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Existence of Exact Solutions for the Eversion of Elastic Cylinders

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Abstract

The existence of eversion deformations of an elastic cylinder into another right circular cylinder is studied. It is found that such deformations are associated with strain-energy functions of separable form W(λ1,λ2,λ3) =φ(λ1)+φ(λ2)+φ (λ3), and thus can serve as a test for materials of this kind. Under certain constitutive assumptions, there always exists a cylindrical eversion deformation that satisfies exact pointwise traction free boundary conditions over the entire surface of the cylinder. For such solutions the cavity must remain open upon eversion.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Houston, Houston, Texas, 77204, USA

    Yi-Chao Chen

  2. Department of Mathematics, University of Glasgow, G12 8QW, Scotland, UK

    D.M. Haughton

Authors
  1. Yi-Chao Chen
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  2. D.M. Haughton
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Chen, YC., Haughton, D. Existence of Exact Solutions for the Eversion of Elastic Cylinders. Journal of Elasticity 49, 79–88 (1997). https://doi.org/10.1023/A:1007431400648

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