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Finite plane strain deformations of an infinite compressible nonlinear elastic body containing either a cylindrical elliptical void or a rigid cylindrical elliptical inclusion

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Summary

We study the title nonlinear problem for a rubberlike material by using the domain perturbation method. The perturbation is deviation from unity of the ratio of the minor to the major axes of the ellipse. For the body containing an ellipsoidal void, two different loadings are considered; one in which the void surface is taken to be traction free and a uniform compressive load is applied at infinity, and the other in which a uniform pressure is applied to the void surface and null tractions at infinity. For the case of a rigid inclusion, uniform normal tensile tractions are applied at infinity. It is shown that a slight deviation from the circular shape of the cavity or the inclusion has a noticeable effect on the maximum stresses induced in the nonlinear elastic body.

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References

  1. Abeyaratne, R., Horgan, C. O.: Initiation of localized plane deformations at a circular cavity in an infinite compressible nonlinearly elastic medium. J. Elasticity15, 243–256 (1985).

    Google Scholar 

  2. Blatz, P. J., Ko, W. L.: Application of finite elasticity to the deformations of rubbery materials. Trans. Soc. Rheology6, 223–251 (1962).

    Google Scholar 

  3. Knowles, J. K., Sternberg, E.: On the ellipticity of the equations of nonlinear elastostatics for a special material. J. Elasticity5, 341–361 (1975).

    Google Scholar 

  4. De Boor, C.: A practical guide to splines. Berlin Heidelberg New York: Springer 1978.

    Google Scholar 

  5. Goodier, J. N.: Trans. ASME55, 39–60 (1933).

    Google Scholar 

  6. Muskhelishvili, N. I.: Some basic problems of the mathematical theory of elasticity. Groningen: Noordhoff 1953.

    Google Scholar 

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Author notes

  1. J. P. Zhang

    Present address: , 264 Grove St., Apt. 1, 02166, Newton, MA, USA

  2. R. C. Batra

    Present address: Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, 24061-0219, Blacksburg, VA, USA

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    1. J. P. Zhang
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    2. R. C. Batra
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    Zhang, J.P., Batra, R.C. Finite plane strain deformations of an infinite compressible nonlinear elastic body containing either a cylindrical elliptical void or a rigid cylindrical elliptical inclusion. Acta Mechanica 110, 139–150 (1995). https://doi.org/10.1007/BF01215421

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    • DOI: https://doi.org/10.1007/BF01215421

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