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Group invariance of a neo-Hookean system: incorporation of stretch change

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Abstract

Invariance of the nonlinear elasto-static system descriptive of the plane-strain deformation of a neo-Hookean material is determined under Lie group transformations which accommodate change in stretch. The associated finite transformations are constructed and the results are set in the context of previous work in the area.

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References

  1. J.M. Hill, Some Partial Solutions of Finite Elasticity. Ph.D. Thesis, University of Queensland (1972).

  2. J.M. Hill, On static similarity deformations for isotropic materials. Quart. Appl. Math. 40 (1982) 287–291.

    Google Scholar 

  3. R. Abeyaratne and C.O. Horgan, Initiation of localised plane deformations at a circular cavity in an infinite compressible nonlinearly elastic medium. J. Elasticity 15 (1985) 243–256.

    Google Scholar 

  4. D.T. Chung, C.O. Horgan and R. Abeyaratne, The finite deformation of internally pressurized hollow cylinders and spheres for a class of compressible elastic materials. Int. J. Solids Structures 22 (1986) 1557–1570.

    Google Scholar 

  5. C. Rogers, On canonical coordinates in nonlinear elasticity, preprint Dept. Applied Mathematics, University of Waterloo (1988).

  6. M. Shahinpoor and J.L. Nowinski, Exact solutions to the problem of forced large amplitude radial oscillations of a thin hyperelastic tube. Int. J. Nonlinear Mech. 6 (1971) 193–208.

    Google Scholar 

  7. C. Rogers and W.F. Ames, Nonlinear Boundary Value Problems in Science and Engineering, Academic Press, New York (1989).

    Google Scholar 

  8. W.W. Klingbeil and R.T. Shield, On a class of solutions in plane finite elasticity. Z. angew. Math. Phys. 17 (1966) 489–511.

    Google Scholar 

  9. M. Singh and A.C. Pipkin, Note on Ericksen's problem. Z. angew. Math. Phys. 16 (1965) 706–709.

    Google Scholar 

  10. J.E. Adkins, A reciprocal property of the finite plane strain equations. J. Mech. Phys. Solids 6 (1958) 267–275.

    Google Scholar 

  11. C. Truesdell and W. Noll, Nonlinear Field Theories of Mechanics, Springer-Verlag, New York (1960).

    Google Scholar 

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Author notes

  1. C. Rogers

    Present address: Department of Mathematical Sciences, University of Technology, LE11 3TU, Loughborough, Leicestershire, England

Authors and Affiliations

  1. Università di Roma, Roma, Italia

    D. Levi

  2. University of Waterloo, Waterloo, Canada

    C. Rogers

Authors
  1. D. Levi
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  2. C. Rogers
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Levi, D., Rogers, C. Group invariance of a neo-Hookean system: incorporation of stretch change. J Elasticity 24, 295–300 (1990). https://doi.org/10.1007/BF00115562

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  • DOI: https://doi.org/10.1007/BF00115562

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