K.R., Rajagopal and A.S., Wineman, New exact solutions in non-linear elasticity. Int. J. Eng. Sci. 23 (1985) 217–234.

    Google Scholar 

  35. J.B., McLeod and K.R., Rajagopal, On the existence of a class of deformations for incompressible isotropic elastic materials. Proc. R. Irish Academy 88A (1988) 91–101.

    Google Scholar 

  36. K.R., Rajagopal and L., Tao, On an inhomogeneous deformation of a generalized neo-Hookean material. J. Elasticity 28 (1992) 165–184.

    Google Scholar 

  37. L. Tao and K.R. Rajagopal, On an inhomogeneous deformation of an isotropic compressible elastic material. Archiwum Mechaniki Stosowanej 42 (1990)

  38. L., Tao, K.R., Rajagopal and A.S., Wineman, Circular shearing and torsion of generalized neo-Hookean materials. IMA Journal of Applied Mathematics 48 (1992) 23–37.

    Google Scholar 

  39. J.P., Zhang and K.R., Rajagopal, Some inhomogeneous motions and deformations within the context of a non-linear elastic solid. International J. Engineering Science 30 (1992) 919–938.

    Google Scholar 

  40. C.B., Sensenig, Non-linear theory for the deformation of prestressed circular plates and rings. Commun. Pure Appl. Math. 18 (1965) 147–156.

    Google Scholar 

  41. J.K., Knowles, The finite anti-plane shear field near the tip of a crack for a class of incompressible elastic solids. Int. J. Fracture 13 (1977) 611–639.

    Google Scholar 

  42. K.H., Meyer and C., Ferri, Sur l'elasticite du caoutchoue. Helvl. Chim. Acta 18 (1935) 570–589.

    Google Scholar 

  43. R.L., Anthony, R.H., Caston and E., Guth, Equations of state for natural and synthetic rubber like materials. J. Phys. Chem. 46 (1942) 826–840.

    Google Scholar 

  44. L.A., Wood and F.L., Roth, Stress-temperature relations in pure-gum vulcanizate of natural rubber. J. Appl. Phys. 15 (1944) 781–789.

    Google Scholar 

  45. M., Shen, D.A., McQuarrie and J.L., Jackson, Thermoelastic behavior of natural rubber. J. Appl. Phys. 38 (1967) 791–798.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, University of Pittsburgh, 15261, Pittsburgh, PA, USA

    K. R. Rajagopal

Authors
  1. K. R. Rajagopal
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rajagopal, K.R. Boundary layers in finite thermoelasticity. J Elasticity 36, 271–301 (1994). https://doi.org/10.1007/BF00040851

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00040851

Keywords

Search

Navigation